s (1/(2x^2+11x+12)) dx?

Question

where s is the intergal

Answer 1

The idea is to integrate simple fractions into Ln(DENOMINATOR OF SIMPLE FRACTION)

to make this expression into a group of simple fractions we need to start the break down process.

1. factor the denominator into
(x+4)(2x+3) to get ∫ 1/[(x+4)(2x+3)]

2. use partial fractions to get 2 added fractions that can be integrated separately.

∫ [A/(2x+3) + B/(x+4)]

3.solving for A & B we get

2Bx+3B+Ax+4A=1
x(2B+A)=0 since there is no x term in the numerator, so
2B=-A and 4A+3B=1 we get

A=2/5 B= -1/5

4. now integrate

(1/5)*Ln(2x+3) - (1/5)*Ln(x+4) + C

Answer 2

2x^2 + 11x+12 can be factorised to
(2x+3)(x+4)
and
1/((2x+3)*(x+4)) = A/(2x+3) + B/(x+4)
solve for A,B (i am lazy and can't be bothered)
now we can integrate
we get
(A/2)*ln(2x+3) + B*ln(x+4) + C

Answer 3

2/5ln(2x+3)-1/5ln(x+4)