# Evaluate the following integral. \int \frac{x}{\sqrt{x-4}}dx

cistG 2021-02-14 Answered
Evaluate the following integral.
$\int \frac{x}{\sqrt{x-4}}dx$
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## Expert Answer

Nathalie Redfern
Answered 2021-02-15 Author has 99 answers
Step 1
Consider the integrals,
$\int \frac{x}{\sqrt{x-4}}dx$
Suppose that,
$\sqrt{x-4}=t$
Differentiating with respect to "x"
$\frac{1}{2\sqrt{x-4}}dx=dt$
$\frac{1}{\sqrt{x-4}}dx=2dt$
Step 2
Substitute all value in given integrals,

$=2\int \left({t}^{2}+4\right)dt$
$=2\left[\frac{{t}^{3}}{3}+4t\right]+C$
$=\frac{2{t}^{3}}{3}+8t+C$
$=\frac{2}{3}{\left(x-4\right)}^{\frac{3}{2}}+8\sqrt{\left(x-4\right)}+C$
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