# Difficult integration

1. Feb 6, 2008

### ookt2c

integrate sin^4(2x) without using the reduction formula.im stuck.
im pretty sure you have to use integration by parts.

2. Feb 6, 2008

### Big-T

Try using double-angle formulae a couple of times.

3. Feb 6, 2008

### rock.freak667

The double angle formula for cos will help I believe.

4. Feb 7, 2008

### mrandersdk

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.

Last edited: Feb 7, 2008
5. Feb 7, 2008