Optimal. Leaf size=17 \[ -2+\frac {5 x}{24}+\frac {5}{3} \log \left (\frac {x}{3}\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 0.71, number of steps used = 3, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 43} \begin {gather*} \frac {5 x}{24}+\frac {5 \log (x)}{3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 43
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{24} \int \frac {40+5 x}{x} \, dx\\ &=\frac {1}{24} \int \left (5+\frac {40}{x}\right ) \, dx\\ &=\frac {5 x}{24}+\frac {5 \log (x)}{3}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 0.59 \begin {gather*} \frac {5}{24} (x+8 \log (x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 8, normalized size = 0.47 \begin {gather*} \frac {5}{24} \, x + \frac {5}{3} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.34, size = 9, normalized size = 0.53 \begin {gather*} \frac {5}{24} \, x + \frac {5}{3} \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 9, normalized size = 0.53
method | result | size |
default | \(\frac {5 x}{24}+\frac {5 \ln \relax (x )}{3}\) | \(9\) |
norman | \(\frac {5 x}{24}+\frac {5 \ln \relax (x )}{3}\) | \(9\) |
risch | \(\frac {5 x}{24}+\frac {5 \ln \relax (x )}{3}\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 8, normalized size = 0.47 \begin {gather*} \frac {5}{24} \, x + \frac {5}{3} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 8, normalized size = 0.47 \begin {gather*} \frac {5\,x}{24}+\frac {5\,\ln \relax (x)}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 10, normalized size = 0.59 \begin {gather*} \frac {5 x}{24} + \frac {5 \log {\relax (x )}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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