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Integral of 1/((36-9x^2)^0.5)

Videos

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

Step-by-step explanation

Problem

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

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

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

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

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

Main topic:

Integration by trigonometric substitution

~ 1.3 seconds