Integrating Int((5+10y^4)dy/(y+2y^5)) - A Step-by-Step Guide

[marmot]

Homework Statement

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

Homework Equations

integration, substitution, partial fractions?

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 can't 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.

 

[Dick]

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

 

[aostraff]

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

after you get it, think of a crafty substitution

 

[Dick]

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

after you get it, think of a crafty substitution

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

 

[marmot]

jesus i feel like a complete retard. i hate when i don't get something as obvious.i factored both and canceled that nasty factor and then everything went smooth, thanks a bunch gentlemen.