You're not going to believe the answer to this integral:

$\displaystyle \int u^2\sqrt{(a + bu)} du$ where a and b are constants

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- Jan 31st 2011, 10:29 AMwonderboy1953New more challenging and interesting calculus puzzle
You're not going to believe the answer to this integral:

$\displaystyle \int u^2\sqrt{(a + bu)} du$ where a and b are constants - Jan 31st 2011, 10:33 AMAckbeet
You can just do v = a + bu.

- Jan 31st 2011, 10:41 AMwonderboy1953
- Jan 31st 2011, 10:49 AMAckbeet
Um, sure. Here goes. I get:

__Spoiler__: - Jan 31st 2011, 10:53 AMwonderboy1953
- Jan 31st 2011, 11:02 AMAckbeet
This answer is entirely equivalent to the following:

__Spoiler__:

Just multiply my answer out to get the other. Is this what your book has? - Feb 1st 2011, 12:23 PMwonderboy1953
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.