Popis integrala iracionalnih funkcija

Slijedi popis integrala (antiderivacija funkcija) iracionalnih funkcija. Za potpun popis integrala funkcija, pogledati tablica integrala i popis integrala.

Integrali koji uključuju Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle r={\sqrt {x^{2}+a^{2}}}}

$\int r\;dx={\frac {1}{2}}\left(xr+a^{2}\,\ln \left(x+r\right)\right)+C$

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int r^{3}\;dx={\frac {1}{4}}xr^{3}+{\frac {1}{8}}3a^{2}xr+{\frac {3}{8}}a^{4}\ln \left(x+r\right)+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int r^{5}\;dx={\frac {1}{6}}xr^{5}+{\frac {5}{24}}a^{2}xr^{3}+{\frac {5}{16}}a^{4}xr+{\frac {5}{16}}a^{6}\ln \left(x+r\right)+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int xr\;dx={\frac {r^{3}}{3}}+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int xr^{3}\;dx={\frac {r^{5}}{5}}+C}

$\int xr^{2n+1}\;dx={\frac {r^{2n+3}}{2n+3}}+C$

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int x^{2}r\;dx={\frac {xr^{3}}{4}}-{\frac {a^{2}xr}{8}}-{\frac {a^{4}}{8}}\ln \left(x+r\right)+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int x^{2}r^{3}\;dx={\frac {xr^{5}}{6}}-{\frac {a^{2}xr^{3}}{24}}-{\frac {a^{4}xr}{16}}-{\frac {a^{6}}{16}}\ln \left(x+r\right)+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int x^{3}r\;dx={\frac {r^{5}}{5}}-{\frac {a^{2}r^{3}}{3}}+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int x^{3}r^{3}\;dx={\frac {r^{7}}{7}}-{\frac {a^{2}r^{5}}{5}}+C}

$\int x^{3}r^{2n+1}\;dx={\frac {r^{2n+5}}{2n+5}}-{\frac {a^{3}r^{2n+3}}{2n+3}}+C$

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int x^{4}r\;dx={\frac {x^{3}r^{3}}{6}}-{\frac {a^{2}xr^{3}}{8}}+{\frac {a^{4}xr}{16}}+{\frac {a^{6}}{16}}\ln \left(x+r\right)+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int x^{4}r^{3}\;dx={\frac {x^{3}r^{5}}{8}}-{\frac {a^{2}xr^{5}}{16}}+{\frac {a^{4}xr^{3}}{64}}+{\frac {3a^{6}xr}{128}}+{\frac {3a^{8}}{128}}\ln \left(x+r\right)+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int x^{5}r\;dx={\frac {r^{7}}{7}}-{\frac {2a^{2}r^{5}}{5}}+{\frac {a^{4}r^{3}}{3}}+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int x^{5}r^{3}\;dx={\frac {r^{9}}{9}}-{\frac {2a^{2}r^{7}}{7}}+{\frac {a^{4}r^{5}}{5}}+C}

$\int x^{5}r^{2n+1}\;dx={\frac {r^{2n+7}}{2n+7}}-{\frac {2a^{2}r^{2n+5}}{2n+5}}+{\frac {a^{4}r^{2n+3}}{2n+3}}+C$

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {r\;dx}{x}}=r-a\ln \left|{\frac {a+r}{x}}\right|=r-a\operatorname {Arsh} {\frac {a}{x}}+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {r^{3}\;dx}{x}}={\frac {r^{3}}{3}}+a^{2}r-a^{3}\ln \left|{\frac {a+r}{x}}\right|+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {r^{5}\;dx}{x}}={\frac {r^{5}}{5}}+{\frac {a^{2}r^{3}}{3}}+a^{4}r-a^{5}\ln \left|{\frac {a+r}{x}}\right|+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {r^{7}\;dx}{x}}={\frac {r^{7}}{7}}+{\frac {a^{2}r^{5}}{5}}+{\frac {a^{4}r^{3}}{3}}+a^{6}r-a^{7}\ln \left|{\frac {a+r}{x}}\right|+C}

$\int {\frac {dx}{r}}=\operatorname {Arsh} {\frac {x}{a}}=\ln \left|x+r\right|+C$

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{dx}{r^3} = \frac{x}{a^2r} + C}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{x\,dx}{r} = r + C}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{x\,dx}{r^3} = -\frac{1}{r} + C}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{x^2\;dx}{r} = \frac{x}{2}r-\frac{a^2}{2}\,\operatorname{Arsh}\frac{x}{a} = \frac{x}{2}r-\frac{a^2}{2}\ln\left|x+r\right| + C}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{dx}{xr} = -\frac{1}{a}\,\operatorname{Arsh}\frac{a}{x} = -\frac{1}{a}\ln\left|\frac{a+r}{x}\right| + C}

