# Which method of integration is appropriate here?

• Apr 16th 2011, 04:18 AM
kselogatr
Which method of integration is appropriate here?
How would you integrate 1 / (v+v^3) ?

I thought it would be [ 1 / (1+3v^2)] ln |v+v^3| by anti-differentiation but I don't think that is correct?

Thanks!
• Apr 16th 2011, 04:21 AM
mr fantastic
Quote:

Originally Posted by kselogatr
How would you integrate 1 / (v+v^3) ?

I thought it would be [ 1 / (1+3v^2)] ln |v+v^3| by anti-differentiation but I don't think that is correct?

Thanks!

Use a partial fraction decomposition. If you need more help, please show all your work and say where you get stuck.

(It is obvius that your answer is wrong. Differentiate it - Do you get back 1/(v + v^3) ....?)
• Apr 16th 2011, 06:27 AM
Prove It
It appears that you tried to do this:

http://quicklatex.com/cache3/ql_8c3b...796c773_l3.png

so that you could use a u substitution.

This is incorrect because you can only pull constants out of the integral, not functions.

Like Mr F said, factorise the denominator then use partial fractions. You should find that your answer has a logarithm term and an arctangent term.