as presented by William Dunham in his book

*Euler, The Master of Us All*. First post here.

The first step is to recall a standard trigonometric substitution in calculus:

We're interested in the integral:

Substituting with x we see that:

And the integral is

Now Euler makes a complex change of variable:

The last step is another standard result from calculus which I will assume for the time being (more here).

Undo the substitution:

We will use two identities involving i:

(For the second one, see the previous post). Now:

Just eponentiate:

Wow, again!

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