# [SOLVED] Integration

• Dec 11th 2009, 07:06 PM
nameck
[SOLVED] Integration
$\displaystyle \int{\left(\frac{x}{x^2 + 1}\right)\,dx}$

how to integrate?
i know $\displaystyle \int{\left(\frac{1}{x^2 + 1}\right)\,dx}$
is tan^-1 x + C

how am i going to start answering this question
• Dec 11th 2009, 07:40 PM
RockHard
Simple. Notice this with simple U-Substitution.

$\displaystyle u+x^2+1$

$\displaystyle du=2x dx$

$\displaystyle \frac{1}{2}du=x dx$
• Dec 11th 2009, 07:42 PM
VonNemo19
Quote:

Originally Posted by nameck
$\displaystyle \int{\left(\frac{x}{x^2 + 1}\right)\,dx}$

how to integrate?
i know $\displaystyle \int{\left(\frac{1}{x^2 + 1}\right)\,dx}$
is tan^-1 x + C

how am i going to start answering this question

Let $\displaystyle u=x^2+1$, then $\displaystyle du=2x\Rightarrow\frac{1}{2}du=dx$.

Now substituting

$\displaystyle \int\frac{\frac{1}{2}}{u}du=\frac{1}{2}\int\frac{1 }{u}du=\frac{1}{2}\ln|u|+C$.

Now back substitute.
• Dec 11th 2009, 07:52 PM
nameck
got it!! thanks guys!! =)