Question

Another integration question

Answer 1

\[\int\limits \frac{ 2x-3 }{ (3x-1)(x+4)(x+5) } \]

Answer 2

partial fractions*

Answer 3

Shoot Jhan :)

Answer 4

\[2x-3 = A(x+4)(x+5)+B(3x-1)(x+5)+C(3x-1)(x+4)\]

Answer 5

btw, it'll be a bit messy :P

Answer 6

\[x=\frac{1}{3}\]\[2(\frac{1}{3})-3 = \frac{208}{9}A\]\[-\frac{7}{3}= \frac{208}{9}A\]\[A= \frac{\cancel{9}3}{208}\cdot (-\frac{7}{\cancel3})= -\frac{21}{208}\]

Answer 7

\[x=-4\]\[-13B = -11 \implies B=\frac{11}{13}\]

Answer 8

What did you do there?

Answer 9

\[x=-5\]\[16C= -13 \implies -\frac{13}{16}=C\]