Trig substitition-lost in identities

[phantomcow2]

Trig substitition--lost in identities

Homework Statement

\int\frac{dx}{x^{2}\sqrt{x^{2}+1}}

Homework Equations

It's pretty obvious that this is a trig substitution problem requiring use of tangent.

The Attempt at a Solution

x=tan\theta
dx=sec^{2}\theta
x^{2}=tan^{2}\theta

Substitute it in.

\frac{sec^{2}\theta}{tan^{2}\theta\sqrt{tan^{2}\theta + 1}}

But the \sqrt{tan^{2}\theta + 1} simplifies to sec\theta

Now before I integrate, I need to simplify. The obvious simplification is the sec^{2}\theta and sec\theta in the denominator, leaving me with
\frac{sec\theta}{tan^{2}\theta}

This is starting to look fishy to me. I think I've begun to develop an instinct telling me when I am doing something incorrectly. I simplify this to \frac{cos\theta}{sin^{2}\theta}

Now I need to ingrate this, but it doesn't look promising. Can someone tell me where I went wrong?

 

[Avodyne]

Nothing wrong so far. Time for another substitution.

 

[phantomcow2]

Oh, haha, you're right! I need to start thinking to substitute more often :p

u= sin and du = cos

Yep, straight forward from here. Thanks so much.