Integrand size = 249, antiderivative size = 33 \[ \int \frac {-12 x^4-24 x^5+12 x^2 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (-x^3+3 x^4+6 x^5+2 x^2 \log (3)+\left (-x-3 x^2\right ) \log ^2(3)\right )+\left (-36 x^2-48 x^3+48 x \log (3)-12 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (9 x^2+12 x^3-12 x \log (3)+3 \log ^2(3)\right )\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+\left (-24 x+6 e^{\frac {1}{3} (-16+x)} x\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )}{-12 x^4+3 e^{\frac {1}{3} (-16+x)} x^4+\left (-24 x^2+6 e^{\frac {1}{3} (-16+x)} x^2\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+\left (-12+3 e^{\frac {1}{3} (-16+x)}\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )} \, dx=x^2+\frac {(x-\log (3))^2}{x+\frac {\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )}{x}} \]
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\[ \int \frac {-12 x^4-24 x^5+12 x^2 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (-x^3+3 x^4+6 x^5+2 x^2 \log (3)+\left (-x-3 x^2\right ) \log ^2(3)\right )+\left (-36 x^2-48 x^3+48 x \log (3)-12 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (9 x^2+12 x^3-12 x \log (3)+3 \log ^2(3)\right )\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+\left (-24 x+6 e^{\frac {1}{3} (-16+x)} x\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )}{-12 x^4+3 e^{\frac {1}{3} (-16+x)} x^4+\left (-24 x^2+6 e^{\frac {1}{3} (-16+x)} x^2\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+\left (-12+3 e^{\frac {1}{3} (-16+x)}\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )} \, dx=\int \frac {-12 x^4-24 x^5+12 x^2 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (-x^3+3 x^4+6 x^5+2 x^2 \log (3)+\left (-x-3 x^2\right ) \log ^2(3)\right )+\left (-36 x^2-48 x^3+48 x \log (3)-12 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (9 x^2+12 x^3-12 x \log (3)+3 \log ^2(3)\right )\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+\left (-24 x+6 e^{\frac {1}{3} (-16+x)} x\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )}{-12 x^4+3 e^{\frac {1}{3} (-16+x)} x^4+\left (-24 x^2+6 e^{\frac {1}{3} (-16+x)} x^2\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+\left (-12+3 e^{\frac {1}{3} (-16+x)}\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{16/3} \left (12 x^4+24 x^5-12 x^2 \log ^2(3)-e^{\frac {1}{3} (-16+x)} \left (-x^3+3 x^4+6 x^5+2 x^2 \log (3)+\left (-x-3 x^2\right ) \log ^2(3)\right )-\left (-36 x^2-48 x^3+48 x \log (3)-12 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (9 x^2+12 x^3-12 x \log (3)+3 \log ^2(3)\right )\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )-\left (-24 x+6 e^{\frac {1}{3} (-16+x)} x\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )}{3 \left (4 e^{16/3}-e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx \\ & = \frac {1}{3} e^{16/3} \int \frac {12 x^4+24 x^5-12 x^2 \log ^2(3)-e^{\frac {1}{3} (-16+x)} \left (-x^3+3 x^4+6 x^5+2 x^2 \log (3)+\left (-x-3 x^2\right ) \log ^2(3)\right )-\left (-36 x^2-48 x^3+48 x \log (3)-12 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (9 x^2+12 x^3-12 x \log (3)+3 \log ^2(3)\right )\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )-\left (-24 x+6 e^{\frac {1}{3} (-16+x)} x\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )}{\left (4 e^{16/3}-e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx \\ & = \frac {1}{3} e^{16/3} \int \left (-\frac {4 x (x-\log (3))^2}{\left (-4 e^{16/3}+e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2}+\frac {-x^3+3 x^4+6 x^5-x \log ^2(3)-3 x^2 \log ^2(3) \left (1-\frac {\log (9)}{3 \log ^2(3)}\right )+9 x^2 \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+12 x^3 \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )-12 x \log (3) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+3 \log ^2(3) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+6 x \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )}{e^{16/3} \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2}\right ) \, dx \\ & = \frac {1}{3} \int \frac {-x^3+3 x^4+6 x^5-x \log ^2(3)-3 x^2 \log ^2(3) \left (1-\frac {\log (9)}{3 \log ^2(3)}\right )+9 x^2 \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+12 x^3 \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )-12 x \log (3) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+3 \log ^2(3) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+6 x \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )}{\left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx-\frac {1}{3} \left (4 e^{16/3}\right ) \int \frac {x (x-\log (3))^2}{\left (-4 e^{16/3}+e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx \\ & = \frac {1}{3} \int \frac {x \left (-x^2+3 x^3+6 x^4-\log ^2(3)+x \left (-3 \log ^2(3)+\log (9)\right )\right )+3 \left (3 x^2+4 x^3-4 x \log (3)+\log ^2(3)\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+6 x \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )}{\left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx-\frac {1}{3} \left (4 e^{16/3}\right ) \int \left (\frac {x^3}{\left (-4 e^{16/3}+e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2}-\frac {2 x^2 \log (3)}{\left (-4 e^{16/3}+e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2}+\frac {x \log ^2(3)}{\left (-4 e^{16/3}+e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2}\right ) \, dx \\ & = \frac {1}{3} \int \left (6 x+\frac {x \left (-6 x^3-x^2 (1-12 \log (3))-\log ^2(3)-x \left (6 \log ^2(3)-\log (9)\right )\right )}{\left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2}+\frac {3 \left (3 x^2-4 x \log (3)+\log ^2(3)\right )}{x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )}\right ) \, dx-\frac {1}{3} \left (4 e^{16/3}\right ) \int \frac {x^3}{\left (-4 e^{16/3}+e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx+\frac {1}{3} \left (8 e^{16/3} \log (3)\right ) \int \frac {x^2}{\left (-4 e^{16/3}+e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx-\frac {1}{3} \left (4 e^{16/3} \log ^2(3)\right ) \int \frac {x}{\left (-4 e^{16/3}+e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx \\ & = x^2+\frac {1}{3} \int \frac {x \left (-6 x^3-x^2 (1-12 \log (3))-\log ^2(3)-x \left (6 \log ^2(3)-\log (9)\right )\right )}{\left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx-\frac {1}{3} \left (4 e^{16/3}\right ) \int \frac {x^3}{\left (-4 e^{16/3}+e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx+\frac {1}{3} \left (8 e^{16/3} \log (3)\right ) \int \frac {x^2}{\left (-4 e^{16/3}+e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx-\frac {1}{3} \left (4 e^{16/3} \log ^2(3)\right ) \int \frac {x}{\left (-4 e^{16/3}+e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx+\int \frac {3 x^2-4 x \log (3)+\log ^2(3)}{x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )} \, dx \\ & = x^2+\frac {1}{3} \int \left (-\frac {6 x^4}{\left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2}-\frac {x \log ^2(3)}{\left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2}+\frac {x^3 (-1+12 \log (3))}{\left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2}-\frac {x^2 \left (6 \log ^2(3)-\log (9)\right )}{\left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2}\right ) \, dx-\frac {1}{3} \left (4 e^{16/3}\right ) \int \frac {x^3}{\left (-4 e^{16/3}+e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx+\frac {1}{3} \left (8 e^{16/3} \log (3)\right ) \int \frac {x^2}{\left (-4 e^{16/3}+e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx-\frac {1}{3} \left (4 e^{16/3} \log ^2(3)\right ) \int \frac {x}{\left (-4 e^{16/3}+e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx+\int \left (\frac {3 x^2}{x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )}-\frac {4 x \log (3)}{x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )}+\frac {\log ^2(3)}{x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )}\right ) \, dx \\ & = x^2-2 \int \frac {x^4}{\left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx+3 \int \frac {x^2}{x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )} \, dx-\frac {1}{3} \left (4 e^{16/3}\right ) \int \frac {x^3}{\left (-4 e^{16/3}+e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx-(4 \log (3)) \int \frac {x}{x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )} \, dx+\frac {1}{3} \left (8 e^{16/3} \log (3)\right ) \int \frac {x^2}{\left (-4 e^{16/3}+e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx-\frac {1}{3} \log ^2(3) \int \frac {x}{\left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx+\log ^2(3) \int \frac {1}{x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )} \, dx-\frac {1}{3} \left (4 e^{16/3} \log ^2(3)\right ) \int \frac {x}{\left (-4 e^{16/3}+e^{x/3}\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx+\frac {1}{3} (-1+12 \log (3)) \int \frac {x^3}{\left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx+\frac {1}{3} \left (-6 \log ^2(3)+\log (9)\right ) \int \frac {x^2}{\left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )^2} \, dx \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(150\) vs. \(2(33)=66\).
