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Integration by Substitution

AP Calculus AB· difficulty 2/5

∫1xln⁡x dx=\displaystyle\int \dfrac{1}{x \ln x}\,dx =

  • A

    1(ln⁡x)2+C\dfrac{1}{(\ln x)^2} + C

  • B

    ln⁡(ln⁡∣x∣)+C\ln(\ln|x|) + C

  • C

    ln⁡(ln⁡x)+C\ln(\ln x) + C

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  • D

    ln⁡x⋅x+C\ln x \cdot x + C

Explanation

u=ln⁡xu = \ln x, du=dx/xdu = dx/x. ∫du/u=ln⁡∣u∣=ln⁡(ln⁡x)\int du/u = \ln|u| = \ln(\ln x) (assuming ln⁡x>0\ln x > 0).

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