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

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

[Out]

ln(x)

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Rubi [A]  time = 0.00, antiderivative size = 2, normalized size of antiderivative = 1.00, 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*}

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Mathematica [A]  time = 0.00, size = 2, normalized size = 1.00 \[ \log (x) \]

Antiderivative was successfully verified.

[In]

Integrate[x^(-1),x]

[Out]

Log[x]

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fricas [A]  time = 0.40, size = 2, normalized size = 1.00 \[ \log \relax (x) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x,x, algorithm="fricas")

[Out]

log(x)

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giac [A]  time = 1.12, size = 3, normalized size = 1.50 \[ \log \left ({\left | x \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x,x, algorithm="giac")

[Out]

log(abs(x))

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maple [A]  time = 0.00, size = 3, normalized size = 1.50 \[ \ln \relax (x ) \]

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 = 0.42, size = 2, normalized size = 1.00 \[ \log \relax (x) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x,x, algorithm="maxima")

[Out]

log(x)

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mupad [B]  time = 0.01, size = 2, normalized size = 1.00 \[ \ln \relax (x) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x,x)

[Out]

log(x)

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sympy [A]  time = 0.06, size = 2, normalized size = 1.00 \[ \log {\relax (x )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x,x)

[Out]

log(x)

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