# Massively complex anti-derivative. Impossible?

1. Jan 18, 2009

### calisoca

1. The problem statement, all variables and given/known data

Find the anti-derivative of the following equation.

2. Relevant equations

$$\frac{df}{dx} = \frac{[\frac{(30x^2 + 10x + 3)(\sqrt[3]{\frac{(4x^3 + 2x^2)}{5x^2}})}{(5)\sqrt[5]{(\frac{(10x^4 + 5x^3 + 3x^2)}{6x})^4}}] \ - \ [\frac{(\frac{(60x^4 - 20x - 20x^2)}{25x^4})(\sqrt[5]{\frac{(10x^4 + 5x^3 + 3x^2)}{6x}})}{(3)(\sqrt[3]{(\frac{(4x^3 + 2x^2)}{5x^2})^2})}]}{(\sqrt[3]{(\frac{(4x^3 + 2x^2)}{5x^2})^2})}$$

3. The attempt at a solution

I have no idea where to even start on this! I can find simple anti-derivatives, but I'm not sure where our professor dug this one up from. He's not offering any help on it, nor any clues, either. No one in my class has any idea where to start on this, either. Most of them are just planning to skip the problem and hope it doesn't show up on the test. Any help would be greatly appreciated, as I'm sure he'll try to put something like this on the test.

Last edited: Jan 18, 2009
2. Jan 18, 2009

### Staff: Mentor

Without even looking I am almost sure it will nicely cancel out and simplify if rearranged. That's one of these tricks professors love to play

Note that some terms repeat here and there.

3. Jan 19, 2009

### calisoca

Yea, I'm starting to see it now. However, if you hadn't mentioned it, I probably never would have seen it! Ha! Anyway, thanks for the pointer. I'm working on it, and I'm slowly getting there. Thanks.