積分100本ノック（問題編）

${\displaystyle \int {\tan }^{3}xdx}$

${\displaystyle {\int }_0^{2\pi }\sqrt{1+\cos x}dx}$

${\displaystyle {\int }_0^1\sqrt{\frac{1-x}{1+x}}dx}$

${\displaystyle {\int }_1^2\frac{1}{2^x}dx}$

${\displaystyle \int \frac{1}{\sin x}dx}$

${\displaystyle \int \frac{1}{\sqrt{1+x^2}}dx}$

${\displaystyle \int x\sqrt{3x-5}dx}$

${\displaystyle {\int }_1^e\sqrt{x}\log xdx}$

${\displaystyle \int (\log x{)}^{2}dx}$

${\displaystyle {\int }_0^2\frac{3x^3+12x+1}{x^2+4}dx}$

${\displaystyle \int \frac{1}{x(1+\log x)}dx}$

${\displaystyle \int \frac{1}{x-\sqrt{x}}dx}$

${\displaystyle {\int }_{\frac{4}{3}}^2\frac{1}{x^2\sqrt{x-1}}dx}$

${\displaystyle \int \frac{1}{\sqrt{x^2+6x+13}}dx}$

${\displaystyle \int \frac{x}{{\cos }^{2}x}dx}$

${\displaystyle \int {\log }_{2}xdx}$

${\displaystyle \int \frac{x-1}{(x+1)(x^2+1)}dx}$

${\displaystyle \int \frac{x+2}{x(x+1{)}^2}dx}$

${\displaystyle \int \frac{1}{{\sin }^{2}x}dx}$

${\displaystyle {\int }_0^{\sqrt{\frac{\pi }{2}}}{x}^3\cos x^{2}dx}$

${\displaystyle \int \tan x\log ({\cos }^{2}x)dx}$

${\displaystyle \int \frac{1}{{\cos }^3\theta }dx}$

${\displaystyle \int \frac{1}{1+\sin x}dx}$

${\displaystyle \int x{2}^{x}dx}$

${\displaystyle {\int }_2^3\frac{x-1}{x^2}{e}^{x}dx}$

${\displaystyle \int \frac{1}{\sin x\cos x}dx}$

${\displaystyle \int 2^{\log x}dx}$

${\displaystyle {\int }_0^1\frac{1}{x^3+1}dx}$

${\displaystyle {\int }_0^2\sqrt{x^2-2x+1}dx}$

${\displaystyle \int \frac{1}{{\cos }^{4}x}dx}$

${\displaystyle {\int }_{-1}^1\frac{x^2}{1+e^x}dx}$

${\displaystyle \int \frac{\sin \frac{1}{x}}{x^3}dx}$

${\displaystyle \int \frac{\sqrt{\tan x}}{\sin 2x}dx}$

${\displaystyle \int x{e}^x\sin xdx}$

${\displaystyle \int \sin (\log x)dx}$

${\displaystyle {\int }_0^1(x+2x^3)\sqrt{1+2x^2}dx}$

${\displaystyle \int \frac{\log (\log x)}{x\log x}dx}$

${\displaystyle {\int }_0^{\frac{\pi }{2}}\frac{\cos x}{\sin x+\cos x}dx}$

${\displaystyle \int \sqrt{e^x}dx}$

${\displaystyle \int \frac{1}{x(\log x{)}^2}dx}$

${\displaystyle \int x\sin x\cos xdx}$

${\displaystyle \int x{e}^x\sin x\cos xdx}$

${\displaystyle {\int }_0^{\pi }\frac{x\sin x}{8+{\sin }^{2}x}dx}$

${\displaystyle {\int }_0^1\frac{x^6}{1+x^{14}}dx}$

${\displaystyle \int \frac{1}{x^4+x}dx}$

${\displaystyle {\int }_0^{2020\pi }|\sin \left(2020x\right)|dx}$

${\displaystyle {\int }_e^{e^2}{x}^{\frac{1}{\log x}}dx}$

${\displaystyle \int x^x(\log x+1)dx}$

${\displaystyle {\int }_1^{2}x(x-3{)}^{6}dx}$

${\displaystyle \int \frac{1}{1-e^{-x}}dx}$

${\displaystyle {\int }_0^{\frac{1}{2}\log 3}\frac{e^x}{1+e^{2x}}dx}$

${\displaystyle {\int }_0^1\log (x^2+1)dx}$

${\displaystyle {\int }_1^2(x^3+2x^2+5x)dx}$

