Just multiply my answer out to get the other. Is this what your book has?
The book has $\displaystyle \dfrac{2}{105b^3}(15b^2u^2 - 12abu +8a^2)(a + bu)^{3/2} + C$ which looks similar to your answer and is probably the same (after algebra verification).
It's interesting to note that such a simple looking integral leads to a monstrous result.