Answer to Question #174631 in Calculus for Phyroe

Question

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

Answer 1

$\int (\sin x + \cos x)^2\,dx = \\ \int \sin^2 x + 2\sin x\cos x + \cos^2 x\,dx = \\ \int (\sin^2 x + \cos^2 x) \,dx + \int 2\sin x \cos x \,dx = \\ \int dx + \int 2\sin x \,d(\sin x) = \\ x + \sin^2 x + C$