# How do I evaluate int(13 x^2 + 12 x^-2)dx?

Jan 27, 2015

I would use the integral of a sum

$\int f \left(x\right) + g \left(x\right) \mathrm{dx} = \int f \left(x\right) \mathrm{dx} + \int g \left(x\right) \mathrm{dx}$

to divide the argument of the igral giving:

$\int 13 {x}^{2} \mathrm{dx} + \int 12 {x}^{-} 2 \mathrm{dx} =$

and integrating:

$\frac{13 {x}^{2 + 1}}{2 + 1} + \frac{12 {x}^{- 2 + 1}}{- 2 + 1} = \frac{13}{3} {x}^{3} - \frac{12}{x} + c$