${\displaystyle {\int }_0^{\pi }\frac{x\sin x}{3+\cos 2x}dx}$

${\displaystyle \int \frac{\log x}{x^2}dx}$

${\displaystyle \int {\left(\frac{\log x}{2}\right)}^{2}dx}$

${\displaystyle \int \cos 2x\cos 4xdx}$

${\displaystyle \int \frac{1}{x(4-(\log x{)}^2)}dx}$

${\displaystyle {\int }_0^{\pi }\frac{\sin x}{1+\cos x}dx}$

${\displaystyle {\int }_{\sqrt{2}}^2\frac{1}{x\sqrt{x^2-1}}dx}$

${\displaystyle \int \frac{1}{x\sqrt{1-x^2}}dx}$

${\displaystyle \int e^{(e^x+x)}dx}$

${\displaystyle \int \frac{1}{3^{2-5x}}dx}$

${\displaystyle \int \frac{(\log x+3{)}^2}{x}dx}$

${\displaystyle {\int }_1^{\sqrt{3}}\frac{1}{x^2}\log \sqrt{1+x^2}dx}$

${\displaystyle \int \frac{x}{(x^2+2)(x^2+3)}dx}$

${\displaystyle {\int }_0^{\frac{\pi }{2}}\frac{(\cos x{)}^{\sqrt{3}}}{(\sin x{)}^{\sqrt{3}}+(\cos x{)}^{\sqrt{3}}}dx}$

${\displaystyle {\int }_0^2\frac{e^x}{e^x+e^{2-x}}dx}$

${\displaystyle {\int }_0^1\frac{2x+2}{x^2+x+1}dx}$

${\displaystyle {\int }_0^{\frac{\pi }{4}}\frac{x^2}{x\sin x+\cos x}dx}$

${\displaystyle {\int }_{-1}^1\frac{x^3}{1+x^2}dx}$

${\displaystyle \int \frac{1}{x(x+1)(x+2)}dx}$

${\displaystyle \int \frac{4(3+3x-x^2)}{(x-1{)}^2(x-1)}dx}$

${\displaystyle \int \frac{x}{1-x^2}dx}$

${\displaystyle {\int }_{-1}^1\frac{{\sin }^2(\pi x)}{1+e^x}dx}$

${\displaystyle \int (x^2-2x)\cos 2xdx}$

${\displaystyle {\int }_0^1{x}^4{e}^{-1}dx}$

${\displaystyle {\int }_1^4\frac{(\sqrt{x}+2{)}^2}{3\sqrt{x}}dx}$

${\displaystyle \int \frac{1}{\cos x}dx}$

${\displaystyle {\int }_0^{\pi }{e}^{2x}\sin xdx}$

${\displaystyle \int e^x{\sin }^{2}xdx}$

${\displaystyle {\int }_0^1\frac{x^5}{x^3+1}dx}$

${\displaystyle {\int }_0^1\sqrt{\frac{x}{1+x}}dx}$

${\displaystyle {\int }_{\frac{1}{2}}^{1}x\sqrt{\frac{1}{x}-1}dx}$

${\displaystyle \int \frac{3^x}{3^x+\log 3}dx}$

${\displaystyle \int {\tan }^{5}xdx}$

${\displaystyle {\int }_2^4\frac{\sqrt{\log (9-x)}}{\sqrt{\log (9-x)}+\sqrt{\log (x+3)}}dx}$

${\displaystyle {\int }_0^1\frac{\log (1+x)}{1+x^2}dx}$

${\displaystyle \int \cos x\cos 2x\cos 3xdx}$

${\displaystyle {\int }_0^1{f}^{-1}(x)dx,f(x)=\tan x(0\le x\le \frac{\pi }{4})}$

${\displaystyle {\int }_0^{\pi }\frac{1}{1+(\sin x{)}^{\cos x}}dx}$

${\displaystyle \int \sqrt{x\sqrt{x\sqrt{x\dots }}}dx}$

${\displaystyle \int \frac{\log x}{(x+1{)}^3}dx}$

${\displaystyle {\int }_e^{e^e}\frac{\log x\cdot \log (\log x)}{x}dx}$

${\displaystyle \int \log \frac{1+x}{1-x}dx}$

${\displaystyle {\int }_0^{2\pi }\sin (\sin x-x)xdx}$

${\displaystyle \int x^{2x}(2\log x+2)dx}$

${\displaystyle {\int }_0^{\frac{\pi }{2}}\sin 2x\cos (\cos x)dx}$

${\displaystyle {\int }_0^{\frac{\pi }{2}}|\sin x-3\cos x|dx}$

${\displaystyle {\int }_0^{\frac{\pi }{4}}\sqrt{\tan x}dx}$