Optimal. Leaf size=19 \[ x+3 \left (18 x+\frac {x^4}{4 \log (x)}\right ) \]
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Rubi [A]
time = 0.08, antiderivative size = 15, normalized size of antiderivative = 0.79, number of steps
used = 8, number of rules used = 5, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.185, Rules used = {12, 6874, 2343,
2346, 2209} \begin {gather*} \frac {3 x^4}{4 \log (x)}+55 x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2209
Rule 2343
Rule 2346
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {-3 x^3+12 x^3 \log (x)+220 \log ^2(x)}{\log ^2(x)} \, dx\\ &=\frac {1}{4} \int \left (220-\frac {3 x^3}{\log ^2(x)}+\frac {12 x^3}{\log (x)}\right ) \, dx\\ &=55 x-\frac {3}{4} \int \frac {x^3}{\log ^2(x)} \, dx+3 \int \frac {x^3}{\log (x)} \, dx\\ &=55 x+\frac {3 x^4}{4 \log (x)}-3 \int \frac {x^3}{\log (x)} \, dx+3 \text {Subst}\left (\int \frac {e^{4 x}}{x} \, dx,x,\log (x)\right )\\ &=55 x+3 \text {Ei}(4 \log (x))+\frac {3 x^4}{4 \log (x)}-3 \text {Subst}\left (\int \frac {e^{4 x}}{x} \, dx,x,\log (x)\right )\\ &=55 x+\frac {3 x^4}{4 \log (x)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 15, normalized size = 0.79 \begin {gather*} 55 x+\frac {3 x^4}{4 \log (x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 14, normalized size = 0.74
method | result | size |
default | \(55 x +\frac {3 x^{4}}{4 \ln \left (x \right )}\) | \(14\) |
risch | \(55 x +\frac {3 x^{4}}{4 \ln \left (x \right )}\) | \(14\) |
norman | \(\frac {\frac {3 x^{4}}{4}+55 x \ln \left (x \right )}{\ln \left (x \right )}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.29, size = 19, normalized size = 1.00 \begin {gather*} 55 \, x + 3 \, {\rm Ei}\left (4 \, \log \left (x\right )\right ) - 3 \, \Gamma \left (-1, -4 \, \log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.32, size = 17, normalized size = 0.89 \begin {gather*} \frac {3 \, x^{4} + 220 \, x \log \left (x\right )}{4 \, \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 12, normalized size = 0.63 \begin {gather*} \frac {3 x^{4}}{4 \log {\left (x \right )}} + 55 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 13, normalized size = 0.68 \begin {gather*} \frac {3 \, x^{4}}{4 \, \log \left (x\right )} + 55 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.47, size = 13, normalized size = 0.68 \begin {gather*} 55\,x+\frac {3\,x^4}{4\,\ln \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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