The integral that I am trying to evaluate is \int\frac{7-x}{x^3-x^2-x-2}dx

caldaridvq

caldaridvq

Answered question

2022-04-22

The integral that I am trying to evaluate is
7xx3x2x2dx

Answer & Explanation

Deandre Barron

Deandre Barron

Beginner2022-04-23Added 17 answers

However, I'll assume this is for a calculus course you are taking. Then, I believe there there is a typo and that the denominator should be x32x2x+2 (the last sign should be + instead of -). This polynomial factors very nicely as (x2)(x1)(x+1) Then in this case partial fractions yields
7xx32xx+2=3x1+43(x+1)+53(x2)
so that
7xx32xx+2dx=3ln|x1|+43ln|x+1|+53ln|x2|+C
Hope that helps,

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