Integration by Parts: Solving 1/(u²(a+bu)²) with Substitution

[nonechelon]

Homework Statement

1/(u²(a+bu)²) a and b are constants u is the variable

Homework Equations

The Attempt at a Solution

i know I am suppose to use substition by parts but i don't know what to use.
thanks for help in advance

 

[Mark44]

Homework Statement

1/(u²(a+bu)²) a and b are constants u is the variable

Homework Equations

The Attempt at a Solution

i know I am suppose to use substition by parts but i don't know what to use.
thanks for help in advance

I'm confused. The title says "Integration by parts". Later on, you said you supposed to use "substitution by parts" which is not a technique I've ever heard of. There's a technique called "substitution".

There's also a technique called "partial fractions" or "partial fraction decomposition" in which you can decompose a complicated rational expression into a sum of simpler rational expressions.

So how are you supposed to do this problem?

 

[nonechelon]

oops i mean integration by parts i don't know why i said substitution.sorry

 

[Defennder]

The best approach would be to decompose the fraction first into it's partial fractions as suggested by Mark44. Then integrate the partial fractions separately.