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

[pugtm]

Homework Statement

$\int x/sqrt{(x^{2}+4)}$

Homework Equations

x=2tanx

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

 

[vela]

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.

 

[pugtm]

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

 

[vela]

What natural log? You apparently made another mistake.

 

[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)

 

[vela]

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

 

[Tomer]

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

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

Anyway, the others are correct about your mistakes :-)

 

[pugtm]

thank you all for your timely assistance