Previous page : The integral of (e^(-px)-e^(-qx))/x dx from 0 to infinity

Next page : The integral of ln(x+1)/(x^2+1) dx from 0 to 1

We can use the result from the previous to solve a classical integral

We may first, for symmetry reasons, rewrite it as

There are several ways to continue from this, but here will use the result from the previous section – and a bit of complex analysis. We will use one of the formulas from the page on some trig identities. We have that

Substituting this into our integral we get

But wait a minute, that’s just an integral of the form we solved in the previous section:

We thus have *p*= –*i* and *q*=*i*. This would give us

But since

we get

This would finally give us

One might wonder if one could actually do this, and if so, under what conditions – but the answer must wait until a future page.

Up a level : IntegralsPrevious page : The integral of (e^(-px)-e^(-qx))/x dx from 0 to infinity

Next page : The integral of ln(x+1)/(x^2+1) dx from 0 to 1Last modified: