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Integration with Inverse Trig Functions

AP Calculus AB· difficulty 2/5

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

  • A

    arcsin⁡x+C\arcsin x + C

  • B

    arctan⁡x+C\arctan x + C

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  • C

    ln⁡(1+x2)+C\ln(1 + x^2) + C

  • D

    x21+x2+C\dfrac{x^2}{1+x^2} + C

Explanation

arctan⁡′(x)=1/(1+x2)\arctan'(x) = 1/(1+x^2).

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