integral (x^2+3x)/sqrt(x))dx?

Question

how to solve integral (x^2+3x)/sqrt(x))dx, plz?

Answer 1

Integrate the expression (x² + 3x)/√x with respect to x.

First simplify the expression.

(x² + 3x)/√x = x^(3/2) + 3√x

Now we can integrate.

∫[(x² + 3x)/√x]dx

= ∫[x^(3/2) + 3√x]dx

= (2/5)x^(5/2) + 3(2/3)x^(3/2) + C

= (2/5)x^(5/2) + 2x^(3/2) + C