Definite integral of sin^4 3x cos^2 2x dx?

[joonoo]

How can you solve this definite integral from 0 to pie/2...

sin^4 3x cos^2 2x dx

I'm in the chapter doing substitution technique for sin^2 and cos^2 but I don't get how I can mix up sin and cos with 3x and 2x, not same x. I looked through book, but not a single example where x part doesn't match. Help me out please. Thank you!

 

[galactus]

How can you solve this definite integral from 0 to \(\displaystyle \L\\\underbrace{pie/2}_{\text{I've never seen\\a dessert as a\\limit of integration}}\)...

sin^4 3x cos^2 2x dx

I'm in the chapter doing substitution technique for sin^2 and cos^2 but I don't get how I can mix up sin and cos with 3x and 2x, not same x. I looked through book, but not a single example where x part doesn't match. Help me out please. Thank you!

Are you sure it's 3x and 2x, instead of both being the same?. If they were the same it would be easier.

Maybe someone else has a slick way, but it's quite laborious.

I ran it thorugh Maple and got back:

\(\displaystyle \L\\\frac{3}{64}sin(4x)+\frac{3}{16}x+\frac{1}{256}sin(8x)+\frac{1}{512}sin(16x)+\frac{1}{192}sin(12x)-\frac{1}{16}sin(2x)-\frac{1}{80}sin(10x)-\frac{1}{24}sin(6x)\)

Whew!