(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have to find the definite integral of: [itex]\int\left(\sqrt[3]{1-x^{7}}-\sqrt[7]{1-x^{3}}\right)dx[/itex] with bounds [0,1]

2. The attempt at a solution

I know that this can be done with hypergeometric functions, but I ca't use them because "we haven't seem them yet", so I have to do this with "everyday" integration tools. The only thing I was told was that I have to start with a substitution and the last part would be a cyclical integral, which tells me that I probably have to also use integration by parts in the middle.

I'm not asking for someone to give me the answer right away, I just need a starting point/mini-guide to help me get to the answer on my own, although I'm grateful with any kind of help (: Thanks!

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# Homework Help: Imposible Integral?

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