積分100本ノック（問題編）

$ \displaystyle \int \tan^3{x} dx $

$ \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{x} dx $

$ \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^2x}dx $

$ \displaystyle \int \log_2xdx $

$ \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^2x}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 x dx $

$ \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(2020x)| 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}\log3} \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{2x} dx $

$ \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 x dx $

$ \displaystyle \int e^x \sin^2 x dx$

$ \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+\log3} dx $

$ \displaystyle \int \tan^5 x dx $

$ \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{3x} dx $

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

$ \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) x dx $

$ \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 $