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Single Variable Calculus

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Integration of Partial Fractions 4

SVCALC-YE4IRV

Evaluate the integral:

$$\int \frac{x^2+9x-10}{(x+4)(x-3)(x+1)^2} dx$$

A

$\cfrac{13}{20}\ln|x+4|+\cfrac{13}{24}\ln|x-3|-\cfrac{5}{28}\ln|x+1|+C$

B

$\cfrac{10}{21}\ln|x+4|+\cfrac{13}{56}\ln|x-3|-\cfrac{17}{24}\ln|x+1|-\cfrac{3}{2(x+1)}+C$

C

$\cfrac{11}{22}\ln|x+4|-\cfrac{10}{57}\ln|x-3|+\cfrac{17}{56}\ln|x+1|-\cfrac{2}{3(x+1)}+C$

D

$\cfrac{17}{24}\ln|x+4|-\cfrac{3}{2}\ln|x-3|-\cfrac{10}{24}\ln|x+1|-\cfrac{13}{2(x+1)}+C$