$\displaystyle \int(x^{2} + 2x - 1)^{3}2x dx$

$\displaystyle du = 2x + 2$

Now putting x to the 4th power, and 4 in the denominator.

$\displaystyle \int \frac{(x^{2} + 2x - 1)^{4}}{4} + C$ Not the Final Answer

However, that's the not the final answer. Some special manipulation needs to be done. That's because the du is larger than dx (of the original problem). It think some sort of division needs to be tried.

Let's try it this way:

$\displaystyle \frac{(x^{2} + 2x - 1)}{1/2} * \frac{ (2x + 2)}{2}$