# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int_3^{\infty}\left(\frac{1}{\left(x-2\right)^{\left(\frac{3}{2}\right)}}\right)dx$

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

$\lim_{c\to\infty }\:\int_{3}^{c}\frac{1}{\sqrt{\left(x-2\right)^{3}}}dx$

Learn how to solve definite integrals problems step by step online. Integrate 1/((x-2)^(3/2)) from 3 to \infty. Replace the integral's limit by a finite value. Apply the formula: \int\frac{n}{\left(x+a\right)^c}dx=\frac{-n}{\left(c-1\right)\left(x+a\right)^{\left(c-1\right)}}, where a=-2, c=\frac{3}{2} and n=1. Divide -1 by \frac{1}{2}. Evaluate the definite integral.

$2$

### Problem Analysis

$\int_3^{\infty}\left(\frac{1}{\left(x-2\right)^{\left(\frac{3}{2}\right)}}\right)dx$

### Main topic:

Definite integrals

~ 0.08 seconds