How do you integrate $4 /((x + 2)(x + 3))$ ?

Question

1824 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-20T06:52:57

The answer is $=4(ln(|x+2|)-ln(|x+3|))+C$

Perform the decomposition into partial fractions

$(4)/((x+2)(x+3))=A/(x+2)+B/(x+3)=(A(x+3)+B(x+2))/((x+2)(x+3))$

The denominators are the same, compare the numerators

$4=A(x+3)+B(x+2)$

Let $x=-2$ , $=>$ , $4=A$

Let $x=-3$ , $=>$ , $4=-B$

Therefore,

$(4)/((x+2)(x+3))=4/(x+2)+(-4)/(x+3)$

$int(4dx)/((x+2)(x+3))=int(4dx)/(x+2)+int(-4dx)/(x+3)$

$=4ln(|x+2|)-4ln(|x+3|)+C$

How do you integrate 4 /((x + 2)(x + 3))4 /((x + 2)(x + 3))?