Tricky integral using substitution

**The Problem**

Use the substitution to find the integral of

**Attempt**

, so .

Therefore, this integral simplifies to .

Rearranging, we get x = , so this becomes x .

Expanding, this becomes .

As everything is now a power of , we can integrate as follows:

.

Multiplying out the fractions:

Multiplying out the brackets:

Cancelling:

And as , we get:

.

I've checked this using 'Show Steps' after inputting the integral into WolframAlpha, and it appears to be correct.

However, the answer given in both the textbook and WolframAlpha is:

.

I would like a hint as to how I would progress from my answer to the answer given.

OK, so what do I do next?

OK, so I took out the common factor to get:

, then I could take out the factor of to get: