1. ## Integral [Calc 2]

There was a question on a previous exam and I can't seem to get the right answer.

$\int\frac{2dx}{x^3 + x}$

My initial method was to use Integration by Parts, but I can't seem to massage it correctly.

$u = \frac{2}{x}$; $du = 2ln(x)dx$

$dv = (x^2 + 1) dx$; $v = \frac{x^3}{3} + x$

Fairly certain this doesn't work though, although my arithmetic could be off.
Could someone please take a jab at this? I would appreciate it greatly. :]

2. Originally Posted by freyrkessenin
There was a question on a previous exam and I can't seem to get the right answer.

$\int\frac{2dx}{x^3 + x}$

My initial method was to use Integration by Parts, but I can't seem to massage it correctly.

$u = \frac{2}{x}$; $du = 2ln(x)dx$

$dv = (x^2 + 1) dx$; $v = \frac{x^3}{3} + x$

Fairly certain this doesn't work though, although my arithmetic could be off.
Could someone please take a jab at this? I would appreciate it greatly. :]
Use a partial fraction decomposition.

3. Originally Posted by mr fantastic
Use a partial fraction decomposition.

Ah. That's why I couldn't do it. I never learned how to do partial fractions. But thanks. :]

4. Put $x=\frac1u$ and you'll get an easy integral.