Time = 0.34 (sec) , antiderivative size = 150, normalized size of antiderivative = 4.55 \[ \int \frac {-12 x^4-24 x^5+12 x^2 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (-x^3+3 x^4+6 x^5+2 x^2 \log (3)+\left (-x-3 x^2\right ) \log ^2(3)\right )+\left (-36 x^2-48 x^3+48 x \log (3)-12 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (9 x^2+12 x^3-12 x \log (3)+3 \log ^2(3)\right )\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+\left (-24 x+6 e^{\frac {1}{3} (-16+x)} x\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )}{-12 x^4+3 e^{\frac {1}{3} (-16+x)} x^4+\left (-24 x^2+6 e^{\frac {1}{3} (-16+x)} x^2\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+\left (-12+3 e^{\frac {1}{3} (-16+x)}\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )} \, dx=\frac {x \left (-24 e^{16/3} x \left (x^2+x^3+\log ^2(3)-x \log (9)\right )+e^{x/3} \left (x^2+7 x^3+6 x^4-12 x^2 \log (3)+\log ^2(3)+6 x \log ^2(3)-x \log (9)\right )+x \left (-24 e^{16/3} x+e^{x/3} (1+6 x)\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )}{\left (-24 e^{16/3} x+e^{x/3} (1+6 x)\right ) \left (x^2+\log \left (-4+e^{\frac {1}{3} (-16+x)}\right )\right )} \]
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Time = 0.49 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.06
method | result | size |
risch | \(x^{2}+\frac {\left (\ln \left (3\right )^{2}-2 x \ln \left (3\right )+x^{2}\right ) x}{x^{2}+\ln \left ({\mathrm e}^{\frac {x}{3}-\frac {16}{3}}-4\right )}\) | \(35\) |
parallelrisch | \(\frac {3 x^{4}+3 x \ln \left (3\right )^{2}-6 x^{2} \ln \left (3\right )+3 x^{3}+3 \ln \left ({\mathrm e}^{\frac {x}{3}-\frac {16}{3}}-4\right ) x^{2}}{3 x^{2}+3 \ln \left ({\mathrm e}^{\frac {x}{3}-\frac {16}{3}}-4\right )}\) | \(57\) |
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Time = 0.27 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.48 \[ \int \frac {-12 x^4-24 x^5+12 x^2 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (-x^3+3 x^4+6 x^5+2 x^2 \log (3)+\left (-x-3 x^2\right ) \log ^2(3)\right )+\left (-36 x^2-48 x^3+48 x \log (3)-12 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (9 x^2+12 x^3-12 x \log (3)+3 \log ^2(3)\right )\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+\left (-24 x+6 e^{\frac {1}{3} (-16+x)} x\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )}{-12 x^4+3 e^{\frac {1}{3} (-16+x)} x^4+\left (-24 x^2+6 e^{\frac {1}{3} (-16+x)} x^2\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+\left (-12+3 e^{\frac {1}{3} (-16+x)}\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )} \, dx=\frac {x^{4} + x^{3} - 2 \, x^{2} \log \left (3\right ) + x \log \left (3\right )^{2} + x^{2} \log \left (e^{\left (\frac {1}{3} \, x - \frac {16}{3}\right )} - 4\right )}{x^{2} + \log \left (e^{\left (\frac {1}{3} \, x - \frac {16}{3}\right )} - 4\right )} \]
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Time = 0.13 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.09 \[ \int \frac {-12 x^4-24 x^5+12 x^2 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (-x^3+3 x^4+6 x^5+2 x^2 \log (3)+\left (-x-3 x^2\right ) \log ^2(3)\right )+\left (-36 x^2-48 x^3+48 x \log (3)-12 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (9 x^2+12 x^3-12 x \log (3)+3 \log ^2(3)\right )\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+\left (-24 x+6 e^{\frac {1}{3} (-16+x)} x\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )}{-12 x^4+3 e^{\frac {1}{3} (-16+x)} x^4+\left (-24 x^2+6 e^{\frac {1}{3} (-16+x)} x^2\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+\left (-12+3 e^{\frac {1}{3} (-16+x)}\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )} \, dx=x^{2} + \frac {x^{3} - 2 x^{2} \log {\left (3 \right )} + x \log {\left (3 \right )}^{2}}{x^{2} + \log {\left (e^{\frac {x}{3} - \frac {16}{3}} - 4 \right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (30) = 60\).
