Answer to Question #162030 in Calculus for Phyroe

Question

Evaluate the ∫1-siny dy/y+cosy

Answer 1

Solution

$I=\int \frac{1-sin y}{y+cos y}dy$

Substitution x = y+cos y,  dx = 1-sin y:

$I=\int \frac{dx}{x}=ln|x|+C=ln|y+cos y|+C$

Answer

$\int \frac{1-sin y}{y+cos y}dy=ln|y+cos y|+C$