Integrand size = 32, antiderivative size = 18 \[ \int \left (78+3 e^{x^3} x^2-108 \log (3)+54 \log ^2(3)-12 \log ^3(3)+\log ^4(3)\right ) \, dx=e^{x^3}+x \left (-3+(3-\log (3))^4\right ) \]
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Time = 0.01 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.67, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {2240} \[ \int \left (78+3 e^{x^3} x^2-108 \log (3)+54 \log ^2(3)-12 \log ^3(3)+\log ^4(3)\right ) \, dx=e^{x^3}+x \left (78+\log ^4(3)-12 \log ^3(3)+54 \log ^2(3)-108 \log (3)\right ) \]
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Rule 2240
Rubi steps \begin{align*} \text {integral}& = x \left (78-108 \log (3)+54 \log ^2(3)-12 \log ^3(3)+\log ^4(3)\right )+3 \int e^{x^3} x^2 \, dx \\ & = e^{x^3}+x \left (78-108 \log (3)+54 \log ^2(3)-12 \log ^3(3)+\log ^4(3)\right ) \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.89 \[ \int \left (78+3 e^{x^3} x^2-108 \log (3)+54 \log ^2(3)-12 \log ^3(3)+\log ^4(3)\right ) \, dx=e^{x^3}+78 x-108 x \log (3)+54 x \log ^2(3)-12 x \log ^3(3)+x \log ^4(3) \]
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Time = 0.04 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.67
method | result | size |
norman | \(\left (\ln \left (3\right )^{4}-12 \ln \left (3\right )^{3}+54 \ln \left (3\right )^{2}-108 \ln \left (3\right )+78\right ) x +{\mathrm e}^{x^{3}}\) | \(30\) |
parallelrisch | \(\left (\ln \left (3\right )^{4}-12 \ln \left (3\right )^{3}+54 \ln \left (3\right )^{2}-108 \ln \left (3\right )+78\right ) x +{\mathrm e}^{x^{3}}\) | \(30\) |
default | \(78 x +x \ln \left (3\right )^{4}+54 x \ln \left (3\right )^{2}-12 x \ln \left (3\right )^{3}+{\mathrm e}^{x^{3}}-108 x \ln \left (3\right )\) | \(34\) |
risch | \(78 x +x \ln \left (3\right )^{4}+54 x \ln \left (3\right )^{2}-12 x \ln \left (3\right )^{3}+{\mathrm e}^{x^{3}}-108 x \ln \left (3\right )\) | \(34\) |
parts | \(78 x +x \ln \left (3\right )^{4}+54 x \ln \left (3\right )^{2}-12 x \ln \left (3\right )^{3}+{\mathrm e}^{x^{3}}-108 x \ln \left (3\right )\) | \(34\) |
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Leaf count of result is larger than twice the leaf count of optimal. 33 vs. \(2 (15) = 30\).
Time = 0.25 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.83 \[ \int \left (78+3 e^{x^3} x^2-108 \log (3)+54 \log ^2(3)-12 \log ^3(3)+\log ^4(3)\right ) \, dx=x \log \left (3\right )^{4} - 12 \, x \log \left (3\right )^{3} + 54 \, x \log \left (3\right )^{2} - 108 \, x \log \left (3\right ) + 78 \, x + e^{\left (x^{3}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 31 vs. \(2 (14) = 28\).
Time = 0.04 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.72 \[ \int \left (78+3 e^{x^3} x^2-108 \log (3)+54 \log ^2(3)-12 \log ^3(3)+\log ^4(3)\right ) \, dx=x \left (- 108 \log {\left (3 \right )} - 12 \log {\left (3 \right )}^{3} + \log {\left (3 \right )}^{4} + 54 \log {\left (3 \right )}^{2} + 78\right ) + e^{x^{3}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 33 vs. \(2 (15) = 30\).
Time = 0.20 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.83 \[ \int \left (78+3 e^{x^3} x^2-108 \log (3)+54 \log ^2(3)-12 \log ^3(3)+\log ^4(3)\right ) \, dx=x \log \left (3\right )^{4} - 12 \, x \log \left (3\right )^{3} + 54 \, x \log \left (3\right )^{2} - 108 \, x \log \left (3\right ) + 78 \, x + e^{\left (x^{3}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 33 vs. \(2 (15) = 30\).
Time = 0.26 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.83 \[ \int \left (78+3 e^{x^3} x^2-108 \log (3)+54 \log ^2(3)-12 \log ^3(3)+\log ^4(3)\right ) \, dx=x \log \left (3\right )^{4} - 12 \, x \log \left (3\right )^{3} + 54 \, x \log \left (3\right )^{2} - 108 \, x \log \left (3\right ) + 78 \, x + e^{\left (x^{3}\right )} \]
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Time = 8.76 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.61 \[ \int \left (78+3 e^{x^3} x^2-108 \log (3)+54 \log ^2(3)-12 \log ^3(3)+\log ^4(3)\right ) \, dx={\mathrm {e}}^{x^3}+x\,\left (54\,{\ln \left (3\right )}^2-108\,\ln \left (3\right )-12\,{\ln \left (3\right )}^3+{\ln \left (3\right )}^4+78\right ) \]
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