Indefinite Integration

$\dfrac{1}{3}\sin^{-1}\left( \dfrac{x-1}{3} \right)+c$

$\sin^{-1}\left( \dfrac{x+1}{3} \right)+c$

$\dfrac{1}{3}\sin^{-1}\left( \dfrac{x+1}{3} \right)+c$

$\sin^{-1}\left( \dfrac{x-1}{3} \right)+c$

$\dfrac{e^{ax}}{a^{2}+b^{2}}(a\sin bx-b\cos bx)+c$

$e^{ax}(b\sin bx-a\cos bx)+c$

$\dfrac{e^{ax}}{a^{2}+b^{2}}(a\sin bx+b\cos bx)+c$

$\dfrac{a^{2}+b^{2}}{e^{ax}}(b\cos bx-a\sin bx)+c$

$x+2 \log (x+2)+c$

$x+\log (x+2)+c$

$x-\log (x+2)+c$

$x-2 \log (x+2)+c$

$x^{4}+\dfrac{1}{x^{3}}+\dfrac{129}{8}$

$x^{4}+\dfrac{1}{x^{3}}-\dfrac{129}{8}$

$x^{3}+\dfrac{1}{x^{4}}+\dfrac{129}{8}$

$x^{3}+\dfrac{1}{x^{4}}-\dfrac{129}{8}$

$\dfrac{2^{x}}{\log 2}+\dfrac{3^{x}}{\log 3}-\dfrac{5^{x}}{\log 5}+c$

$\dfrac{2/5}{x\log(2/5)}+\dfrac{3/5}{x\log(3/5)}+c$

$\dfrac{(2/5)^{x}}{\log(2/5)}+\dfrac{(3/5)^{x}}{\log(3/5)}+c$

none of these

$\log\left| x+4+\sqrt{x^{2}+4x+29} \right|+c$

$\log\left| x-4+\sqrt{x^{2}+4x+29} \right|+c$

$\log\left| x+2+\sqrt{x^{2}+4x+29} \right|+c$

$\log\left| x-2+\sqrt{x^{2}+4x+29} \right|+c$

$\dfrac{1}{2} \tan ^{-1} x^{2}+c$, where $c$ is the constant of integration

$2 \tan ^{-1} x+c$, where $c$ is the constant of integration

$\dfrac{1}{2} \tan ^{-1} x+c$, where c is the constant of integration

$\tan ^{-1} x^{2}+c^{\prime}$ where c is the constant of integration

$\tan x+\cot x+c$, where c is the constant of integration.

$\tan x-\cot x+c$, where c is the constant of integration.

$\tan x \cot x+c$, where c is the constant of integration.

$\tan x-\cot 2 x+c_{\prime}$, where c is the constant of integration.

$-\tan x+\cot x+c$

$\tan x+\cot x+c$

$\tan x-\cot x+c$

$2\tan x-\cot x+c$

$\log\left| (x+3)+\sqrt{x^{2}-6x-5} \right|+c$

$\log\left| (x+3)-\sqrt{x^{2}+6x+5} \right|+c$

$\log\left| (x-3)+\sqrt{x^{2}-6x+5} \right|+c$

$\log\left| (x+3)+\sqrt{x^{2}+6x+5} \right|+c$

$\dfrac{-1}{\tan x+1}+c$

$\dfrac{-1}{\tan x-1}+c$

$\dfrac{1}{\tan x+1}+c$

$\dfrac{1}{\tan x-1}+c$

$-\dfrac{1}{14} \cos 7 x-\dfrac{1}{2} \cos x+c$

$-\dfrac{1}{14} \cos 7 x+\dfrac{1}{2} \cos x+c$

$\dfrac{1}{14} \cos 7 x-\dfrac{1}{2} \cos x+c$

$\dfrac{1}{14} \cos 7 x+\dfrac{1}{2} \cos x+c$

$\dfrac{e^{x}}{1+x^{2}}+c$

$-\dfrac{e^{x}}{1+x^{2}}+c$

$\dfrac{e^{x}}{{\left( 1+x^{2} \right)}^{2}}+c$

$-\dfrac{e^{x}}{{\left( 1+x^{2} \right)}^{2}}+c$

$\dfrac{2}{\sqrt{7}} \tan ^{-1}\left(\dfrac{2 x+5}{\sqrt{7}}\right)+c$

$-\dfrac{2}{\sqrt{7}} \tan ^{-1}\left(\dfrac{2 x-5}{\sqrt{7}}\right)+c$

$\dfrac{2}{\sqrt{7}} \tan ^{-1}\left(\dfrac{2 x-5}{\sqrt{7}}\right)+c$

$-\dfrac{2}{\sqrt{7}} \tan ^{-1}\left(\dfrac{2 x+5}{\sqrt{7}}\right)+c$

0

-1

1

$\dfrac{-1}{4}$