Evaluate the integral \(\int \frac{2x}{1+x^2}\,dx\).
\(\log(1+x^2) + C\)
Evaluate the integral \(\int \frac{(\log x)^2}{x}\,dx\).
\(\frac{1}{3}(\log|x|)^3 + C\)
Evaluate the integral \(\int \frac{1}{x + x\log x}\,dx\).
\(\log|1+\log x| + C\)
Evaluate the integral \(\int \sin x\,\sin(\cos x)\,dx\).
\(\cos(\cos x) + C\)
Evaluate the integral \(\int \sin(ax+b)\,\cos(ax+b)\,dx\).
\(-\frac{1}{4a}\cos\big(2(ax+b)\big) + C\)
Evaluate the integral \(\int \sqrt{ax+b}\,dx\).
\(\frac{2}{3a}(ax+b)^{3/2} + C\)
Evaluate the integral \(\int x\sqrt{x+2}\,dx\).
\(\frac{2}{5}(x+2)^{5/2} - \frac{4}{3}(x+2)^{3/2} + C\)
Evaluate the integral \(\int x\sqrt{1+2x^2}\,dx\).
\(\frac{1}{6}(1+2x^2)^{3/2} + C\)
Evaluate the integral \(\int (4x+2)\sqrt{x^2+x+1}\,dx\).
\(\frac{4}{3}(x^2+x+1)^{3/2} + C\)
Evaluate the integral \(\int \frac{1}{x-\sqrt{x}}\,dx\).
\(2\log|\sqrt{x}-1| + C\)
Evaluate the integral \(\int \frac{x}{\sqrt{x+4}}\,dx\), \(x>0\).
\(\frac{2}{3}\sqrt{x+4}(x-8) + C\)
Evaluate the integral \(\int (x^3-1)^{1/3}x^5\,dx\).
\(\frac{1}{7}(x^3-1)^{7/3} + \frac{1}{4}(x^3-1)^{4/3} + C\)
Evaluate the integral \(\int \frac{x^2}{(2+3x^3)^3}\,dx\).
\(-\frac{1}{18(2+3x^3)^2} + C\)
Evaluate the integral \(\int \frac{1}{x(\log x)^m}\,dx\), \(x>0\), \(m\ne 1\).
\(\frac{(\log x)^{1-m}}{1-m} + C\)
Evaluate the integral \(\int \frac{x}{9-4x^2}\,dx\).
\(-\frac{1}{8}\log|9-4x^2| + C\)
Evaluate the integral \(\int e^{2x+3}\,dx\).
\(\frac{1}{2}e^{2x+3} + C\)
Evaluate the integral \(\int \frac{x}{e^{x^2}}\,dx\).
\(-\frac{1}{2e^{x^2}} + C\)
Evaluate the integral \(\int \frac{e^{\tan^{-1}x}}{1+x^2}\,dx\).
\(e^{\tan^{-1}x} + C\)
Evaluate the integral \(\int \frac{e^{2x}-1}{e^{2x}+1}\,dx\).
\(\log(e^x + e^{-x}) + C\)
Evaluate the integral \(\int \frac{e^{2x}-e^{-2x}}{e^{2x}+e^{-2x}}\,dx\).
\(\frac{1}{2}\log(e^{2x}+e^{-2x}) + C\)
Evaluate the integral \(\int \tan^2(2x-3)\,dx\).
\(\frac{1}{2}\tan(2x-3) - x + C\)
Evaluate the integral \(\int \sec^2(7-4x)\,dx\).
\(-\frac{1}{4}\tan(7-4x) + C\)
Evaluate the integral \(\int \frac{\sin^{-1}x}{\sqrt{1-x^2}}\,dx\).
\(\frac{1}{2}(\sin^{-1}x)^2 + C\)
Evaluate the integral \(\int \frac{2\cos x - 3\sin x}{6\cos x + 4\sin x}\,dx\).
\(\frac{1}{2}\log|2\sin x + 3\cos x| + C\)
Evaluate the integral \(\int \frac{1}{\cos^2 x\,(1-\tan x)^2}\,dx\).
\(\frac{1}{1-\tan x} + C\)
Evaluate the integral \(\int \frac{\cos\sqrt{x}}{\sqrt{x}}\,dx\).
\(2\sin\sqrt{x} + C\)
Evaluate the integral \(\int \sqrt{\sin 2x}\,\cos 2x\,dx\).
\(\frac{1}{3}(\sin 2x)^{3/2} + C\)
Evaluate the integral \(\int \frac{\cos x}{\sqrt{1+\sin x}}\,dx\).
\(2\sqrt{1+\sin x} + C\)
Evaluate the integral \(\int \cot x\,\log(\sin x)\,dx\).
\(\frac{1}{2}(\log \sin x)^2 + C\)
Evaluate the integral \(\int \frac{\sin x}{1+\cos x}\,dx\).
\(-\log|1+\cos x| + C\)
Evaluate the integral \(\int \frac{\sin x}{(1+\cos x)^2}\,dx\).
\(\frac{1}{1+\cos x} + C\)
Evaluate the integral \(\int \frac{1}{1+\cot x}\,dx\).
\(\frac{x}{2} - \frac{1}{2}\log|\cos x + \sin x| + C\)
Evaluate the integral \(\int \frac{1}{1-\tan x}\,dx\).
\(\frac{x}{2} - \frac{1}{2}\log|\cos x - \sin x| + C\)
Evaluate the integral \(\int \frac{\sqrt{\tan x}}{\sin x\cos x}\,dx\).
\(2\sqrt{\tan x} + C\)
Evaluate the integral \(\int \frac{(1+\log x)^2}{x}\,dx\).
\(\frac{1}{3}(1+\log x)^3 + C\)
Evaluate the integral \(\int \frac{(x+1)(x+\log x)^2}{x}\,dx\).
\(\frac{1}{3}(x+\log x)^3 + C\)
Evaluate the integral \(\int \frac{x^3\sin(\tan^{-1}x^4)}{1+x^8}\,dx\).
\(-\frac{1}{4}\cos(\tan^{-1}x^4) + C\)
\(\int \frac{10x^9 + 10^x\log_e 10}{x^{10}+10^x}\,dx\) equals
\(10^x - x^{10} + C\)
\(10^x + x^{10} + C\)
\((10^x - x^{10})^{-1} + C\)
\(\log(10^x + x^{10}) + C\)
\(\int \frac{dx}{\sin^2 x\cos^2 x}\) equals
\(\tan x + \cot x + C\)
\(\tan x - \cot x + C\)
\(\tan x\cot x + C\)
\(\tan x - \cot 2x + C\)