Question:medium
\[
\int \left(27x^3(1-x^3)\right)^{\frac{2}{3}}\,dx
=
\]
\[
\int \left(27x^3(1-x^3)\right)^{\frac{2}{3}}\,dx
=
\]
Show Hint
Always simplify constant coefficients like \(27^{2/3}\) first. It makes the substitution steps much cleaner.
Updated On: Jun 25, 2026
- \(-\frac{3}{4}(1 - x^3)^{4/3} + C\)
- \(-\frac{3}{5}(1 - x^3)^{5/3} + C\)
- \(-\frac{9}{3}(1 - x^3)^{4/3} + C\)
- \(-\frac{9}{4}(1 - x^3)^{4/3} + C\)
- \(-\frac{9}{5}(1 - x^3)^{5/3} + C\)
Show Solution
The Correct Option is
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