Integrali koji uključuju Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle s = \sqrt{x^2-a^2}}

Pretpostavlja se da je Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2>a^2} , za Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2<a^2} vidi sljedeću sekciju:

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int xs\;dx = \frac{1}{3}s^3 + C}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{s\;dx}{x} = s - a\cos^{-1}\left|\frac{a}{x}\right|}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{dx}{s} = \int\frac{dx}{\sqrt{x^2-a^2}} =\ln\left|\frac{x+s}{a}\right| + C}

Valja uočiti da je Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \ln\left|\frac{x+s}{a}\right| =\mathrm{sgn}(x)\operatorname{Arch}\left|\frac{x}{a}\right| =\frac{1}{2}\ln\left(\frac{x+s}{x-s}\right)} , pri čemu se uzima pozitivna vrijednost od Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \operatorname{Arch}\left|\frac{x}{a}\right|} .

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{x\;dx}{s} = s + C}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{x\;dx}{s^3} = -\frac{1}{s} + C}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{x\;dx}{s^5} = -\frac{1}{3s^3} + C}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{x\;dx}{s^7} = -\frac{1}{5s^5} + C}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{x\;dx}{s^{2n+1}} = -\frac{1}{(2n-1)s^{2n-1}} + C}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{x^{2m}\;dx}{s^{2n+1}} = -\frac{1}{2n-1}\frac{x^{2m-1}}{s^{2n-1}}+\frac{2m-1}{2n-1}\int\frac{x^{2m-2}\;dx}{s^{2n-1}} + C}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{x^2\;dx}{s} = \frac{xs}{2}+\frac{a^2}{2}\ln\left|\frac{x+s}{a}\right| + C}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{x^2\;dx}{s^3} = -\frac{x}{s}+\ln\left|\frac{x+s}{a}\right| + C}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{x^4\;dx}{s} = \frac{x^3s}{4}+\frac{3}{8}a^2xs+\frac{3}{8}a^4\ln\left|\frac{x+s}{a}\right| + C}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{x^4\;dx}{s^3} = \frac{xs}{2}-\frac{a^2x}{s}+\frac{3}{2}a^2\ln\left|\frac{x+s}{a}\right| + C}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{x^4\;dx}{s^5} = -\frac{x}{s}-\frac{1}{3}\frac{x^3}{s^3}+\ln\left|\frac{x+s}{a}\right| + C}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{x^{2m}\;dx}{s^{2n+1}} = (-1)^{n-m}\frac{1}{a^{2(n-m)}}\sum_{i=0}^{n-m-1}\frac{1}{2(m+i)+1}{n-m-1 \choose i}\frac{x^{2(m+i)+1}}{s^{2(m+i)+1}}+ C \qquad\mbox{(}n>m\ge0\mbox{)}}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{dx}{s^3}=-\frac{1}{a^2}\frac{x}{s} + C}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{dx}{s^5}=\frac{1}{a^4}\left[\frac{x}{s}-\frac{1}{3}\frac{x^3}{s^3}\right] + C}

Obrada nije uspjela. (MathML sa SVG ili PNG za rezervu (preporučljivo za moderne preglednike i alate za pristupačnost): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int\frac{dx}{s^7} =-\frac{1}{a^6}\left[\frac{x}{s}-\frac{2}{3}\frac{x^3}{s^3}+\frac{1}{5}\frac{x^5}{s^5}\right] + C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {dx}{s^{9}}}={\frac {1}{a^{8}}}\left[{\frac {x}{s}}-{\frac {3}{3}}{\frac {x^{3}}{s^{3}}}+{\frac {3}{5}}{\frac {x^{5}}{s^{5}}}-{\frac {1}{7}}{\frac {x^{7}}{s^{7}}}\right]+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {x^{2}\;dx}{s^{5}}}=-{\frac {1}{a^{2}}}{\frac {x^{3}}{3s^{3}}}+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {x^{2}\;dx}{s^{7}}}={\frac {1}{a^{4}}}\left[{\frac {1}{3}}{\frac {x^{3}}{s^{3}}}-{\frac {1}{5}}{\frac {x^{5}}{s^{5}}}\right]+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {x^{2}\;dx}{s^{9}}}=-{\frac {1}{a^{6}}}\left[{\frac {1}{3}}{\frac {x^{3}}{s^{3}}}-{\frac {2}{5}}{\frac {x^{5}}{s^{5}}}+{\frac {1}{7}}{\frac {x^{7}}{s^{7}}}\right]+C}

