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ok, i did this integral and it's not letting me put all of my work in here because it's too many characters but here's the integral and then my answer. If someone could see if they get the same thing, that would be great....

int (2x^2 + 5)/((x^2 + 1)(x^2 + 4))

answer i got: (1/(x^2 + 1)) + (1/(x^2 + 4))

2007-06-23 11:14:34 · 2 answers · asked by Anonymous in Science & Mathematics Mathematics

2 answers

int (2x^2 + 5)/((x^2 + 1)(x^2 + 4))
first separate this using partial fractions

(2x^2 + 5)/((x^2 + 1)(x^2 + 4)) = A/(x^2+1) + B/(x^2+4)
A(x^2+4) + B(x^2+1) = 2x^2 + 5
Ax^2 + Bx^2 + 4A + B = 2x^2 + 5
A+B=2, and 4A+B = 5, so A=B=1

int(1/(x^2 + 1)) + 1/(x^2 + 4))
so you did the partial fractions correctly, now just integrate using int(1/(x^2+a^2)) = (1/a)arctan(x/a)

int(1/(x^2 + 1)) + int(1/(x^2 + 4))

arctan(x) + (1/2)arctan(x/2) + C

2007-06-23 12:17:51 · answer #1 · answered by hawkeye3772 4 · 0 0

If you add 1/(x² + 1) + 1/(x² + 4) you get (2x² + 5) / [(x² + 1)(x² + 4)], so the integral of the answer you got is the answer you want.

int 1/(x² + 1) = arctan x and
int 1/(x² + 4) = [arctan x/2] / 2,
so just add those.

2007-06-23 12:20:14 · answer #2 · answered by Philo 7 · 0 0

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