3.3 \(\int \frac{1}{x} \, dx\)

Optimal. Leaf size=2 \[ \log (x) \]

[Out]

Log[x]

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Rubi [A]  time = 0.0001821, antiderivative size = 2, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 3, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {29} \[ \log (x) \]

Antiderivative was successfully verified.

[In]

Int[x^(-1),x]

[Out]

Log[x]

Rule 29

Int[(x_)^(-1), x_Symbol] :> Simp[Log[x], x]

Rubi steps

\begin{align*} \int \frac{1}{x} \, dx &=\log (x)\\ \end{align*}

Mathematica [A]  time = 0.0000746, size = 2, normalized size = 1. \[ \log (x) \]

Antiderivative was successfully verified.

[In]

Integrate[x^(-1),x]

[Out]

Log[x]

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Maple [A]  time = 0., size = 3, normalized size = 1.5 \begin{align*} \ln \left ( x \right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x,x)

[Out]

ln(x)

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Maxima [A]  time = 0.922497, size = 3, normalized size = 1.5 \begin{align*} \log \left (x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x,x, algorithm="maxima")

[Out]

log(x)

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Fricas [A]  time = 1.7818, size = 11, normalized size = 5.5 \begin{align*} \log \left (x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x,x, algorithm="fricas")

[Out]

log(x)

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Sympy [A]  time = 0.04991, size = 2, normalized size = 1. \begin{align*} \log{\left (x \right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x,x)

[Out]

log(x)

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Giac [A]  time = 1.05146, size = 4, normalized size = 2. \begin{align*} \log \left ({\left | x \right |}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x,x, algorithm="giac")

[Out]

log(abs(x))