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Antiderivatives and Indefinite Integrals

AP Calculus AB· difficulty 1/5

∫(x−2+x) dx=\int (x^{-2} + x)\,dx =

  • A

    x−1+x2/2+Cx^{-1} + x^2/2 + C

  • B

    ln⁡∣x∣+x2/2+C\ln|x| + x^2/2 + C

  • C

    −x−1+x2/2+C-x^{-1} + x^2/2 + C

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  • D

    x3/3+x2/2+Cx^3/3 + x^2/2 + C

Explanation

∫x−2 dx=−x−1+C\int x^{-2}\,dx = -x^{-1} + C. ∫x dx=x2/2\int x\,dx = x^2/2.

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