arcsinx-2-dx-

Question Number 91996 by student work last updated on 04/May/20

\int {(arcsinx)}^{2} dx = ?

Commented by jagoll last updated on 04/May/20

let \sin^{- 1} (x) = t

x = \sin t \Rightarrow dx = \cos t dt

\int t^{2} \cos t dt =

t^{2} \sin t + 2 t \cos t - 2 \sin t + c

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

Commented by jagoll last updated on 04/May/20

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