# How do you integrate int (x^2+2x-3)/x^4dx?

Jan 23, 2017

Separate into 3 integrals.
Perform the division on each integrand and express on each as a negative power.
Use the power rule to integrate each one.

#### Explanation:

Separate into 3 integrals:

$\int \frac{{x}^{2} + 2 x + 3}{x} ^ 4 \mathrm{dx} = \int {x}^{2} / {x}^{4} \mathrm{dx} + 2 \int \frac{x}{x} ^ 4 \mathrm{dx} + 3 \int \frac{1}{x} ^ 4 \mathrm{dx}$

Perform the division on each integrand and express on each as a negative power.

$\int \frac{{x}^{2} + 2 x + 3}{x} ^ 4 \mathrm{dx} = \int {x}^{-} 2 \mathrm{dx} + 2 \int {x}^{-} 3 \mathrm{dx} + 3 \int {x}^{-} 4 \mathrm{dx}$

Use the power rule to integrate each one.

$\int \frac{{x}^{2} + 2 x + 3}{x} ^ 4 \mathrm{dx} = - {x}^{-} 1 - {x}^{-} 2 - {x}^{-} 3 + C$