find-pi-4-pi-4-cosx-2-5sinx-dx-

Question Number 65776 by mathmax by abdo last updated on 03/Aug/19

f i n d \int_{- \frac{π}{4}}^{\frac{π}{4}} \frac{c o s x}{2 + 5 s i n x} d x

Commented by kaivan.ahmadi last updated on 04/Aug/19

u = 2 + 5 s i n x \Rightarrow d u = 5 c o s x d x

\frac{1}{5} \int \frac{d u}{u} = \frac{1}{5} l n u = \frac{1}{5} l n (2 + 5 s i n x) ∣_{- \frac{π}{4}}^{\frac{π}{4}} =