Another Partial Integration Q's

• Sep 19th 2008, 04:56 AM
ah-bee
Another Partial Integration Q's
I got quite far with this one but i just cant seem to finish it off. Just can't see how i can finish it or maybe i did it incorrectly. Integrate: (4-x)/(x((x^2+2)^2)) I did partial fractions and ended up with ln |x| - (ln |x^2+2|)/2 + 1/(x^2+2) + integral of (1/(x^2+2)^2) just cant seem to do that last integral, ive got some lecture notes on how to deal with that sort of integral but i cant seem to do it.
• Sep 19th 2008, 05:24 AM
mr fantastic
Quote:

Originally Posted by ah-bee
I got quite far with this one but i just cant seem to finish it off. Just can't see how i can finish it or maybe i did it incorrectly. Integrate: (4-x)/(x((x^2+2)^2)) I did partial fractions and ended up with ln |x| - (ln |x^2+2|)/2 + 1/(x^2+2) + integral of (1/(x^2+2)^2) just cant seem to do that last integral, ive got some lecture notes on how to deal with that sort of integral but i cant seem to do it.

Many approaches are possible. One approach:

Note that $\displaystyle \frac{1}{(x^2 + 2)^2} = \frac{1}{4} \left( \frac{1}{x^2 + 2} - \frac{x^2 - 2}{(x^2 + 2)^2}\right)$.

The integral of the first term inside the brackets is a standard form. The integral of the second term is $\displaystyle \frac{-x}{x^2 + 2}$.
• Sep 19th 2008, 05:34 AM
ah-bee
do you get that good by practice or is it a natural gift? i can say that im getting very good through practice, like seeing what to do with different integrations but some situations i have never experienced before.
• Sep 19th 2008, 05:41 AM
mr fantastic
Quote:

Originally Posted by ah-bee
do you get that good by practice or is it a natural gift? i can say that im getting very good through practice, like seeing what to do with different integrations but some situations i have never experienced before.

Practice. Experience is essential for successfully solving integrals.