解説したい問題

以下の定積分を求めよ。
1.
\begin{align} \int_0^\frac{π}{4}\frac{x}{\sin2x+2\cos^2 x}dx \end{align}
2.
\begin{align} \int_0^\frac{π}{4}\frac{1}{1+2\sin^2x}dx \end{align}
3.
\begin{align} \int_0^π\frac{1}{1+\sin^2x}dx \end{align}
4.
\begin{align} \int_0^π\frac{1}{3+\sin^2x}dx \end{align}
5.
\begin{align} \int_0^\frac{π}{2}\left(\frac{3}{2+\sin x}\right)^2dx \end{align}
6.
\begin{align} \int_0^\frac{π}{2}\sqrt{\tan x}dx \end{align}