Can you please show me how to do this...
thanks.
This calls for integration by parts. In general, if you have an integral: , where both and are functions of , the integral can be rewritten as:
Usually, you want to pick a that is easy to differentiate and can usually differentiate down to 0. In this case, let's pick as . Differentiating, we get . When we let , we can integrate that to get . Having these, we can simply rewrite the original integral as:
Notice how the integral there cannot be easily integrated, so for that integral we need to do integration by parts a second time. Same rules apply; make your easy to differentiate. Let's pick as . Differentiating, we get . Picking as your , when we integrate we will get . We can therefore rewrite the previous expression as:
The final integral is simply , we just simply write:
. I'll leave it up to you to evaluate the integral from to .