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Step-by-step Solution

Integral of 1/((4-9x^2)^0.5)

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Answer

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

Step-by-step explanation

Problem to solve:

$\int\frac{1}{\sqrt{4-9x^2}}dx$
1

Primero factorizamos dentro del radical para reescribir los términos de una manera más cómoda

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

Sacando la constante del radical

$\int\frac{1}{3\sqrt{\frac{4}{9}-x^2}}dx$

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Answer

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

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