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Integration with Inverse Trig Functions

AP Calculus AB· difficulty 2/5

∫11−x2 dx=\displaystyle\int \dfrac{1}{\sqrt{1-x^2}}\,dx =

  • A

    ln⁡∣1−x2∣+C\ln|1-x^2| + C

  • B

    arcsin⁡x+C\arcsin x + C

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  • C

    arctan⁡x+C\arctan x + C

  • D

    arccos⁡x+C\arccos x + C

Explanation

arcsin⁡′(x)=1/1−x2\arcsin'(x) = 1/\sqrt{1 - x^2}.

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