Verify the formulas in Exercises 71–82 by

Chapter 4, Problem 82E

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Verify the formulas in Exercises $71–82$ by differentiation.

$\int\left(\sin ^{-1} x\right)^{2} d x=x\left(\sin ^{-1} x\right)^{2}-2 x+2 \sqrt{1-x^{2}} \sin ^{-1} x+C$

Equation Transcription:

71–82

$\int\limits_{\ }^{\ }(si{n}^{-1}x{)}^{2}dx=x\ (si{n}^{-1}x{)}^{2}\ -2x\ +2\ \sqrt{1-{x}^{2}}\ si{n}^{-1}\ x\ +\ C$

Text Transcription:

71–82

the integral of (sin ^-1x)^2 dx = x (sin^-1x)^2 -2x + 2 square root of 1-x^2 sin ^-1 x+ C

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