# integration of reciprocal function

• May 2nd 2009, 08:16 PM
slaypullingcat
integration of reciprocal function
Given that we may write x/(x+4)^2 as (x+4)-4/(x+4)^2, find the integral (limits 1 and 0) of x/(x+4)^2 dx.

Thank you
• May 2nd 2009, 09:20 PM
Reckoner
Quote:

Originally Posted by slaypullingcat
Given that we may write x/(x+4)^2 as (x+4)-4/(x+4)^2, find the integral (limits 1 and 0) of x/(x+4)^2 dx.

Thank you

$\int_0^1\frac x{(x+4)^2}\,dx=\int_0^1\frac{x+4-4}{(x+4)^2}\,dx$

$=\int_0^1\frac{dx}{x+4}-4\int_0^1\frac{dx}{(x+4)^2}$

Use the log rule for the first integral, and the power rule for the second.