If $x \neq(2 n+1) \frac{\pi}{2}$, then $\int \frac{\cos ^3 x}{(1+\sin x)^4} d x=$

If $\frac{x^2-2}{\left(x^2+1\right)\left(x^2+3\right)}=\frac{A x+B}{x^2+1}+\frac{C x+D}{x^2+3}$, then $D=$

Let $g(x)$ be the anti-derivative of $f(x)$. Then, the function for which $\log _e\left(1+(g(x))^2\right)+c$ is an anti-derivative is

If $f(x)=\int\left[\tan ^2 x+\cot ^2 x+\frac{4\left(\sin ^3 x+\cos ^3 x\right)}{\sin ^2 2 x}\right] d x$ and $f\left(\frac{\pi}{4}\right)=0$, then $3\left[f\left(\frac{\pi}{6}\right)+2\right]=$