evaluate the integral or state that it diverges:

integral from 0 to 1 of ((x+1)/sqrt((x^2)+2x))dx

Printable View

- May 20th 2010, 06:16 PMsmartartbugImproper Integrals 2
evaluate the integral or state that it diverges:

integral from 0 to 1 of ((x+1)/sqrt((x^2)+2x))dx - May 20th 2010, 06:34 PMlilaziz1
Partial fractions should do the job:

$\displaystyle \int_0^1 \frac{x+1}{x^2+2x}dx = \int_0^1 \frac{x+1}{x(x+2)}dx = \int_0^1 \left[\frac{A}{x} + \frac{B}{x+2}\right]dx $

$\displaystyle A(x+2) + Bx = x+1 $

set x = -2 to get B; set x = 0 to get A. - May 20th 2010, 08:04 PMKrizalid
the problem has been misread, the integrand is actually $\displaystyle \frac{x+1}{\sqrt{x^2+2x}}.$

- May 20th 2010, 08:28 PMDrDank
- May 20th 2010, 08:59 PMKrizalid
just to mention that the integral converges by limit comparison test with $\displaystyle \int_0^1\frac{dx}{\sqrt x}.$