# Thread: Trigonometric Integrals

1. ## Trigonometric Integrals

How can I solve this problem:

$\int \frac{dx}{\sqrt{3}\sin(x)+\cos(x)}$

Using the fact that $\cos({\frac{\pi}{6}})=\frac{\sqrt{3}}{2}$ ?

Thank you!

2. Originally Posted by adam63
How can I solve this problem:

$\int \frac{dx}{\sqrt{3}\sin(x)+\cos(x)}$

Using the fact that $\cos({\frac{\pi}{6}})=\frac{\sqrt{3}}{2}$ ?

Thank you!
http://www.wolframalpha.com/input/?i...Cos&#91;x]%29]

Click Show Steps

3. Well, thank you, but I already know this site and checked for the integral there - the solution did not involve what I need - I have to use that trigonometric equation somehow.

4. $
\int \frac{dx}{\sqrt{3}\sin x+\cos x} = \int \frac{dx}{\frac{\cos\frac{\pi}{6}}{\sin\frac{\pi}{ 6}}\sin x+\cos x} = \sin\frac{\pi}{6}\int \frac{dx}{\cos\frac{\pi}{6}\sin x + \sin\frac{\pi}{6}\cos x} =
$

$
= \frac{1}{2}\int\frac{dx}{\sin(x+\frac{\pi}{6})}
$

I suppose you can continue from here

5. Originally Posted by Unbeatable0
$
\int \frac{dx}{\sqrt{3}\sin x+\cos x} = \int \frac{dx}{\frac{\cos\frac{\pi}{6}}{\sin\frac{\pi}{ 6}}\sin x+\cos x} = \sin\frac{\pi}{6}\int \frac{dx}{\cos\frac{\pi}{6}\sin x + \sin\frac{\pi}{6}\cos x} =
$

$
= \frac{1}{2}\int\frac{dx}{\sin(x+\frac{\pi}{6})}
$

I suppose you can continue from here
Wow, beautiful, thank you very much !!!