# Homework Help: Evaluating an indefinite integral

1. Nov 13, 2009

### Wm_Davies

1. The problem statement, all variables and given/known data
Evaluate the indefinite integral.

$$\int \left({\sqrt[5]{x^5}}-\frac{6}{5 x}+\frac{1}{4 x^{7}} \right) dx$$

3. The attempt at a solution

O.k. the only anti-derivative I am having trouble getting is the first one $${\sqrt[5]{x^5}}$$.

I am not sure what formula I would use or how to do it. I looked through the book, but I didn't see anything addressing this. Any help would be appreciated.

I imagine that it would be easier to write it as $$(x^{5})^{\frac{1}{5}}$$

Working through it I get $$(\frac{x^{6}}{6})^{\frac{1}{5}}$$

then I am stuck...

2. Nov 13, 2009

### bitrex

Remember that when you raise a power to a power, that by the Law of Exponents the powers multiply.

3. Nov 13, 2009

### Staff: Mentor

Simplify first!!
$$\sqrt[5]{x^5}~=~x$$

4. Nov 13, 2009

### Wm_Davies

Yeah, I can't believe I missed that. So then the anti-derivative should be $$\frac{x^{2}}{2}$$ + a constant?

5. Nov 13, 2009

### Staff: Mentor

Yes, but you won't need a constant for each term in the integrand - just one for all three.