積分100本ノック（解答編）

${\displaystyle \frac{1}{2}{\tan }^{2}x+\log |\cos x|+C}$

${\displaystyle 4\sqrt{2}}$

${\displaystyle \frac{\pi }{2}-1}$

${\displaystyle \frac{1}{4\log 2}}$

${\displaystyle \frac{1}{2}\log \frac{1-\cos x}{1+\cos x}+C}$

${\displaystyle \log (x+\sqrt{x^2+1})+C}$

${\displaystyle \frac{2}{45}(3x-5)\sqrt{3x-5}(3x+\frac{10}{3})+C}$

${\displaystyle \frac{2}{9}e\sqrt{e}+\frac{4}{9}}$

${\displaystyle x(\log x{)}^2-2(x\log x-x)+C}$

${\displaystyle 6+\frac{\pi }{8}}$

${\displaystyle \log |1+\log x|+C}$

${\displaystyle 2\log |\sqrt{x}-1|+C}$

${\displaystyle \frac{\pi }{12}+\frac{1}{2}-\frac{\sqrt{3}}{4}}$

${\displaystyle \log |x+3+\sqrt{x^2+6x+13}|+C}$

${\displaystyle x\tan x+\log |\cos x|+C}$

${\displaystyle \frac{1}{\log 2}(x\log x-x)+C}$

${\displaystyle -\log |x+1|+\frac{1}{2}\log (x^2+1)+C}$

${\displaystyle 2\log |x|-2\log |x+1|+\frac{1}{x+1}+C}$

${\displaystyle -\frac{1}{\tan x}+C}$

${\displaystyle \frac{\pi }{4}-\frac{1}{2}}$

${\displaystyle -(\log |\cos x|{)}^2+C}$

${\displaystyle \frac{1}{2}\frac{\sin \theta }{\cos \theta }+\frac{1}{4}\log \left|\frac{1+\sin \theta }{1-\sin \theta }\right|+C}$

${\displaystyle \tan x-\frac{1}{\cos x}+C}$

${\displaystyle \frac{x{2}^x}{\log 2}-\frac{2^x}{(\log 2{)}^2}+C}$

${\displaystyle \frac{e^3}{3}-\frac{e^2}{2}}$

${\displaystyle \log |\tan x|+C}$

${\displaystyle \frac{x{2}^{\log x}}{\log 2+1}+C}$

${\displaystyle \frac{1}{3}\log 2+\frac{\sqrt{3}}{9}\pi }$

${\displaystyle 1}$

${\displaystyle \tan x+\frac{1}{3}{\tan }^{3}x+C}$

${\displaystyle \frac{1}{3}}$

${\displaystyle \frac{\cos \frac{1}{x}}{x}-\sin \frac{1}{x}+C}$

${\displaystyle \sqrt{\tan x}+C}$

${\displaystyle \frac{1}{2}x{e}^x(\sin x-\cos x)+\frac{1}{2}{e}^x\cos x+C}$

${\displaystyle \frac{1}{2}x\{\sin (\log x)-\cos (\log x)\}+C}$

${\displaystyle \frac{1}{10}(9\sqrt{3}-1)}$

${\displaystyle \frac{1}{2}\{\log (\log x){\}}^2+C}$

${\displaystyle \frac{\pi }{4}}$

${\displaystyle 2e^{\frac{x}{2}}+C}$

${\displaystyle -\frac{1}{\log x}+C}$

${\displaystyle -\frac{1}{4}x\cos 2x+\frac{1}{8}\sin 2x+C}$

${\displaystyle \frac{1}{50}{e}^x(5x+3)\sin 2x+\frac{1}{25}{e}^x(2-5x)\cos 2x+C}$

