Solve by not using partial fractions.

I liked this particular integral, I solved it on another forum to show that sometimes we can avoid the annoying algebra when doing the partial fractions.

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- Jan 1st 2011, 08:34 PMKrizalidRational integral
Solve by not using partial fractions.

I liked this particular integral, I solved it on another forum to show that sometimes we can avoid the annoying algebra when doing the partial fractions. - Jan 1st 2011, 11:50 PMsimplependulum

Sub. on the third integral , we have

For the second integral , use integration by parts ,

Therefore ,

- Jan 2nd 2011, 06:05 AMTheCoffeeMachine
I observe that:

So we have:

Where for the last integral we use the substitution to get:

Letting in the remaining integral we have:

Thus

- Jan 2nd 2011, 08:50 AMKrizalid
good! pretty different solutions from the one i have:

consider (1); now from put and the integral becomes (2).

on the original integral put then

from (1) and (2) the latter equals

and the original integral equals

- Jan 3rd 2011, 08:23 AMJester
What about letting right away. The integral becomes

or

or

Integrating gives

Then backsubstitute noting that