anonymous
  • anonymous
How do I do the integral of sin^(-1)(x)dx?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\int\limits_{}^{}\sin^{-1}x dx\]
anonymous
  • anonymous
i am going to guess parts
anonymous
  • anonymous
matter of fact i am almost sure it is parts \[\int u dv =uv-\int vdu\] with \[u=\sin^{-1}(x), du =\frac{1}{\sqrt{1-x^2}}, dv=1dx, v =x\]

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anonymous
  • anonymous
same sort of trick as \[\int \ln(x)dx\]
anonymous
  • anonymous
you get \[x\sin^{-1}(x)-\int \frac{x}{\sqrt{1-x^2}}dx\] and the second integral is a relatively easy \(u\) sub with \(u=1-x^2, du=-2xdx\) etc
anonymous
  • anonymous
Oh I see where the parts are now, thank you.

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