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

1 Answer
Douglas K.
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(x^2+2x+3)/x^4dx = intx^2/x^4dx + 2intx/x^4dx + 3int1/x^4dx#

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

#int(x^2+2x+3)/x^4dx = intx^-2dx + 2intx^-3dx + 3intx^-4dx#

Use the power rule to integrate each one.

#int(x^2+2x+3)/x^4dx = -x^-1 - x^-2 - x^-3 + C#

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