$\int \frac{x^2}{\sqrt{a^2-x^2}} \mathrm{~d} x \quad(a>0)$ ．
$\int \frac{\mathrm{d} x}{\sqrt{\left(x^2+1\right)^3}}$ ．
$\int \frac{\sqrt{x^2-9}}{x} \mathrm{~d} x$ ．
$\int \frac{\mathrm{d} x}{x \sqrt{x^2-1}}$ ．
$\int \frac{\mathrm{d} x}{x+\sqrt{1-x^2}}$ ．
$\int \frac{\sqrt{x}}{\sqrt{x}-\sqrt[3]{x}} \mathrm{~d} x$ ．
$\int \sqrt{1+\mathrm{e}^x} \mathrm{~d} x$ ．
$\int \frac{x^3+1}{\left(x^2+1\right)^2} \mathrm{~d} x$.
思考题：你能用几种方法来求 $\int \sqrt{x^2+x+1} \mathrm{~d} x$ ？试试看！