upper number is 1 lower number of the integral is 0 u^3(u^-1/2+u^-1/5)du

Do you want that integral evaluated?

I
ntegrate it term by term. There are only two terms. The integrand is
u^5/2 + u^14/15

The indefinite integral is
(2/7)*u^7/2 + (15/29)*u^29/15

Evaluate it at the lower and upper limits and take the difference. The value at the lower limit is zero.

It looks like the answer is (2/7) + (15/29)