## How to solve this integral? int (x^2 + 2x - 3) / (x + 1) dx

Limits, differentiation, related rates, integration, trig integrals, etc.

### How to solve this integral? int (x^2 + 2x - 3) / (x + 1) dx

Please, help me solve this intergral:

Int (x^2 + 2x - 3) / (x + 1) dx,

when x > -1

Thank you.
mitnord

Posts: 13
Joined: Mon Feb 23, 2009 11:17 pm

mitnord wrote:Int (x^2 + 2x - 3) / (x + 1) dx, when x > -1

By doing the long division, the integrand becomes:

. . . . .$x\, +\, 1\, +\, \frac{-4}{x\, +\, 1}$

The polynomial part is simple enough to integrate.

For the rational part, a simple substitution should work:

. . . . .$u\, =\, x\, +\, 1\mbox{, so }\, du\, =\, dx$

Then integrate (-4)(1/u), and back-substitute.

stapel_eliz

Posts: 1714
Joined: Mon Dec 08, 2008 4:22 pm