Question

Evaluate $\int \dfrac{dx}{9x^2+4}$​

Answer 1

Step-by-step explanation:

We have,

$\rm \int \dfrac{dx}{9x^2+4}$

$\rm \int \dfrac{dx}{9(x^2+\frac{4}{9})}$

$\rm \dfrac{1}{9}\int \dfrac{dx}{x^2+\frac{4}{9}}$

using the formula we have,

$\rm = \dfrac{1}{9}· \dfrac{1}{(2/3)} \tan ^{-1} \dfrac{x}{(2/3)} +c$

$\rm = \dfrac{1}{9}· \dfrac{3}{2} \tan ^{-1} \dfrac{3x}{2} +c$

$\rm = \dfrac{1}{6}\tan ^{-1} \dfrac{3x}{2} +c$

Answer 2

Step-by-step explanation:

Answer:

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Step-by-step explanation:

hope it help you.

thanks