Question

Integrate [(x^2 + 1)e^x] / (x+1)^2

Answer 1

i've found the answer on wollframalpha but i've got little idea of how to proceed with this

Answer 2

seriously tricky. no trig sub, and I don't think partial fractions will get us anywhere...

Answer 3

right i've also tried using integration by parts but it got too complicated

Answer 4

the only thing i figered correctly was that the denominator is (x+1) as the (x+1)^2 is the result of applying the quotient rule.

Answer 5

I see, but that says little about the numerator. I'll have to ponder this for a while... I'll let you know if I get anywhere.

Answer 6

yes - that doesnt help much - ok thanx

Answer 7

thinking out loud if we divide the fraction we get\[ \int\limits(1-{2x \over (x+1)^2})e^xdx\]this looks like we could use partial fractions, then integration be parts... maybe

Answer 8

I think I have an idea.
\(\large \frac{(x^2+1)e^x}{(x+1)^2}=\frac{e^x[(x+1)^2-2x]}{(x+1)^2}=e^x-\frac{2x}{(x+1)^2}e^x.\)

Answer 9

yay we agreed!

Answer 10

The first term is too easy to integrate, and the second term can be integrated by parts.

Answer 11

ya seedee

Answer 12

ya setti! :D

Answer 13

hahaha

Answer 14

thanx guys