Integrali koji uključuju $t={\sqrt {a^{2}-x^{2}}}$

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int t\;dx={\frac {1}{2}}\left(xt+a^{2}\arcsin {\frac {x}{a}}\right)+C\qquad {\mbox{(}}|x|\leq |a|{\mbox{)}}}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int xt\;dx=-{\frac {1}{3}}t^{3}+C\qquad {\mbox{(}}|x|\leq |a|{\mbox{)}}}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {t\;dx}{x}}=t-a\ln \left|{\frac {a+t}{x}}\right|+C\qquad {\mbox{(}}|x|\leq |a|{\mbox{)}}}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {dx}{t}}=\arcsin {\frac {x}{a}}+C\qquad {\mbox{(}}|x|\leq |a|{\mbox{)}}}

$\int {\frac {x^{2}\;dx}{t}}={\frac {1}{2}}\left(-xt+a^{2}\arcsin {\frac {x}{a}}\right)+C\qquad {\mbox{(}}|x|\leq |a|{\mbox{)}}$

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int t\;dx={\frac {1}{2}}\left(xt-\operatorname {sgn} x\,\operatorname {Arch} \left|{\frac {x}{a}}\right|\right)+C\qquad {\mbox{(za }}|x|\geq |a|{\mbox{)}}}

Integrali koji uključuju Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle R={\sqrt {ax^{2}+bx+c}}}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {dx}{R}}={\frac {1}{\sqrt {a}}}\ln \left|2{\sqrt {a}}R+2ax+b\right|+C\qquad {\mbox{(za }}a>0{\mbox{)}}}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {dx}{R}}={\frac {1}{\sqrt {a}}}\,\operatorname {Arsh} {\frac {2ax+b}{\sqrt {4ac-b^{2}}}}+C\qquad {\mbox{(za }}a>0{\mbox{, }}4ac-b^{2}>0{\mbox{)}}}

$\int {\frac {dx}{R}}={\frac {1}{\sqrt {a}}}\ln |2ax+b|\quad {\mbox{(za }}a>0{\mbox{, }}4ac-b^{2}=0{\mbox{)}}+C$

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {dx}{R}}=-{\frac {1}{\sqrt {-a}}}\arcsin {\frac {2ax+b}{\sqrt {b^{2}-4ac}}}+C\qquad {\mbox{(za }}a<0{\mbox{, }}4ac-b^{2}<0{\mbox{, }}\left|2ax+b\right|<{\sqrt {b^{2}-4ac}}{\mbox{)}}}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {dx}{R^{3}}}={\frac {4ax+2b}{(4ac-b^{2})R}}+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {dx}{R^{5}}}={\frac {4ax+2b}{3(4ac-b^{2})R}}\left({\frac {1}{R^{2}}}+{\frac {8a}{4ac-b^{2}}}\right)+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {dx}{R^{2n+1}}}={\frac {2}{(2n-1)(4ac-b^{2})}}\left({\frac {2ax+b}{R^{2n-1}}}+4a(n-1)\int {\frac {dx}{R^{2n-1}}}\right)+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {x}{R}}\;dx={\frac {R}{a}}-{\frac {b}{2a}}\int {\frac {dx}{R}}+C}

$\int {\frac {x}{R^{3}}}\;dx=-{\frac {2bx+4c}{(4ac-b^{2})R}}+C$

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {x}{R^{2n+1}}}\;dx=-{\frac {1}{(2n-1)aR^{2n-1}}}-{\frac {b}{2a}}\int {\frac {dx}{R^{2n+1}}}+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {dx}{xR}}=-{\frac {1}{\sqrt {c}}}\ln \left({\frac {2{\sqrt {c}}R+bx+2c}{x}}\right)+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {dx}{xR}}=-{\frac {1}{\sqrt {c}}}\operatorname {Arsh} \left({\frac {bx+2c}{|x|{\sqrt {4ac-b^{2}}}}}\right)+C}

Integrali koji uključuju Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle S={\sqrt {ax+b}}}

$\int {\frac {dx}{x{\sqrt {ax+b}}}}\,=\,{\frac {-2}{\sqrt {b}}}\operatorname {Arth} {\sqrt {\frac {ax+b}{b}}}+C$

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {\sqrt {ax+b}}{x}}\,dx\;=\;2\left({\sqrt {ax+b}}-{\sqrt {b}}\operatorname {Arth} {\sqrt {\frac {ax+b}{b}}}\right)+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {x^{n}}{\sqrt {ax+b}}}\,dx\;=\;{\frac {2}{a(2n+1)}}\left(x^{n}{\sqrt {ax+b}}-bn\int {\frac {x^{n-1}}{\sqrt {ax+b}}}\,dx\right)+C}

Obrada nije uspjela. (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int x^{n}{\sqrt {ax+b}}\,dx\;=\;{\frac {2}{2n+1}}\left(x^{n+1}{\sqrt {ax+b}}+bx^{n}{\sqrt {ax+b}}-nb\int x^{n-1}{\sqrt {ax+b}}\,dx\right)+C}

Izvori

• Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables 1972, Dover: New York. (See chapter 3.)