# Integration by Partial Fractions

## Homework Statement

∫ 4x/(x^3+x^2+x+1) dx

## The Attempt at a Solution

I really dont know where to start, you cant complete the square, the degree of the numerator is less than the denominator so you cant use long division to simplify it.

I cant really simplify the denominator as well, so im stuck.

Help is greatly appreciated.!

Edit: I dont need you to work out the whole problem, i just need help getting started.

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If you will look hard at the denominator you will see that it is a geometric sum. You can replace that long expression with something simpler, which is the sum of the terms. Not sure what that would be? Look up geometric sum.

At that point maybe partial fractions will help.

Mark44
Mentor

## Homework Statement

∫ 4x/(x^3+x^2+x+1) dx

## The Attempt at a Solution

I really dont know where to start, you cant complete the square, the degree of the numerator is less than the denominator so you cant use long division to simplify it.

I cant really simplify the denominator as well, so im stuck.

Help is greatly appreciated.!

Edit: I dont need you to work out the whole problem, i just need help getting started.

Try factoring the denominator. The rational root theorem says that there are only two possibilities for rational roots - and one of them does work.

• 1 person
Solved. Thank you Mark