Thread: [SOLVED] Integration by Parts

I've having trouble integrating this expression by parts:



The first expression is the one I want to solve by using the second equation.

I've tried solving it by parts but I can't seem to impliment the limits.

Just so you know, the answer is:

4[((llamda^3)/2*Pi)]^(1/4)

Hello,

Write

You can see that x is (with some constant) the derivative of

So let and

Ah cheers, that's nifty.

What do I do if it's x^3 in front of the integral instead of x^2?

[Edit: Nevermind just worked it out, seems obvious now ]

And here comes the next inevitable question.

What happens if it's x^4 in front of the exponential expression? Is there a similar easy trick?

Originally Posted by Gingerbread Man

And here comes the next inevitable question.

What happens if it's x^4 in front of the exponential expression? Is there a similar easy trick?

Yup, isolating a factor x to get and then integration by parts, successively



If you want another method... : you can recognize the Gamma function (http://en.wikipedia.org/wiki/Gamma_function), by letting .

Thankyou!