arcsin-x-2-dx-

Question Number 127110 by benjo_mathlover last updated on 26/Dec/20

\int {(\arcsin x)}^{2} d x = ?

Answered by liberty last updated on 27/Dec/20

l e t t i n g \arcsin x = ℓ \Rightarrow x = \sin ℓ \land d x = \cos ℓ d ℓ

I = \int ℓ^{2} \cos ℓ d ℓ = ℓ^{2} \sin ℓ + 2 ℓ \cos ℓ - 2 \sin ℓ + c

= x {(\arcsin x)}^{2} + 2 \sqrt{1 - x^{2}} \arcsin x - 2 x + c

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