I need to find the Integral of Sqrt(x^2+2x)dx. It is a Integration by Partial Fractions exercise.

I don't even know where to start. Any help on where to start would be greatly appreciated.

Printable View

- February 5th 2009, 06:01 PMdjo201Urgent Integration Help
I need to find the Integral of Sqrt(x^2+2x)dx. It is a Integration by Partial Fractions exercise.

I don't even know where to start. Any help on where to start would be greatly appreciated. - February 5th 2009, 06:06 PMKrizalid
I don't see the way of applying partial fractions here. Do we have a typo?

- February 5th 2009, 06:08 PMdjo201
- February 5th 2009, 06:11 PMmr fantastic
- February 5th 2009, 06:12 PMKrizalid
Then integrate by parts or use a trig. substitution.

- February 5th 2009, 06:16 PMdjo201
Not a typo there neither. It's the integral of the square root of (x^2 + 2x) dx

Krizalid: If it isn't necessary I don't have to use trigonometric expressions. If it's the only way, please explain a bit further.

EDIT: If this helps, the solution given by the book is:

(1/2)[(x+1)Sqrt(x^2+2x)-ln|x+1+Sqrt(x^2+2x)|]+c - February 5th 2009, 06:32 PMdjo201
Sorry for Double Post.

I got confused. It's not from the Partial Fractions Section. It's a Trig. Substitution exercise. - February 5th 2009, 07:09 PMKrizalid
I know something was wrong.

Well then, to perform a trig. substitution, we have so you need to put

(I closed your duplicate thread on calculus section, there's no reason to make an identical one.) - February 5th 2009, 07:12 PMdjo201
- February 5th 2009, 07:15 PMKrizalid
Yes, the first one is doable by parts and the second one requires some clever solution:

Note that by differentiating the denominator you get the numerator. - February 5th 2009, 07:23 PMdjo201
- February 5th 2009, 07:27 PMKrizalid

Strongly recommended lecture: make your partial integration faster. (See my signature.)

---

Or if you want to use the classic way, put and - February 5th 2009, 07:45 PMdjo201
- February 5th 2009, 07:48 PMKrizalid
No, I'm not gonna kill ya 'cause you're doing a good work. Now observe that,

Is this familiar few posts ago? - February 5th 2009, 07:53 PMdjo201