Monday Math 77

Find .

Using , we see

Next, we try to eliminate the ex term in the numerator. By noting that , we do so as follows:
.
For the second integral, we make the u-substitution u=2x to get

and renaming the variable back to x, we get
.

Now, we showed here that . Thus, our integral is
.

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One Response to “Monday Math 77”

1. Monday Math 78 « Twisted One 151’s Weblog Says:

[…] parts, with and ; then and Now, using and , integration by parts tells us: . Now, we proved here that , so the above is just this for the case n=2, so since and (see here), then our integral is […]