Question

Find the partial fractions decomposition and an antiderivative.

Answer 1

Factor the bottom

Answer 2

So it becomes (x-2)(x+1)

Answer 3

Then set it equal to A/(x-2) + B/(x+1)

Answer 4

\[\frac{ 6x }{ (x-2)(x+1) }=\frac{ A }{ x-2}+\frac{ B }{ x+1 }\]

Answer 5

Cross multiplication results in 6x= A(x+1) + B(x-2)

Answer 6

Plug in 2 for x, and you get 12= 3A +0*B

Answer 7

A=4. plug in -1 for x and you get B=2

Answer 8

So the partial fraction decomposition is 4/(x-2) + 2(x+1)

Answer 9

ohh okay thanks!

Answer 10

@Snipa420 what would be the anti derivative for this one?