Asked by Alison
Consider the indefinite integral (6x^3+3x^2-19x-10)/(x^2-4)dx
Then the integrand decomposes in the form ax + b + (c/(x-2)) + (d/(x+2)
I found b and c to equal 3 and d to equal 2, but I'm having trouble finding A and finding the final integration by integrating term by term.
Then the integrand decomposes in the form ax + b + (c/(x-2)) + (d/(x+2)
I found b and c to equal 3 and d to equal 2, but I'm having trouble finding A and finding the final integration by integrating term by term.
Answers
Answered by
Reiny
I did a long algebraic division and got
(6x^3+3x^2-19x-10)/(x^2-4)
= 6x + 3 + (5x+2)/(x^2 - 4)
= 6x + 3 + 2/(x+2) + 3/(x-2)
the integral of that would simply be
3x^2 + 3x + 2ln(x+2) + 3ln(x-2) + a constant
(6x^3+3x^2-19x-10)/(x^2-4)
= 6x + 3 + (5x+2)/(x^2 - 4)
= 6x + 3 + 2/(x+2) + 3/(x-2)
the integral of that would simply be
3x^2 + 3x + 2ln(x+2) + 3ln(x-2) + a constant
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