Optimal. Leaf size=16 \[ 15 x^2 \log ^2\left (e^4+x+x^2\right ) \]
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Rubi [A] time = 0.24, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 10, integrand size = 62, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.161, Rules used = {6688, 12, 14, 800, 634, 618, 204, 628, 2525, 6687} \begin {gather*} 15 x^2 \log ^2\left (x^2+x+e^4\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 204
Rule 618
Rule 628
Rule 634
Rule 800
Rule 2525
Rule 6687
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int 30 x \log \left (e^4+x+x^2\right ) \left (\frac {x (1+2 x)}{e^4+x+x^2}+\log \left (e^4+x+x^2\right )\right ) \, dx\\ &=30 \int x \log \left (e^4+x+x^2\right ) \left (\frac {x (1+2 x)}{e^4+x+x^2}+\log \left (e^4+x+x^2\right )\right ) \, dx\\ &=15 x^2 \log ^2\left (e^4+x+x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.24, size = 16, normalized size = 1.00 \begin {gather*} 15 x^2 \log ^2\left (e^4+x+x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 15, normalized size = 0.94 \begin {gather*} 15 \, x^{2} \log \left (x^{2} + x + e^{4}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.65, size = 15, normalized size = 0.94 \begin {gather*} 15 \, x^{2} \log \left (x^{2} + x + e^{4}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.61, size = 16, normalized size = 1.00
method | result | size |
norman | \(15 \ln \left ({\mathrm e}^{4}+x^{2}+x \right )^{2} x^{2}\) | \(16\) |
risch | \(15 \ln \left ({\mathrm e}^{4}+x^{2}+x \right )^{2} x^{2}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.85, size = 15, normalized size = 0.94 \begin {gather*} 15 \, x^{2} \log \left (x^{2} + x + e^{4}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.19, size = 15, normalized size = 0.94 \begin {gather*} 15\,x^2\,{\ln \left (x^2+x+{\mathrm {e}}^4\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 15, normalized size = 0.94 \begin {gather*} 15 x^{2} \log {\left (x^{2} + x + e^{4} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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