Question

$\int\limits^0_ \frac{ \pi }{4} { \frac{1}{1- sin^{2}x } } \, dx$

Answer 1

[tex] \int\limits^0_{ \frac{\pi}{4} } { \frac{1}{sin^2x+cos^2x-sin^2x} } \, dx =\\ =\int\limits^0_{ \frac{\pi}{4} } { \frac{1}{cos^2x} } \, dx =tgx|^0_{ \frac{\pi}{4} }\\= =tg0-tg\frac{\pi}{4}=0-1=-1[/tex]