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Step-by-step Solution

Integral of $\frac{1}{\sqrt{36-9x^2}}$ with respect to x

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Answer

$\frac{1}{3}arcsin\left(\frac{1}{2}x\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{1}{\sqrt{36-9x^2}}dx$
1

First, factor the terms inside the radical for an easier handling

$\int\frac{1}{\sqrt{9\left(4-x^2\right)}}dx$
2

Taking the constant out of the radical

$\int\frac{1}{3\sqrt{4-x^2}}dx$

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Answer

$\frac{1}{3}arcsin\left(\frac{1}{2}x\right)+C_0$