# Math Help - trigonometric integral

1. ## trigonometric integral

hello

Anyone know how to solve this ??

$\int \dfrac{ sin\theta - cos\theta }{ \sqrt{sin 2\theta} } d\theta$

2. $sin(2\theta)=1+sin(2\theta)-1=sin^2(\theta)+cos^2(\theta)+sin(2\theta)-1=(sin(\theta)+cos(\theta))^2-1$

so your integral = $\displaystyle \int \dfrac{ sin(\theta) - cos(\theta) } { \sqrt{ (sin(\theta)+cos(\theta))^2-1 } } \, d\theta$

Put $t=sin(\theta)+cos(\theta)$ so that $- ( sin(\theta)-cos(\theta) ) d\theta = dt$

your integral becomes: $\displaystyle - \int \dfrac{dt}{\sqrt{t^2-1}} \, dt$

A quick trigonometric substitution will finish it.

3. Originally Posted by Liverpool
hello

Anyone know how to solve this ??

$\int \dfrac{ sin\theta - cos\theta }{ \sqrt{sin 2\theta} } d\theta$
Wolfram says this ... (won't show the steps to get there)

4. Thanks.