[SOLVED] Integration

**nameck** · December 11th 2009, 07:06 PM

$\int{\left(\frac{x}{x^2 + 1}\right)\,dx}$

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

how am i going to start answering this question

**RockHard** · December 11th 2009, 07:40 PM

Simple. Notice this with simple U-Substitution.

$u+x^2+1$

$du=2x dx$

$\frac{1}{2}du=x dx$

**VonNemo19** · December 11th 2009, 07:42 PM

Originally Posted by nameck

$\int{\left(\frac{x}{x^2 + 1}\right)\,dx}$

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

how am i going to start answering this question

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

Now substituting

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

Now back substitute.

**nameck** · December 11th 2009, 07:52 PM

got it!! thanks guys!! =)

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