Optimal. Leaf size=27 \[ x \left (6-x+\frac {4+x+\frac {\log (3)}{x}-\log (x)}{4 x}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 26, normalized size of antiderivative = 0.96, number of steps
used = 3, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {12, 14}
\begin {gather*} -x^2+\frac {25 x}{4}-\frac {\log (x)}{4}+\frac {\log (3)}{4 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {-x+25 x^2-8 x^3-\log (3)}{x^2} \, dx\\ &=\frac {1}{4} \int \left (25-\frac {1}{x}-8 x-\frac {\log (3)}{x^2}\right ) \, dx\\ &=\frac {25 x}{4}-x^2+\frac {\log (3)}{4 x}-\frac {\log (x)}{4}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 23, normalized size = 0.85 \begin {gather*} \frac {1}{4} \left (25 x-4 x^2+\frac {\log (3)}{x}-\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 21, normalized size = 0.78
method | result | size |
default | \(\frac {25 x}{4}-x^{2}+\frac {\ln \left (3\right )}{4 x}-\frac {\ln \left (x \right )}{4}\) | \(21\) |
risch | \(\frac {25 x}{4}-x^{2}+\frac {\ln \left (3\right )}{4 x}-\frac {\ln \left (x \right )}{4}\) | \(21\) |
norman | \(\frac {\frac {25 x^{2}}{4}-x^{3}+\frac {\ln \left (3\right )}{4}}{x}-\frac {\ln \left (x \right )}{4}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 20, normalized size = 0.74 \begin {gather*} -x^{2} + \frac {25}{4} \, x + \frac {\log \left (3\right )}{4 \, x} - \frac {1}{4} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 24, normalized size = 0.89 \begin {gather*} -\frac {4 \, x^{3} - 25 \, x^{2} + x \log \left (x\right ) - \log \left (3\right )}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 19, normalized size = 0.70 \begin {gather*} - x^{2} + \frac {25 x}{4} - \frac {\log {\left (x \right )}}{4} + \frac {\log {\left (3 \right )}}{4 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 21, normalized size = 0.78 \begin {gather*} -x^{2} + \frac {25}{4} \, x + \frac {\log \left (3\right )}{4 \, x} - \frac {1}{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 = 1.12, size = 20, normalized size = 0.74 \begin {gather*} \frac {25\,x}{4}-\frac {\ln \left (x\right )}{4}+\frac {\ln \left (3\right )}{4\,x}-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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