Find the integral of:

Question

f(x)= (x^4 + 2 sqrt x )/x^2

I tried...

= x^2 + 2 sqrt x / x^2
= x^2 + 2 x^-1.5

=1/3 x^3 + ???

Answer 1

first term is fine.

f(x) = (x^4 + 2x^(1/2))/x^2
= x^2 + 2x^(-1.5)

integral of that is
(1/3)x^3 - (4/5)x^(-1/2) + constant , (remember, we have to raise the exponent by 1)
= (1/3)x^3 - 4/(5√x) + constant