# difficult integration

by ookt2c
Tags: difficult, integration
 P: 16 integrate sin^4(2x) without using the reduction formula.im stuck. im pretty sure you have to use integration by parts.
 P: 64 Try using double-angle formulae a couple of times.
 HW Helper P: 6,213 The double angle formula for cos will help I believe.
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.