This is as step by step as I can make it.

The original integral is

It's always a good idea to try to get the denominator to be as simple as possible. (Though there are exceptions to that.) So this gives the idea of the substitution

To sub this back into the integral we need to know what v is. So solving for v in terms of u we get:

But we are not done. We also need to find an expression for dv in terms of u also. So

Solving this for dv gives

Now we need to sub in our values for v and dv into the original integral:

Factoring out the constants gives

And subbing back in gives

-Dan