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.