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$\int \sqrt{\frac{x^{4}}{a^{6} - x^{6}}} d x is equal to$

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13sin−1x3a3+C

13sin−1x3a+C

13sin−1x3a6+C

−13sin−1x3a3+C

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detailed solution

Correct option is A

Let I=∫x4a6−x6dxI=∫x2a6−x32dx Put x3=tx2dx=13dtI=∫13dta32−t2=13sin−1⁡ta3+C=13sin−1⁡x3a3+C

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∫x4a6−x6dx is equal to

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$\int \sqrt{\frac{x^{4}}{a^{6} - x^{6}}} d x is equal to$