Question

Can someone help me with integrating rational functions? (specifics posted below)

Answer 1

The original integral is \[\int\limits_{}^{}\frac{ 2y^3+14y^2+38y+58 }{ (y+5)^2(y+1)^2 }dx\] and we're using partial fractions to integrate so after I split it up I had
\[\int\limits_{}^{}\frac{ 2 }{ y+5 }+\frac{ -2 }{ (y+5)^2 }+\frac{ 2 }{ (y+1)^2 }dx\] and I know from my online homework that those coefficients are correct because it made us enter them separately. My problem now is with integrating the ones with the squares on the bottom, I thought it was an arctan one at first but it wasn't working out for me.

Answer 2

i meant dy all around up there not dx, sorry

Answer 3

I assume that your partial fractions are correct. just answer your question
\[\int \frac{-2}{(y+5)^2}dx\] let u = y+5 so, du = dy, you have \[\int -2u^{-2}du = ??\] quite easy, right? how is it hard to you?

Answer 4

oh, I am sorry for my dx, too. hehehe

Answer 5

I was too used to looking for ln integrals and arctan integrals to think to try usub... so burned out by this. thank you lol