Question

what is integral of sin x power 4 value?

Answer 1

$\int\limits sin^4{x} \, dx \\ \int\limits ((1 - cos{2x})/2)^2 \, dx \\ \int\limits (1 - 2cos{2x} + cos^2 {x})/4 \, dx$
$1/4 \int\limits dx - 1/4\int\limits 2cos{2x} \, dx + 1/4 \int\limits cos^2{x} \, dx$
using cosine half- angle
$1/4x - 1/4sin(2x) +1/4 \int\limits(1 + cos{4x})/2 \, dx$
$3/8x - 1/4sin(2x) + 1/8 sin(4x) + C$