Chanel Hunter

2023-02-26

Integrate the function.$\int \frac{x{\mathrm{cos}}^{-1}x}{\sqrt{1-{x}^{2}}}dx$

Marin Valencia

Let $I=\int \frac{x{\mathrm{cos}}^{-1}x}{\sqrt{1-{x}^{2}}}dx⇒I=\int {\mathrm{cos}}^{-1}x\frac{x}{\sqrt{1-{x}^{2}}}dx$
Consider ${\mathrm{cos}}^{-1}x$ as first function and $\frac{x}{\sqrt{1-{x}^{2}}}$ as a second function and integration the components, we obtain

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