How do you integrate f(x) = (x+6)/(x+1)?

1 Answer
Feb 19, 2015

we can rewrite the function into a form which is easily integrated

Think of the function like this

(x+6)/((1)(x+1))=A/1+B/(x+1)

We are doing a partial fraction decomposition.
Multiply the expression above by (1)(x+1)

x+6=A(x+1)+B(1)

x+6=Ax +A +B

Equating coefficients we get

A=1 and A+B=6

Since A=1 we can conclude that B=5

Therefore we can rewrite as follows

int(x+6)/(x+1)dx=int1+5/(x+1)dx

Integrating we get

x+5ln|x+1|+C