how to solve this integration ???

[mw.arden]

hey guys, i wonder how to solve this problem ive been working on it a day now and couldn't work out how to solve it



, i made some progress by using t^6 instead of x :



and reached here when i found 1+t^4 has no real roots and that was when i started crying!!!

thanks for your helps in advance

 

[stapel]

\(\displaystyle \displaystyle{ \int \,} \dfrac{\sqrt{x\,}}{x\, +\, \sqrt[3]{x\,}}\, dx\)

Are you sure that this integrand is correct? Because the result, when you plug "Sqrt[x]/(x+x^(1/3))" into the Integrator, isn't pretty, and certainly isn't anything one would expect to be required to "find".

\(\displaystyle \displaystyle{ \int \,} \dfrac{t^2}{1\, +\, t^4}\, dt\)

and reached here when i found 1+t^4 has no real roots....

Um... Why would roots of the denominator be relevant...? What are you trying to accomplish? Thank you!