Optimal. Leaf size=19 \[ 4 \left (-1+\frac {1-x}{x}+\log (4)-\log (x)\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.53, 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*} \frac {4}{x}-4 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {4}{x^2}-\frac {4}{x}\right ) \, dx\\ &=\frac {4}{x}-4 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 10, normalized size = 0.53 \begin {gather*} -4 \left (-\frac {1}{x}+\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 11, normalized size = 0.58
method | result | size |
default | \(\frac {4}{x}-4 \ln \left (x \right )\) | \(11\) |
norman | \(\frac {4}{x}-4 \ln \left (x \right )\) | \(11\) |
risch | \(\frac {4}{x}-4 \ln \left (x \right )\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 10, normalized size = 0.53 \begin {gather*} \frac {4}{x} - 4 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 11, normalized size = 0.58 \begin {gather*} -\frac {4 \, {\left (x \log \left (x\right ) - 1\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 7, normalized size = 0.37 \begin {gather*} - 4 \log {\left (x \right )} + \frac {4}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 11, normalized size = 0.58 \begin {gather*} \frac {4}{x} - 4 \, \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 = 0.02, size = 10, normalized size = 0.53 \begin {gather*} \frac {4}{x}-4\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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