Integral [Calc 2]

freyrkessenin · #1 $Old$ 11-20-2008, 01:43 AM

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. :]

mr fantastic · #2 $Old$ 11-20-2008, 01:49 AM

Quote:

Originally Posted by freyrkessenin $View Post$

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.