$\int \frac{\ln \tan x}{\cos x \sin x} \mathrm{~d} x$;
$\int \frac{\ln (x+1)-\ln x}{x(x+1)} \mathrm{d} x$;
$\int \frac{1}{\mathrm{e}^x+1} \mathrm{~d} x ;$
$\int \frac{x \mathrm{~d} x}{4 x^2+4 x+5} .$
设$f(x)=\mathrm{e}^{-x} $ 求 $\int \frac{f^{\prime}(\ln x)}{x} \mathrm{~d} x$
思考题：怎么求函数 $f(x)=\max \left(1, x^2\right)=\left\{\begin{array}{ll}1, & |x| \leq 1 \\ x^2 & |x|>1\end{array}\right.$ 的不定积分？试试看！