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

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Answer 1 · 2015-02-19T20:19:15

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 #