How do you find the antiderivative of ∫x2√1−x3dx?

1 Answer
mason m
Jan 14, 2017

−23√1−x3+C

Explanation:

Rewriting the function:

I=∫x2√1−x3dx=∫x2(1−x3)−12dx

To deal with the −1/2 power, let u=1−x3. This implies that du=−3x2.dx. Rewriting the integral:

I=−13∫(1−x3)−12(−3x2.dx)=−13∫u−12.du

Now use the rule ∫un.du=un+1n+1:

I=−13(u1212)=−23√u=−23√1−x3+C

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