解答题 （共 23 题 ），解答过程应写出必要的文字说明、证明过程或演算步骤
$\int x^2 \cos ^2 \frac{x}{2} d x$
$\int \frac{1}{1+\cos x} d x$
$\int \frac{1}{1+\sin x} d x$
$\int \frac{x}{4+x^4} d x$
$\int \frac{x^2+2}{(x+1)^3} d x$
$\int \frac{x^5}{\sqrt{1-x^2}} d x$
$\int \frac{\sqrt{x+1}-1}{\sqrt{x+1}+1} d x$
$\int \frac{1}{x \ln x \ln (\ln 8)} d x$
$\int \frac{x^7}{x^4+2} d x$
$\int_{\frac{\pi}{4}}^{\frac{\pi}{3}} \frac{\tan x}{\ln (\cos x)} d x$
$\int_{-1}^1 \frac{1}{1+x^2} d x$
$\int \frac{1}{2+\sin x} d x$
$\int_0^\pi \sqrt{\sin ^3 x-\sin ^5 x} d x$
$I=\int_0^{\frac{\pi}{2}} \frac{\sin \theta}{\sin \theta+\cos \theta} d \theta$
$\int \frac{x^3}{x^8-2} d x$
$\int \frac{x^{2 n-1}}{x^n+1} d x$