# Homework Help: Odd integral

1. Feb 2, 2009

### marmot

1. The problem statement, all variables and given/known data

I want to deal with this int((5+10y^4)dy/(y+2y^5))

2. Relevant equations

integration, substitution, partial fractions?

3. The attempt at a solution

I tried a bunch of random things. I think it hs to do with substitution because if I make u=y+2y^5, du/dy=1+10y^4 which is strikingly similar to the numerator, so there must be a cancellation. this integral is part of a dif equation, but i cant see to go past this! i know for sure this is the correct set up because i used my calculator to integrate and it solved the differential equation.

2. Feb 2, 2009

### Dick

Uh, the ratio of those two polynomials is a VERY SIMPLE THING. Can you find it? Factor them.

3. Feb 2, 2009

### aostraff

Try this :
5 + 10y^4 = 4 + 1 + 10y^4

after you get it, think of a crafty substitution

4. Feb 2, 2009

### Dick

Think of a crafty cancellation before you do the crafty substitution.

5. Feb 3, 2009

### marmot

jesus i feel like a complete retard. i hate when i dont get something as obvious.i factored both and cancelled that nasty factor and then everything went smooth, thanks a bunch gentlemen.