1. trig integral

i need help with this integral....i seem to be getting no where with it

(1/8)[integral]sin^2(2x)cos(2x)

thanks

2. Originally Posted by johntuan
i need help with this integral....i seem to be getting no where with it

(1/8)[integral]sin^2(2x)cos(2x)

thanks
substitute

$\displaystyle \sin 2x = t$

so that,

$\displaystyle 2\cos 2x \;dx = dt$

$\displaystyle \cos 2x \;dx = \frac{dt}{2}$

Spoiler:
$\displaystyle \frac{1}{8}\int \sin ^2 2x\; \cos 2x~dx=\frac{1}{16}\int t^2~dt$

3. Originally Posted by johntuan
i need help with this integral....i seem to be getting no where with it

(1/8)[integral]sin^2(2x)cos(2x)

thanks
$\displaystyle sin^2(2x) = 1-cos^2(2x)$

$\displaystyle \frac{1}{8} \int cos(2x) - cos^3(2x)$

Which should be easier to integrate

4. Originally Posted by e^(i*pi)
$\displaystyle sin^2(2x) = 1-cos^2(2x)$

$\displaystyle \frac{1}{8} \int cos(2x) - cos^3(2x)$

Which should be easier to integrate

if i continued to integrate would it lead me to the answer of

(1/8)[(1/3)(1/2)sin^3(2t)]......?

5. Originally Posted by johntuan
if i continued to integrate would it lead me to the answer of

(1/8)[(1/3)(1/2)sin^3(2t)]......?