Find the integral of \(x\sin x\).
\(-x\cos x+\sin x+C\)
Find the integral of \(x\sin 3x\).
\(-\dfrac{x}{3}\cos 3x+\dfrac{1}{9}\sin 3x+C\)
Find the integral of \(x^2 e^x\).
\(e^x(x^2-2x+2)+C\)
Find the integral of \(x\log x\).
\(\dfrac{x^2}{2}\log x-\dfrac{x^2}{4}+C\)
Find the integral of \(x\log 2x\).
\(\dfrac{x^2}{2}\log 2x-\dfrac{x^2}{4}+C\)
Find the integral of \(x^2\log x\).
\(\dfrac{x^3}{3}\log x-\dfrac{x^3}{9}+C\)
Find the integral of \(x\sin^{-1}x\).
\(\dfrac{1}{4}(2x^2-1)\sin^{-1}x+\dfrac{x\sqrt{1-x^2}}{4}+C\)
Find the integral of \(x\tan^{-1}x\).
\(\dfrac{x^2}{2}\tan^{-1}x-\dfrac{x}{2}+\dfrac{1}{2}\tan^{-1}x+C\)
Find the integral of \(x\cos^{-1}x\).
\(\dfrac{(2x^2-1)\cos^{-1}x}{4}-\dfrac{x}{4}\sqrt{1-x^2}+C\)
Find the integral of \((\sin^{-1}x)^2\).
\(x(\sin^{-1}x)^2+2\sqrt{1-x^2}\sin^{-1}x-2x+C\)
Find the integral of \(\dfrac{x\cos^{-1}x}{\sqrt{1-x^2}}\).
\(-\sqrt{1-x^2}\cos^{-1}x+x+C\)
Find the integral of \(x\sec^2 x\).
\(x\tan x+\log|\cos x|+C\)
Find the integral of \(\tan^{-1}x\).
\(x\tan^{-1}x-\dfrac{1}{2}\log(1+x^2)+C\)
Find the integral of \(x(\log x)^2\).
\(\dfrac{x^2}{2}(\log x)^2-\dfrac{x^2}{2}\log x+\dfrac{x^2}{4}+C\)
Find the integral of \((x^2+1)\log x\).
\(\left(\dfrac{x^3}{3}+x\right)\log x-\dfrac{x^3}{9}-x+C\)
Find the integral of \(e^x(\sin x+\cos x)\).
\(e^x\sin x+C\)
Find the integral of \(\dfrac{x e^x}{(1+x)^2}\).
\(\dfrac{e^x}{1+x}+C\)
Find the integral of \(e^x\left(\dfrac{1+\sin x}{1+\cos x}\right)\).
\(e^x\tan\dfrac{x}{2}+C\)
Find the integral of \(e^x\left(\dfrac{1}{x}-\dfrac{1}{x^2}\right)\).
\(\dfrac{e^x}{x}+C\)
Find the integral of \(\dfrac{(x-3)e^x}{(x-1)^3}\).
\(\dfrac{e^x}{(x-1)^2}+C\)
Find the integral of \(e^{2x}\sin x\).
\(\dfrac{e^{2x}}{5}(2\sin x-\cos x)+C\)
Find the integral of \(\sin^{-1}\left(\dfrac{2x}{1+x^2}\right)\).
\(2x\tan^{-1}x-\log(1+x^2)+C\)
\(\displaystyle \int x^2 e^{x^3}\,dx\) equals
\(\dfrac{1}{3}e^{x^3}+C\)
\(\dfrac{1}{3}e^{x^2}+C\)
\(\dfrac{1}{2}e^{x^3}+C\)
\(\dfrac{1}{2}e^{x^2}+C\)
\(\displaystyle \int e^x\sec x(1+\tan x)\,dx\) equals
\(e^x\cos x+C\)
\(e^x\sec x+C\)
\(e^x\sin x+C\)
\(e^x\tan x+C\)