SOLUTION: Give the integral of (2x)/(x^2+x-12) with respect to x.
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Question 1182692: Give the integral of (2x)/(x^2+x-12) with respect to x.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13209) (Show Source): You can put this solution on YOUR website!
Use partial fraction decomposition.
Multiply through by the least common denominator:
Equate the coefficients of the linear and constant terms on the two sides of the equation to get two equation to solve for A and B.
A+B=2
4B-3A=0
3B+3A=6
7B=6
B=6/7
A=8/7
Rewrite the expression as the sum of two fractions with denominators that are linear polynomials:
Integrate using integral(1/(x-a))= log(x-a) plus a constant.
Answer by ikleyn(52879) (Show Source): You can put this solution on YOUR website!
.
Many people, when are asked about the integral of , mistakenly answer ln(x) + Const.
This answer is INCORRECT.
The CORRECT answer is ln(|x|) + Const.
And it works for BOTH positive and negative values of x (for all real values of x except of 0 (zero) ).
Correspondingly, the integral of is ln(|x-a|) + Const1 (at x =/= a);
the integral of is ln(x+b|) + Const2 (at x =/= -b).
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