Question

Evaluate the integral of (sin x + cos x)² dx

Answer 1

Evaluate the integral of (sin x + cos x)² dx

Solution. Simplify the integral function:

$( sinx+cosx)^2=sin^2x+cos^2x+2sinxcosx=1+sin(2x).$

Then: $\intop(sinx+cosx)^2dx=\intop(1+sin(2x))dx=x-\frac{1}{2}cos(2x)+\rm constant.$

Answer: $\intop(sinx+cosx)^2dx=x-\frac{1}{2}cos(2x)+\rm constant.$