Question

$\mathtt{\huge\star{\red{\underline{Question}}}}\huge\star$
$\huge \: Integrate$

✯$\huge\frac{1}{{\sqrt{9 - 25{x}^{2}}}}$​

Answer 1

Step-by-step explanation:

$\huge\int\frac{1}{{\sqrt{9 - 25{x}^{2}}}}dx$

=$\huge\int\frac{1}{{\sqrt{25 - (\frac{9}{25} - {x}^{2})}}}$

=$\huge\frac{1}{5}\int\frac{1}{{\sqrt{\frac{{3}{5}}^{2} - {x}^{2}dx$

=$\huge\frac{1}{5}$sin-¹ $\huge\frac{x}{3/5} + C$

= $\huge\frac{1}{5}sin{inv}{1}frac{5x}{3} + C$

$\huge\red{\boxed{\green{\mathbb{\overbrace{\underbrace{\fcolorbox{pink}{aqua}{\underline{\red{Hope it helps}}}}}}}}}$

Answer 2

$\huge\int\frac{1}{{\sqrt{9 - 25{x}^{2}}}}dx$

=$\huge\int\frac{1}{{\sqrt{25 - (\frac{9}{25} - {x}^{2})}}}$

=$\huge\frac{1}{5}\frac{1} {{\sqrt{\frac{{3}{5}}^{2}} - {x}^{2}}}} dx$

=$\huge\frac{1}{5}$

= $sin-¹ \huge\frac{x}{3/5} + C$

= $\huge\frac{1}{5}sin{inv}{1}frac{5x}{3} + C$

$\huge\blue{\boxed{\blue{ \bold{\fcolorbox{red}{black}{\green{☺︎︎Hope\:It\:Helps☺︎︎}}}}}}$

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