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# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int_3^4\left(\frac{1}{\left(x+1\right)\left(x-3\right)}\right)dx$
1

Rewrite the fraction $\frac{1}{\left(x+1\right)\left(x-3\right)}$ in $2$ simpler fractions using partial fraction decomposition

$\frac{1}{\left(x+1\right)\left(x-3\right)}=\frac{A}{x+1}+\frac{B}{x-3}$
2

Find the values of the unknown coefficients. The first step is to multiply both sides of the equation by $\left(x+1\right)\left(x-3\right)$

$1=\left(x+1\right)\left(x-3\right)\left(\frac{A}{x+1}+\frac{B}{x-3}\right)$

## Answer

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$\int_3^4\left(\frac{1}{\left(x+1\right)\left(x-3\right)}\right)dx$

### Main topic:

Integrals by partial fraction expansion

~ 1.41 seconds