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calc 2 integrand problem?
Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and then evaluate the integral. Do not include the + C in your answer.
\displaystyle \int \displaystyle \frac{2x^3-2x+1}{x^2-3 x} dx.
1 Answer
- az_lenderLv 76 years agoFavorite Answer
First quotient term = 2;
partial product = 2x^2 - 6x;
remainder = 4x + 1.
So now the integrand is:
[2 + (4x+1)/(x^2 - 3x)] dx.
Now do the "partial fractions"--
(4x+1)/(x^2-3x) = A/x + B/(x-3).
4x + 1 = Ax - 3A + Bx.
Constant terms: 1 = -3A
Linear terms: 4 = A + B
Multiply last eqn by 3, obtaining:
12 = 3A + 3B.
Add the "constant term" eqn, obtaining:
13 = 3B.
Hence, B = 3/13 and A = 4 - B = 49/13.
