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Q.∫xa3−x3+x3/2 dx\int \dfrac{\sqrt{x}}{\sqrt{a^3 - x^3} + \sqrt{x^{3/2}}} \, dx equals

a
23sin⁡−1(x3/2a3/2)+C\dfrac{2}{3} \sin^{-1} \left( \dfrac{x^{3/2}}{a^{3/2}} \right) + C
b
13sin⁡−1(x3/2a3/2)+C\dfrac{1}{3} \sin^{-1} \left( \dfrac{x^{3/2}}{a^{3/2}} \right) + C
c
sin⁡−1(xa)+C\sin^{-1} \left( \dfrac{x}{a} \right) + C
d
23tan⁡−1(x3/2a3/2)+C\dfrac{2}{3} \tan^{-1} \left( \dfrac{x^{3/2}}{a^{3/2}} \right) + C

Correct Answer: Option A

The correct solution involves applying the fundamental concept to derive the final value step by step...

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