Finding The Integral

1. Jul 20, 2009

Stratosphere

1. The problem statement, all variables and given/known data
$$\ y=\int x^{1/3} dx$$

2. Relevant equations
$$\ y=\int a x^{p/q} dx= a\frac{x^{(p/q)+1}}{(p/q)+1}+c$$

3. The attempt at a solution
I found the answer to it but I was wondering if you can also take the reciprocal of the exponent after adding the one to it and then multiply that by a, the theorem doesn't seem to imply that though. For all of the very low complex ones I'm doing it seems to work but I'm not sure about more advanced ones.

Last edited: Jul 20, 2009
2. Jul 20, 2009

HallsofIvy

Presumably you know that
$$\int x^r dx= \frac{1}{r+1}x^{r+1}+ c$$
for r any real number.

That's exactly what your "relevant equation" says!

3. Jul 21, 2009

g_edgar

$$\int x^{1/3}\,dx = \frac{x^{\frac{1}{3}+1}}{\frac{1}{3}+1} +C = \frac{x^{4/3}}{4/3} +C = \frac{3}{4}\,x^{4/3} +C$$

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