Question

Evaluate:

$\int {\sin }^{4}x{\cos }^{3}x.dx$

Answer 1

$2sinccosD=sin\{C-D\}+sin\{C+D\}$

$\int sin4xcos3xdx=\int \frac{1}{2}[sin\{4x-3x\}+sin\{4x+3x\}]dx$

$\frac{1}{2}\int [sinx+sin7x]dx$

$\frac{1}{2}[-cosx-\frac{cos7x}{7}]C$

$-\frac{1}{2}cosx-\frac{1}{14}cos7x+C$