Optimal. Leaf size=13 \[ \frac {1}{8} (5+x+4 (8+\log (x))) \]
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Rubi [A]
time = 0.00, antiderivative size = 12, normalized size of antiderivative = 0.92, number of steps
used = 3, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 45}
\begin {gather*} \frac {x}{8}+\frac {\log (x)}{2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 45
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{8} \int \frac {4+x}{x} \, dx\\ &=\frac {1}{8} \int \left (1+\frac {4}{x}\right ) \, dx\\ &=\frac {x}{8}+\frac {\log (x)}{2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 10, normalized size = 0.77 \begin {gather*} \frac {1}{8} (x+4 \log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 9, normalized size = 0.69
method | result | size |
default | \(\frac {\ln \left (x \right )}{2}+\frac {x}{8}\) | \(9\) |
norman | \(\frac {\ln \left (x \right )}{2}+\frac {x}{8}\) | \(9\) |
risch | \(\frac {\ln \left (x \right )}{2}+\frac {x}{8}\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 8, normalized size = 0.62 \begin {gather*} \frac {1}{8} \, x + \frac {1}{2} \, \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 = 8, normalized size = 0.62 \begin {gather*} \frac {1}{8} \, x + \frac {1}{2} \, \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 = 7, normalized size = 0.54 \begin {gather*} \frac {x}{8} + \frac {\log {\left (x \right )}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{8} \, x + \frac {1}{2} \, \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 = 4.99, size = 8, normalized size = 0.62 \begin {gather*} \frac {x}{8}+\frac {\ln \left (x\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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