Evaluate the integral \(\int \sin^2(2x+5)\,dx\).
\(\frac{x}{2}-\frac{1}{8}\sin(4x+10)+C\)
Evaluate the integral \(\int \sin 3x\,\cos 4x\,dx\).
\(-\frac{1}{14}\cos 7x+\frac{1}{2}\cos x+C\)
Evaluate the integral \(\int \cos 2x\,\cos 4x\,\cos 6x\,dx\).
\(\frac{1}{4}\left[\frac{1}{12}\sin 12x + x + \frac{1}{8}\sin 8x + \frac{1}{4}\sin 4x\right]+C\)
Evaluate the integral \(\int \sin^3(2x+1)\,dx\).
\(-\frac{1}{2}\cos(2x+1)+\frac{1}{6}\cos^3(2x+1)+C\)
Evaluate the integral \(\int \sin^3 x\,\cos^3 x\,dx\).
\(\frac{1}{6}\cos^6 x-\frac{1}{4}\cos^4 x+C\)
Evaluate the integral \(\int \sin x\,\sin 2x\,\sin 3x\,dx\).
\(\frac{1}{4}\left[\frac{1}{6}\cos 6x-\frac{1}{4}\cos 4x-\frac{1}{2}\cos 2x\right]+C\)
Evaluate the integral \(\int \sin 4x\,\sin 8x\,dx\).
\(-\frac{1}{2}\left[\frac{1}{4}\sin 4x-\frac{1}{12}\sin 12x\right]+C\)
Evaluate the integral \(\int \frac{1-\cos x}{1+\cos x}\,dx\).
\(2\tan\frac{x}{2}-x+C\)
Evaluate the integral \(\int \frac{\cos x}{1+\cos x}\,dx\).
\(x-\tan\frac{x}{2}+C\)
Evaluate the integral \(\int \sin^4 x\,dx\).
\(\frac{3x}{8}-\frac{1}{4}\sin 2x+\frac{1}{32}\sin 4x+C\)
Evaluate the integral \(\int \cos^4 2x\,dx\).
\(\frac{3x}{8}+\frac{1}{8}\sin 4x+\frac{1}{64}\sin 8x+C\)
Evaluate the integral \(\int \frac{\sin^2 x}{1+\cos x}\,dx\).
\(x-\sin x+C\)
Evaluate the integral \(\int \frac{\cos 2x-\cos 2\alpha}{\cos x-\cos \alpha}\,dx\).
\(2(\sin x + x\cos\alpha)+C\)
Evaluate the integral \(\int \frac{\cos x-\sin x}{1+\sin 2x}\,dx\).
\(-\frac{1}{\cos x+\sin x}+C\)
Evaluate the integral \(\int \tan^3 2x\,\sec 2x\,dx\).
\(\frac{1}{6}\sec^3 2x-\frac{1}{2}\sec 2x+C\)
Evaluate the integral \(\int \tan^4 x\,dx\).
\(\frac{1}{3}\tan^3 x-\tan x+x+C\)
Evaluate the integral \(\int \frac{\sin^3 x+\cos^3 x}{\sin^2 x\cos^2 x}\,dx\).
\(\sec x-\cosec x+C\)
Evaluate the integral \(\int \frac{\cos 2x+2\sin^2 x}{\cos^2 x}\,dx\).
\(\tan x+C\)
Evaluate the integral \(\int \frac{1}{\sin x\cos^3 x}\,dx\).
\(\log|\tan x|+\frac{1}{2}\tan^2 x+C\)
Evaluate the integral \(\int \frac{\cos 2x}{(\cos x+\sin x)^2}\,dx\).
\(\log|\cos x+\sin x|+C\)
Evaluate the integral \(\int \sin^{-1}(\cos x)\,dx\).
\(\frac{\pi x}{2}-\frac{x^2}{2}+C\)
Evaluate the integral \(\int \frac{1}{\cos(x-a)\,\cos(x-b)}\,dx\).
\(\frac{1}{\sin(a-b)}\log\left|\frac{\cos(x-a)}{\cos(x-b)}\right|+C\)
\(\int \frac{\sin^2 x-\cos^2 x}{\sin^2 x\cos^2 x}\,dx\) is equal to
\(\tan x+\cot x+C\)
\(\tan x+\cosec x+C\)
\(-\tan x+\cot x+C\)
\(\tan x+\sec x+C\)
\(\int \frac{e^x(1+x)}{\cos^2(e^x x)}\,dx\) equals
\(-\cot(e^x x)+C\)
\(\tan(xe^x)+C\)
\(\tan(e^x)+C\)
\(\cot(e^x)+C\)