# Difficult integration

by ookt2c
Tags: difficult, integration
 P: 230 Difficult integration don't know what the reduction formula is, maybe it is the trick i'm about to give you $$\int sin(2x)^4 dx = \frac{1}{2} \int sin(u)^4 du = \frac{1}{2} \int (sin(u)^2)^{3/2} sin(u) du = \frac{1}{2} \int (1-cos(u)^2)^{3/2} sin(u)du = \frac{1}{2} \int (1-t^2)^{3/2} dt = \int sqrt((1-t^2)^3)$$ maybe you can do this???, of cause you have to keep track of all the substitutions to get how sin and y are related but that should be possible.