Question

How to integrate this: 1/[(x+1)(x+2)] dx
I tried integrate but With unsuccessful

Answer 1

partial fractions will do it

Answer 2

use Partial fractions.

Answer 3

Aah thanks! I don't know this in calculus

Answer 4

\[\frac{1}{(x+1)(x+2)}=\frac{a}{x+1}+\frac{b}{x+2}\]

Answer 5

What is a and b ?constants?

Answer 6

yes they are to be determined.
are you familiar with Partial fractions ?

Answer 7

No =P. . And I need to learn this very quickly to a exam

Answer 8

Please, someone could solve for me the integral? It would a great help!

Answer 9

continuing from where satellite left
Multiply both sides with (x+1)(x+2) you will get

1=a(x+2)+b(x+1)
put x=-1 in this you will get
1=a(-1+2)+b(0)
OR
a=1
now put x=-2 in 1=a(x+2)+b(x+1), you will get
1=a(0)+b(-2+1)
b=-1
so partial fractions are
\[\Large \frac{1}{(x+1)(x+2)}=\frac{1}{x+1}-\frac{1}{x+2}\]
integrate right hand side
\[\Large \int\limits_{}^{}\frac{1}{x+1}dx-\int\limits_{}^{}\frac{1}{x+2}dx\]

Answer 10

@Fellowroot Plz do not provide whole solution.