Question

Solve:$\int ({\sin }^{4}x-{\cos }^{4}x)dx=$

Answer 1

$=\int ({\sin }^{2}x-{\cos }^{2}x)({\sin }^{2}x+{\cos }^{2}x)dx$
$=\int ({\sin }^{2}x-{\cos }^{2}x)dx$
$=-\int \cos 2xdx$
$=-\frac{\sin 2x}{2}+C$
$=-\sin x\cos x+C$