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:

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

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