Question

integrate Sinx to the power4

Answer 1

$\int\limits {sin^4x} \ dx$
$\int\limits { \frac{(1-cos(2x))^2}{2^2} } \ dx$
$\frac{1}{4} \int\limits {1-2cos(2x)+cos^2(2x)} \ dx$
$\frac{1}{4}[x- \frac{2sin(2x)}{2}+ \int\limits { \frac{1+cox(4x)}{2} } \ dx ]$
$\frac{1}{4}[x- \frac{2sin(2x)}{2}+ \frac{1}{2}(x+ \frac{sin(4x)}{4} ) ]$
$\frac{1}{4}x+ \frac{1}{4}sin(2x)+ \frac{1}{8}x+ \frac{1}{32}sin(4x) +C$