MathAnalysisCalculusIntegrals

Integration by parts

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Consider the following integral

$\int x^2 \arcsin(x) \ dx$

What is $v \cdot du$ if we were to apply integrations by part by choosing $u= \arcsin(x)$ and $dv=x^2 \ dx$ ?

Select one option from the list

\frac{-2x}{\sqrt{1-x^2}}

\frac{1}{x \cdot \sqrt{1-x^2}}

\frac{x^2}{3 \cdot \sqrt{1-x^2}}

\frac{x^3}{3 \cdot \sqrt{1-x^2}}

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