Question

integrate 4x-7/x^2-x-6 dx

Answer 1

\[\int\limits_{}^{}4x-7/x ^{2}-x-6 dx\]

Answer 2

\frac{n}{d} if your doing the latex coding

Answer 3

(x-3)(x+2) on the denom, then partial it

Answer 4

it should result in: A ln(x-3) + Bln(x+2)

where A and B are the numerators from the partials

Answer 5

then u set it = to the numerator

Answer 6

yep

Answer 7

ok, i'll try that. thank you!

Answer 8

the "cover up" technique might be simplest

Answer 9

\[\frac{4x-7}{(x-3)(x+2)}=\frac{A}{x-3}+\frac{B}{x+2}\]
\[when\ x=3:\ \frac{4.3-7}{\cancel{(3-3)}(3+2)}=\frac{A=8/5}{x-3}+\frac{B}{x+2}\]

\[when\ x=-2:\ \frac{4.-2-7}{(-2-3)\cancel{(-2+2)}}=\frac{8/5}{x-3}+\frac{B=-15/-5}{x+2}\]

Answer 10

12-7=5 ; not 8 :)

Answer 11

ok. so far i got B=3

Answer 12

yep

Answer 13

and A=1

Answer 14

A=5/5 = 1 is what i get when i learn to multiply

Answer 15

ok. i got A=1 too

Answer 16

i got ln(x-3)+3ln(x+2)

Answer 17

i had a quick question. how do you know when to use partial fraction decomposition?

Answer 18

if the top is not the derivative of the bottom, we look to arctan or partials

Answer 19

oh ok. Thank you :)