Question

Integral of cost/(1+(sint)^2

Answer 1

\[let~i=\int\limits \frac{ \cos t }{ \left( 1+\sin t \right)^{2} }dt\]
put 1+sin t=u
cos t dt=du
\[I=\int\limits u ^{-2}du=\frac{ u ^{-1} }{-1 }+c=\frac{ -1 }{ u }+c\]
put the value of u and get the solution.