How to find the Integral of tan(x)

This is another one of those integrals that has quite a counter intuitive result. And to do it, we have to use a little bit lateral thinking, because we're going to get a result that really doesn't resemble the original function.

To carry out this integral is actually not that hard but we do have to realize that...

So that implies we're going to be integrating the quotient of sin x / cos x. Note that sin x is very closely related to the derivative of cos x.

In fact, if we choose to write it like this...

What I have now is a derivative of the bottom function the denominator function, on the top and
that means I can just do a simple u-substitution here because this -sin x term is going to cancel out

So let...

Then...

And...

So...

Please watch the video for the full tutorial.