Question:
Let
\[
\int \frac{x^{1/2}}{\sqrt{1 - x^3}} \, dx = \frac{3}{3} \, g(x) + C
\]
then
Let
\[
\int \frac{x^{1/2}}{\sqrt{1 - x^3}} \, dx = \frac{3}{3} \, g(x) + C
\]
then
Show Hint
The inverse sine function can appear when integrating functions involving square roots and cubes.
Updated On: Jan 14, 2026
- \( f(x) = \sqrt{x} \)
- \( f(x) = x^3 \)
- \( g(x) = \sin^{-1} x \)
- None of these
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The Correct Option is B
Solution and Explanation
The integral can be simplified and \( g(x) \) turns out to be the inverse sine function \( \sin^{-1} x \).
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