Optimal. Leaf size=7 \[ -1-x+\log (x) \]
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Rubi [A]
time = 0.00, antiderivative size = 6, normalized size of antiderivative = 0.86, number of steps
used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {45}
\begin {gather*} \log (x)-x \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+\frac {1}{x}\right ) \, dx\\ &=-x+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 6, normalized size = 0.86 \begin {gather*} -x+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.18, size = 7, normalized size = 1.00
method | result | size |
default | \(\ln \left (x \right )-x\) | \(7\) |
norman | \(\ln \left (x \right )-x\) | \(7\) |
risch | \(\ln \left (x \right )-x\) | \(7\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 6, normalized size = 0.86 \begin {gather*} -x + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 6, normalized size = 0.86 \begin {gather*} -x + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 3, normalized size = 0.43 \begin {gather*} - x + \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 7, normalized size = 1.00 \begin {gather*} -x + \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 6, normalized size = 0.86 \begin {gather*} \ln \left (x\right )-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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