Integrate the functions in Exercises: 1 9-25x^2 - Vidyadip

Question

Integrate the functions in Exercises:
$\frac{1}{\sqrt{9-25\text{x}^2}}$

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Answer

$\int\frac{1}{\sqrt{9-25\text{x}^2}}\text{ dx}=\int\frac{1}{\sqrt{(3)^2-(5\text{x})^2}}\text{ dx}$
$=\frac{\sin^{-1}\frac{5\text{x}}{3}}{5\rightarrow\text{Coeff. of x}}+\text{c}$$\ \ \ \ \ \ \ \bigg[\because\int\frac{1}{\sqrt{\text{a}^2-\text{x}^2}}\text{ dx}=\sin^{-1}\frac{\text{x}}{\text{a}}\bigg]$
$=\frac{1}{5}\sin^{-1}\bigg(\frac{5\text{x}}{3}\bigg)+\text{c}$

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