$\int \frac{x^3}{x+3} \mathrm{~d} x$ ．
$\int \frac{x^2+1}{(x+1)^2(x-1)} \mathrm{d} x$
$\int \frac{\mathrm{d} x}{\left(x^2+1\right)\left(x^2+x+1\right)}$
$\int \frac{\mathrm{d} x}{3+\sin ^2 x}$
$\int \frac{5}{3 \sin x-4 \cos x} \mathrm{~d} x$
$\int \frac{d x}{\sqrt[3]{(x+1)^2(x-1)^4}}$
思考题：确定系数 $A, B$ 使下式成立 $\int \frac{\mathrm{d} x}{(a+b \cos x)^2}=\frac{A \sin x}{a+b \cos x}+B \int \frac{\mathrm{~d} x}{a+b \cos x}$ ．