# Math Help - [SOLVED] Trigonometric integral

1. ## [SOLVED] Trigonometric integral

How do you solve the following indefinite integral:

$
\int {\sin^3 (2x)}{\sqrt{\cos (2x)}} dx
$

2. Originally Posted by baseballman
How do you solve the following indefinite integral:

$
\int {\sin^3 (2x)}{\sqrt{\cos (2x)}} dx
$
Have you tried a trig substitution? $u = \sin (2x)$ or $u = \cos (2x)$ or something?

3. Write the integral as $\int sin^2(2x)\sqrt{cos(2x)}(sin(2x)dx)= \int (1- cos^2(2x)\sqrt{cos(2x)}(sin(2x)dx)$ and use the substitution u= cos(2x).

4. Got this answer:

$
\frac{1}
{3}\sqrt {{{\cos }^3}(2x)} + \frac{1}
{7}\sqrt {{{\cos }^7}(2x)} + C
$

Thanks for your quick response.