How do you use partial fractions to find the integral #int (x+1)/(x^2+4x+3) dx#?

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Answer 1 · 2017-03-04T19:50:15

#int(x+1)/(x^2+4x+3)dx#

We can begin by factoring the denominator of the integrand:

#=>int(x+1)/((x+1)(x+3))dx#

Cancel like terms:

#=>intcancel((x+1))/(cancel((x+1))(x+3))dx#

#=>int1/(x+3)dx#

We can now use a simple substitution:

#u=x+3, du=dx#

#=>int 1/udu#

#=>ln(|u|)+C#

Substituting back in:

#=>ln(|x+3|)+C#