Question

(x^2+3x-2)dx intergrate

Answer 1

The result follows from the power rule: for n ≠ -1, we have

$\displaystyle \int x^n\,\mathrm dx = \dfrac{x^{n+1}}{n+1}+C$

So

$\displaystyle \int (x^2+3x-2)\,\mathrm dx = \int x^2\,\mathrm dx + 3\int x\,\mathrm dx - 2\int\mathrm dx \\\\ = \boxed{\frac{x^3}3 + \frac{3x^2}2 - 2x + C}$