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Integration with Inverse Trig Functions

AP Calculus AB· difficulty 3/5

∫14+x2 dx=\displaystyle\int \dfrac{1}{4 + x^2}\,dx =

  • A

    14+x2+C\dfrac{1}{4 + x^2} + C

  • B

    12arctan⁡(x/2)+C\dfrac{1}{2}\arctan(x/2) + C

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  • C

    14arctan⁡x+C\dfrac{1}{4}\arctan x + C

  • D

    arctan⁡(x/2)+C\arctan(x/2) + C

Explanation

Pattern 1/(a2+x2)1/(a^2 + x^2): antiderivative (1/a)arctan⁡(x/a)(1/a)\arctan(x/a).

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