$\underset{-\pi /2}{\overset{\pi /2}{\int }}{\sin }^{4}x\left[1+\log \left(\frac{2+\sin x}{2-\sin x}\right)\right]dx$

$\underset{-\frac{\pi }{2}}{\overset{\pi /2}{\int }}{\sin }^{4}xdx+$$\underset{-\frac{\pi }{2}}{\overset{\pi /2}{\int }}{\sin }^{4}x\left(\log \frac{2+\sin x}{2-\sin x}\right)dx$

Even        +      odd function

$2\underset{0}{\overset{\pi /2}{\int }}{\sin }^{4}xdx+0=2.\frac{3}{4}.\frac{1}{2}.\frac{\pi }{2}=\frac{3\pi }{8}$