Integrand size = 42, antiderivative size = 23 \[ \int \left (12+4 x-6 x^2+\left (24 x^2-16 x^3\right ) \log ^2(8)+\left (16 x^3-10 x^4\right ) \log ^4(8)\right ) \, dx=2+(4-2 x) \left (-4+x+\left (x+x^2 \log ^2(8)\right )^2\right ) \]
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Leaf count is larger than twice the leaf count of optimal. \(50\) vs. \(2(23)=46\).
Time = 0.01 (sec) , antiderivative size = 50, normalized size of antiderivative = 2.17, number of steps used = 3, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (12+4 x-6 x^2+\left (24 x^2-16 x^3\right ) \log ^2(8)+\left (16 x^3-10 x^4\right ) \log ^4(8)\right ) \, dx=-2 x^5 \log ^4(8)+4 x^4 \log ^4(8)-4 x^4 \log ^2(8)-2 x^3+8 x^3 \log ^2(8)+2 x^2+12 x \]
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Rubi steps \begin{align*} \text {integral}& = 12 x+2 x^2-2 x^3+\log ^2(8) \int \left (24 x^2-16 x^3\right ) \, dx+\log ^4(8) \int \left (16 x^3-10 x^4\right ) \, dx \\ & = 12 x+2 x^2-2 x^3+8 x^3 \log ^2(8)-4 x^4 \log ^2(8)+4 x^4 \log ^4(8)-2 x^5 \log ^4(8) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(50\) vs. \(2(23)=46\).
Time = 0.01 (sec) , antiderivative size = 50, normalized size of antiderivative = 2.17 \[ \int \left (12+4 x-6 x^2+\left (24 x^2-16 x^3\right ) \log ^2(8)+\left (16 x^3-10 x^4\right ) \log ^4(8)\right ) \, dx=12 x+2 x^2-2 x^3+8 x^3 \log ^2(8)-4 x^4 \log ^2(8)+4 x^4 \log ^4(8)-2 x^5 \log ^4(8) \]
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Time = 0.06 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.09
method | result | size |
gosper | \(-2 x \left (81 \ln \left (2\right )^{4} x^{4}-162 x^{3} \ln \left (2\right )^{4}+18 x^{3} \ln \left (2\right )^{2}-36 x^{2} \ln \left (2\right )^{2}+x^{2}-x -6\right )\) | \(48\) |
norman | \(\left (72 \ln \left (2\right )^{2}-2\right ) x^{3}+\left (324 \ln \left (2\right )^{4}-36 \ln \left (2\right )^{2}\right ) x^{4}+12 x +2 x^{2}-162 x^{5} \ln \left (2\right )^{4}\) | \(48\) |
default | \(-162 x^{5} \ln \left (2\right )^{4}+324 \ln \left (2\right )^{4} x^{4}-36 x^{4} \ln \left (2\right )^{2}+72 x^{3} \ln \left (2\right )^{2}-2 x^{3}+2 x^{2}+12 x\) | \(51\) |
risch | \(-162 x^{5} \ln \left (2\right )^{4}+324 \ln \left (2\right )^{4} x^{4}-36 x^{4} \ln \left (2\right )^{2}+72 x^{3} \ln \left (2\right )^{2}-2 x^{3}+2 x^{2}+12 x\) | \(51\) |
parallelrisch | \(-162 x^{5} \ln \left (2\right )^{4}+324 \ln \left (2\right )^{4} x^{4}-36 x^{4} \ln \left (2\right )^{2}+72 x^{3} \ln \left (2\right )^{2}-2 x^{3}+2 x^{2}+12 x\) | \(51\) |
parts | \(-162 x^{5} \ln \left (2\right )^{4}+324 \ln \left (2\right )^{4} x^{4}-36 x^{4} \ln \left (2\right )^{2}+72 x^{3} \ln \left (2\right )^{2}-2 x^{3}+2 x^{2}+12 x\) | \(51\) |
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Time = 0.23 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.91 \[ \int \left (12+4 x-6 x^2+\left (24 x^2-16 x^3\right ) \log ^2(8)+\left (16 x^3-10 x^4\right ) \log ^4(8)\right ) \, dx=-162 \, {\left (x^{5} - 2 \, x^{4}\right )} \log \left (2\right )^{4} - 2 \, x^{3} - 36 \, {\left (x^{4} - 2 \, x^{3}\right )} \log \left (2\right )^{2} + 2 \, x^{2} + 12 \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 46 vs. \(2 (22) = 44\).
Time = 0.02 (sec) , antiderivative size = 46, normalized size of antiderivative = 2.00 \[ \int \left (12+4 x-6 x^2+\left (24 x^2-16 x^3\right ) \log ^2(8)+\left (16 x^3-10 x^4\right ) \log ^4(8)\right ) \, dx=- 162 x^{5} \log {\left (2 \right )}^{4} + x^{4} \left (- 36 \log {\left (2 \right )}^{2} + 324 \log {\left (2 \right )}^{4}\right ) + x^{3} \left (-2 + 72 \log {\left (2 \right )}^{2}\right ) + 2 x^{2} + 12 x \]
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Time = 0.19 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.91 \[ \int \left (12+4 x-6 x^2+\left (24 x^2-16 x^3\right ) \log ^2(8)+\left (16 x^3-10 x^4\right ) \log ^4(8)\right ) \, dx=-162 \, {\left (x^{5} - 2 \, x^{4}\right )} \log \left (2\right )^{4} - 2 \, x^{3} - 36 \, {\left (x^{4} - 2 \, x^{3}\right )} \log \left (2\right )^{2} + 2 \, x^{2} + 12 \, x \]
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Time = 0.25 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.91 \[ \int \left (12+4 x-6 x^2+\left (24 x^2-16 x^3\right ) \log ^2(8)+\left (16 x^3-10 x^4\right ) \log ^4(8)\right ) \, dx=-162 \, {\left (x^{5} - 2 \, x^{4}\right )} \log \left (2\right )^{4} - 2 \, x^{3} - 36 \, {\left (x^{4} - 2 \, x^{3}\right )} \log \left (2\right )^{2} + 2 \, x^{2} + 12 \, x \]
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Time = 8.68 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.09 \[ \int \left (12+4 x-6 x^2+\left (24 x^2-16 x^3\right ) \log ^2(8)+\left (16 x^3-10 x^4\right ) \log ^4(8)\right ) \, dx=-162\,{\ln \left (2\right )}^4\,x^5+\left (324\,{\ln \left (2\right )}^4-36\,{\ln \left (2\right )}^2\right )\,x^4+\left (72\,{\ln \left (2\right )}^2-2\right )\,x^3+2\,x^2+12\,x \]
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