Evaluating an indefinite integral

[Wm_Davies]

Homework Statement

Evaluate the indefinite integral.

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

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...

 

[bitrex]

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

 

[Mark44]

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

 

[Wm_Davies]

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

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

 

[Mark44]

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