# Thread: Integration Problem

1. ## Integration Problem

I'm having a lot of trouble with this question:

$\displaystyle \int \frac{1}{\sqrt{x^2-4x}} dx$

Can any math pros help me with it?

2. Originally Posted by dragonic2020
I'm having a lot of trouble with this question:

$\displaystyle \int \frac{1}{\sqrt{x^2-4x}} dx$

Can any math pros help me with it?
$\displaystyle = \int \frac{1}{\sqrt{(x - 2)^2 - 4}} \, dx = \frac{1}{2} \int \frac{1}{\sqrt{\frac{(x - 2)^2}{4} - 1}} \, dx$.

Now make either of the following substitutions:

1. $\displaystyle \cosh t = \frac{x - 2}{2}$ (the easy way), or

2. $\displaystyle \sec t = \frac{x - 2}{2}$ (the hard way).

There are other fancy ways that will probably work but the above is the usual approach.

3. Put $\displaystyle x=\frac{4}{1-{{z}^{2}}}$ and you'll get an easy integral.