# Trig substitution should be simple but it's driving me nuts

1. Sep 13, 2011

### pugtm

1. The problem statement, all variables and given/known data
$\int x/sqrt{(x^{2}+4)}$

2. Relevant equations
x=2tanx

3. The attempt at a solution
x=2tanx
$\int$2tan$\vartheta$/$\sqrt{tan^2\vartheta}$+4
2/2 *$\int$tan/sec

$\int$sin=-cos

now is the part where i am stuck
i know from using substitution that the answr should be $\sqrt{x^2+4}$
but no matter how i manipulate it, it comes out strange.
all help is appreciated

2. Sep 13, 2011

### vela

Staff Emeritus
The integral you're trying to evaluate is
$$\int\frac{x}{\sqrt{x^2+4}}\,dx$$
Note the presence of the dx. That's what you forgot to account for when you did the trig substitution.

3. Sep 13, 2011

### pugtm

how do you get rid of the natural log at the end?

4. Sep 13, 2011

### vela

Staff Emeritus
What natural log? You apparently made another mistake.

5. Sep 13, 2011

### pugtm

the new integral is
int 2tan(x)sec(x)^2/Sqrt(4tan(x)^2+4)
the sec^2 cancel out making it the integral of 2tan(x)=-2lncos(x)

6. Sep 13, 2011

### vela

Staff Emeritus
Slow down and look at it more carefully.
$$\int \frac{2 \tan \theta \ \sec^2\theta}{\sqrt{4\tan^2\theta+4}}\,d\theta = \int \frac{2 \tan \theta \ \sec^2\theta}{2\sqrt{\sec^2\theta}}\,d\theta$$

7. Sep 13, 2011

### Tomer

I'm not sure that's what you mean, but I hope you noticed that there's a much simpler substitution possible :-)