Optimal. Leaf size=12 \[ -2+e+\frac {5 x}{3}-\log (x) \]
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Rubi [A]
time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.83, 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, 45}
\begin {gather*} \frac {5 x}{3}-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 45
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {-3+5 x}{x} \, dx\\ &=\frac {1}{3} \int \left (5-\frac {3}{x}\right ) \, dx\\ &=\frac {5 x}{3}-\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 10, normalized size = 0.83 \begin {gather*} \frac {5 x}{3}-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 9, normalized size = 0.75
method | result | size |
default | \(\frac {5 x}{3}-\ln \left (x \right )\) | \(9\) |
norman | \(\frac {5 x}{3}-\ln \left (x \right )\) | \(9\) |
risch | \(\frac {5 x}{3}-\ln \left (x \right )\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 8, normalized size = 0.67 \begin {gather*} \frac {5}{3} \, x - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 8, normalized size = 0.67 \begin {gather*} \frac {5}{3} \, 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 = 7, normalized size = 0.58 \begin {gather*} \frac {5 x}{3} - \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 = 9, normalized size = 0.75 \begin {gather*} \frac {5}{3} \, 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 = 0.02, size = 8, normalized size = 0.67 \begin {gather*} \frac {5\,x}{3}-\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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