${\displaystyle \frac{\pi }{6}\log 2}$

${\displaystyle \frac{\pi }{28}}$

${\displaystyle -\frac{1}{3}\log |1+x^{-3}|+C}$

${\displaystyle 4040}$

${\displaystyle e^3-e^2}$

${\displaystyle x^x+C}$

${\displaystyle \frac{1263}{56}}$

${\displaystyle \log |e^x-1|+C}$

${\displaystyle \frac{\pi }{12}}$

${\displaystyle \log 2-2+\frac{\pi }{2}}$

${\displaystyle \frac{191}{12}}$

${\displaystyle \frac{{\pi }^2}{8}}$

${\displaystyle -\frac{\log x+1}{x}+C}$

${\displaystyle -\frac{(\log x{)}^2+2\log x+2}{x}+C}$

${\displaystyle \frac{1}{12}\sin 6x+\frac{1}{4}\sin 2x+C}$

${\displaystyle \frac{1}{4}(-\log |2-\log x|+\log |2+\log x|)+C}$

${\displaystyle \frac{\pi }{2}}$

${\displaystyle \frac{\pi }{12}}$

${\displaystyle \frac{1}{2}\log |\sqrt{1-x^2}-1|-\frac{1}{2}\log |\sqrt{1-x^2}+1|+C}$

${\displaystyle e^{e^x}+C}$

${\displaystyle \frac{3^{-2+5x}}{5\log 3}+C}$

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

${\displaystyle (\frac{1}{2}-\frac{1}{\sqrt{3}})\log 2+\frac{\pi }{12}}$

${\displaystyle \frac{1}{2}\log \frac{x^2+2}{x^2+3}+C}$

${\displaystyle \frac{\pi }{4}}$

${\displaystyle 1}$

${\displaystyle \log 3+\frac{\sqrt{3}}{9}\pi }$

${\displaystyle \frac{4-\pi }{4+\pi }}$

${\displaystyle 0}$

${\displaystyle \frac{1}{2}\log \frac{|x(x+2)|}{(x+1{)}^2}+C}$

${\displaystyle \log \left|\frac{1}{(x-1{)}^3(x+1)}\right|-\frac{10}{x-1}+C}$

${\displaystyle -\frac{1}{2}\log |1-x^2|+C}$

${\displaystyle \frac{1}{2}}$

${\displaystyle \frac{1}{4}\{(2x^2-4x-1)\sin 2x+2(x-1)\cos 2x\}+C}$

${\displaystyle -\frac{65}{e}+24}$

${\displaystyle \frac{74}{9}}$

${\displaystyle \frac{1}{2}\log \left(\frac{1+\sin x}{1-\sin x}\right)+C}$

${\displaystyle \frac{1}{5}(e^{2\pi }+1)}$

${\displaystyle \frac{1}{5}{e}^x({\sin }^{2}x-\sin 2x+C)}$

${\displaystyle \frac{1}{3}(1-\log 2)}$

${\displaystyle \sqrt{2}-\log (\sqrt{2}+1)}$

${\displaystyle \frac{\pi }{16}}$

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

${\displaystyle \frac{1}{4}{\tan }^{4}x-\frac{1}{2}{\tan }^{2}x-\log |\cos x|+C}$

${\displaystyle 1}$

${\displaystyle \frac{\pi }{8}\log 2}$

${\displaystyle \frac{1}{48}(12x+6\sin 2x+3\sin 4x+2\sin 6x)+C}$

${\displaystyle \frac{\pi }{4}-\frac{1}{2}\log 2}$

${\displaystyle \frac{\pi }{2}}$

${\displaystyle \frac{1}{2}{x}^2+C}$

${\displaystyle \frac{1}{2}\{\frac{x(x+2)}{(x+1{)}^2}\log x-\log (x+1)+\frac{1}{x+1}\}+C}$

${\displaystyle \frac{e^2+1}{4}}$

${\displaystyle \log (1-x^2)+x\log \frac{1+x}{1-x}+C}$

${\displaystyle 0}$

${\displaystyle x^{2x}+C}$

${\displaystyle 2(\sin 1+\cos 1-1)}$

${\displaystyle 4\sqrt{10}}$

${\displaystyle \frac{1}{\sqrt{2}}\{\log (\sqrt{2}-1)+\frac{\pi }{2}\}}$