Need some help with an integral.

1. Oct 23, 2013

Nick20

Hey! Need some help on an integral I've been trying to solve. I haven't been working enough with my math, so I am working on catching up before finals..

I was working with partial fractions and u substitution when I couldn't figure this one out:

∫(x+5)/(x^2+4x+8)dx

it's not that hard but I am missing one small detail in order to solve it, I am sure.

I believe the answer has something to do with

∫1/(a^2+x^2)dx = 1/a arctan(x/a) + C

Thanks

2. Oct 23, 2013

arildno

1. Complete the square in the denominator!
2. In the numerator, write 5=2+3, and then see if an idea pops up in how to solve the problem!

3. Oct 23, 2013

Nick20

Sooo if I say:

∫(x+2+3)/((x+2)^2+4)dx and substitute x+2 with u, and dx with du

∫(u+3)/(u^2+4)du am I on the right track? I'll have it done in a minute and check the answer.

thanks.

************EDIT****************

lots of stuff happend and then:

1/2 ln((x+2)^2+4) + 3/2 arctan((x+2)/2) ?

Last edited: Oct 23, 2013
4. Oct 23, 2013

Staff: Mentor

You can check your antiderivative by differentiating it. If you end up with the original integrand, you're golden.

5. Oct 24, 2013

arildno

The right stuff happened!

6. Oct 24, 2013

R136a1

Don't forget the arbitrary constant +C

7. Oct 24, 2013

Nick20

Don't worry, I didn't :) I just forgot to write it here :)