- #1
phantomcow2
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Trig substitition--lost in identities
\int\frac{dx}{x^{2}\sqrt{x^{2}+1}}
It's pretty obvious that this is a trig substitution problem requiring use of tangent.
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?
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?
