Integration by PartsDate: 04/10/2008 at 11:55:52 From: Arpita Subject: integration I'm trying to integrate e^x(x+1)/(x+2)^2 and am stuck. I tried letting x+2 = t with 1 = dt/dx but didn't get anywhere. Can you help me? Date: 04/11/2008 at 08:56:22 From: Doctor Ali Subject: Re: integration Hi Arpita! Thanks for writing to Dr. Math. Here's how I'd approach it: - | x+1 x | --------- * e dx | (x+2)^2 - Write it this way in order to expand the denominator: - | x+2-1 x | --------- * e dx | (x+2)^2 - Break the fraction into two separate fractions: - - | e^x | e^x | ------- dx - | --------- dx | (x+2) | (x+2)^2 - - Let the first integral be as it is. Use integration by parts to integrate the second one. We assume that dv = dx/(x+2)^2 We do this way because we know the integral of dv. 1 v = - ----- x+2 Use the main formula of integration by parts: - - | udv = uv - | vdu - - Can you continue the process yourself? Please write back if you still have any difficulties. - Doctor Ali, The Math Forum http://mathforum.org/dr.math/ |
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