Primitive of Arcsine Function
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Theorem
- $\ds \int \arcsin x \rd x = x \arcsin x + \sqrt {1 - x^2} + C$
Proof
From Primitive of $\arcsin \dfrac x a$:
- $\ds \int \arcsin \frac x a \rd x = x \arcsin \frac x a + \sqrt {a^2 - x^2} + C$
The result follows by setting $a = 1$.
$\blacksquare$
Also see
Sources
- 1976: K. Weltner and W.J. Weber: Mathematics for Engineers and Scientists ... (previous) ... (next): $6$. Integral Calculus: Appendix: Table of Fundamental Standard Integrals
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Appendix: Table $2$: Integrals
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Appendix: Table $2$: Integrals