Now, looking at the other integral from Oct 13th...

In my opinion, this was scarier than the first, but looking at it again, what makes it scary is the various powers. e to the power of x to the power of 2 and such.

But why should this be scary? There's practically only one tool that one could use to solve this: the only tool that includes functions of functions, integration by substitution:

In our case, the inner function:

so:

and the outer function:

Plugging all these into our "integration by substitution" tool gives:

But this is slightly different to the original integral due to that minus sign. Of course this is trivial to deal with as:

Great! So now we have the structure we require to apply integration by substitution! We can substitute all of that with , and all the scary bits go away. So:

Then substituting (=) back in: