Optimal. Leaf size=18 \[ x+x^3 \log \left (e^{\log ^2(x)} (28+\log (3))\right ) \]
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Rubi [A]
time = 0.04, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps
used = 5, number of rules used = 4, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {2341, 30, 2635,
12} \begin {gather*} x^3 \log \left ((28+\log (3)) e^{\log ^2(x)}\right )+x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rule 2341
Rule 2635
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+2 \int x^2 \log (x) \, dx+3 \int x^2 \log \left (e^{\log ^2(x)} (28+\log (3))\right ) \, dx\\ &=x-\frac {2 x^3}{9}+\frac {2}{3} x^3 \log (x)+x^3 \log \left (e^{\log ^2(x)} (28+\log (3))\right )-3 \int \frac {2}{3} x^2 \log (x) \, dx\\ &=x-\frac {2 x^3}{9}+\frac {2}{3} x^3 \log (x)+x^3 \log \left (e^{\log ^2(x)} (28+\log (3))\right )-2 \int x^2 \log (x) \, dx\\ &=x+x^3 \log \left (e^{\log ^2(x)} (28+\log (3))\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 18, normalized size = 1.00 \begin {gather*} x+x^3 \log \left (e^{\log ^2(x)} (28+\log (3))\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.26, size = 33, normalized size = 1.83
method | result | size |
risch | \(x^{3} \ln \left ({\mathrm e}^{\ln \left (x \right )^{2}}\right )+\ln \left (\ln \left (3\right )+28\right ) x^{3}+x\) | \(22\) |
default | \(x +x^{3} \ln \left (x \right )^{2}+\left (\ln \left (\left (\ln \left (3\right )+28\right ) {\mathrm e}^{\ln \left (x \right )^{2}}\right )-\ln \left (x \right )^{2}\right ) x^{3}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 40 vs.
\(2 (17) = 34\).
time = 0.29, size = 40, normalized size = 2.22 \begin {gather*} -\frac {2}{9} \, x^{3} {\left (3 \, \log \left (x\right ) - 1\right )} + x^{3} \log \left ({\left (\log \left (3\right ) + 28\right )} e^{\left (\log \left (x\right )^{2}\right )}\right ) + \frac {2}{3} \, x^{3} \log \left (x\right ) - \frac {2}{9} \, x^{3} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 19, normalized size = 1.06 \begin {gather*} x^{3} \log \left (x\right )^{2} + x^{3} \log \left (\log \left (3\right ) + 28\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 19, normalized size = 1.06 \begin {gather*} x^{3} \log {\left (x \right )}^{2} + x^{3} \log {\left (\log {\left (3 \right )} + 28 \right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 19, normalized size = 1.06 \begin {gather*} x^{3} \log \left (x\right )^{2} + x^{3} \log \left (\log \left (3\right ) + 28\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.29, size = 21, normalized size = 1.17 \begin {gather*} x+x^3\,\ln \left ({\mathrm {e}}^{{\ln \left (x\right )}^2}\right )+x^3\,\ln \left (\ln \left (3\right )+28\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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