How do you integrate #int(6x^2+7x-6)/((x^2-4)(x+2))dx# using partial fractions?
2 Answers
Given:
Decompose the integrand into partial fractions:
Multiply both sides by
Find the value of A by letting
Find the value of B by letting
Find the value of C by letting
Here is the decomposition:
Therefore, we can write the following equation:
The integrals on the right are trival:
2 ln|x-2| +4 ln |x+2| + 1/(x+2) +C
Explanation:
First of all the denominator can be put in a different shape as
The numerator would thus become
On simplification this adds up to
Now comparing like terms with
The integral thus becomes
Or,
0r,
2 ln|x-2| +4 ln |x+2|+ 1/(x+2) +C Ans