Question

Help? Step-by-step?

integral from 0 to infinity of (1)/(x^2+7x+12)dx

Answer 1

x^2+7x+12 what can you write this as?

Answer 2

(x+4)(x+3)

Answer 3

now can you use integration by parts?

Answer 4

@yrelhan4 @monroe17
no need for integration by parts
can we write the term in numerator as (x+4) - (x+3)??????

Answer 5

yup.

Answer 6

^huh?

Answer 7

explain your method to her nik. its much easier. good job.

Answer 8

cool
integral of 1 /(x+4)(x+3) = integral of (x+4) - (x+3)/ (x+4)(x+3)
did u understand this step? @monroe17

Answer 9

is the numerator minus(x+3) because it was originally in the denominator and your moving it to the numerator? and the denominator stays the same?

Answer 10

no that's not right ;/

Answer 11

why is it not right?

Answer 12

because if that was so, wouldn't all of the numerator be negative? not just -(x+3)?

Answer 13

omg it is { (x+4) - (x+3) }/ (x+4)(x+3)

Answer 14

? I'm confused as to why.

Answer 15

in order to make integration simpler , it is one of the techniques
because the second step is as follow
integral of x+4/(x+4)(x+3) - x+3/(x+4)(x+3)
then u can cut the like terms and see integration become very simple

Answer 16

@monroe17 can u write 1 = 4 - 3 ?