# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

Learn how to solve definite integrals problems step by step online.

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

Learn how to solve definite integrals problems step by step online. Integrate 1/((x+1)(x-3)) from 3 to 4. Rewrite the fraction \frac{1}{\left(x+1\right)\left(x-3\right)} in 2 simpler fractions using partial fraction decomposition. 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). Multiplying polynomials. Simplifying.

The integral diverges.

### Problem Analysis

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

### Main topic:

Definite integrals

~ 1.66 seconds