How Can You Integrate sin^4(2x) Without Using the Reduction Formula?

[ookt2c]

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

 

[Big-T]

Try using double-angle formulae a couple of times.

 

[rock.freak667]

The double angle formula for cos will help I believe.

 

[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.

 

[sutupidmath]

This thread is already somewhere else. I mean the exact same question.

https://www.physicsforums.com/showthread.php?t=213617