Time = 0.68 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.00 \[ \int \frac {-12 x^4-24 x^5+12 x^2 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (-x^3+3 x^4+6 x^5+2 x^2 \log (3)+\left (-x-3 x^2\right ) \log ^2(3)\right )+\left (-36 x^2-48 x^3+48 x \log (3)-12 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (9 x^2+12 x^3-12 x \log (3)+3 \log ^2(3)\right )\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+\left (-24 x+6 e^{\frac {1}{3} (-16+x)} x\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )}{-12 x^4+3 e^{\frac {1}{3} (-16+x)} x^4+\left (-24 x^2+6 e^{\frac {1}{3} (-16+x)} x^2\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+\left (-12+3 e^{\frac {1}{3} (-16+x)}\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )} \, dx=\frac {3 \, x^{4} + 3 \, x^{3} - 2 \, x^{2} {\left (3 \, \log \left (3\right ) + 8\right )} + 3 \, x \log \left (3\right )^{2} + 3 \, x^{2} \log \left (-4 \, e^{\frac {16}{3}} + e^{\left (\frac {1}{3} \, x\right )}\right )}{3 \, x^{2} + 3 \, \log \left (-4 \, e^{\frac {16}{3}} + e^{\left (\frac {1}{3} \, x\right )}\right ) - 16} \]
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Time = 0.54 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.48 \[ \int \frac {-12 x^4-24 x^5+12 x^2 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (-x^3+3 x^4+6 x^5+2 x^2 \log (3)+\left (-x-3 x^2\right ) \log ^2(3)\right )+\left (-36 x^2-48 x^3+48 x \log (3)-12 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (9 x^2+12 x^3-12 x \log (3)+3 \log ^2(3)\right )\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+\left (-24 x+6 e^{\frac {1}{3} (-16+x)} x\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )}{-12 x^4+3 e^{\frac {1}{3} (-16+x)} x^4+\left (-24 x^2+6 e^{\frac {1}{3} (-16+x)} x^2\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+\left (-12+3 e^{\frac {1}{3} (-16+x)}\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )} \, dx=\frac {x^{4} + x^{3} - 2 \, x^{2} \log \left (3\right ) + x \log \left (3\right )^{2} + x^{2} \log \left (e^{\left (\frac {1}{3} \, x - \frac {16}{3}\right )} - 4\right )}{x^{2} + \log \left (e^{\left (\frac {1}{3} \, x - \frac {16}{3}\right )} - 4\right )} \]
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Time = 0.63 (sec) , antiderivative size = 293, normalized size of antiderivative = 8.88 \[ \int \frac {-12 x^4-24 x^5+12 x^2 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (-x^3+3 x^4+6 x^5+2 x^2 \log (3)+\left (-x-3 x^2\right ) \log ^2(3)\right )+\left (-36 x^2-48 x^3+48 x \log (3)-12 \log ^2(3)+e^{\frac {1}{3} (-16+x)} \left (9 x^2+12 x^3-12 x \log (3)+3 \log ^2(3)\right )\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+\left (-24 x+6 e^{\frac {1}{3} (-16+x)} x\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )}{-12 x^4+3 e^{\frac {1}{3} (-16+x)} x^4+\left (-24 x^2+6 e^{\frac {1}{3} (-16+x)} x^2\right ) \log \left (-4+e^{\frac {1}{3} (-16+x)}\right )+\left (-12+3 e^{\frac {1}{3} (-16+x)}\right ) \log ^2\left (-4+e^{\frac {1}{3} (-16+x)}\right )} \, dx=\frac {3\,x}{2}+\frac {4\,\ln \left (3\right )+6\,{\ln \left (3\right )}^2+\frac {1}{2}}{12\,x+2}+x^2+\frac {\frac {x^3\,{\mathrm {e}}^{\frac {x}{3}-\frac {16}{3}}-12\,x^2\,{\ln \left (3\right )}^2-3\,x^4\,{\mathrm {e}}^{\frac {x}{3}-\frac {16}{3}}+12\,x^4+x\,{\mathrm {e}}^{\frac {x}{3}-\frac {16}{3}}\,{\ln \left (3\right )}^2-2\,x^2\,{\mathrm {e}}^{\frac {x}{3}-\frac {16}{3}}\,\ln \left (3\right )+3\,x^2\,{\mathrm {e}}^{\frac {x}{3}-\frac {16}{3}}\,{\ln \left (3\right )}^2}{{\mathrm {e}}^{\frac {x}{3}-\frac {16}{3}}-24\,x+6\,x\,{\mathrm {e}}^{\frac {x}{3}-\frac {16}{3}}}-\frac {3\,\ln \left ({\mathrm {e}}^{-\frac {16}{3}}\,{\left ({\mathrm {e}}^x\right )}^{1/3}-4\right )\,\left ({\mathrm {e}}^{\frac {x}{3}-\frac {16}{3}}-4\right )\,\left (3\,x^2-4\,\ln \left (3\right )\,x+{\ln \left (3\right )}^2\right )}{{\mathrm {e}}^{\frac {x}{3}-\frac {16}{3}}-24\,x+6\,x\,{\mathrm {e}}^{\frac {x}{3}-\frac {16}{3}}}}{\ln \left ({\mathrm {e}}^{-\frac {16}{3}}\,{\left ({\mathrm {e}}^x\right )}^{1/3}-4\right )+x^2}+\frac {12\,\left (6\,x^2\,{\ln \left (3\right )}^2+12\,x\,\ln \left (3\right )+x\,{\ln \left (3\right )}^2-4\,x^2\,\ln \left (3\right )-24\,x^3\,\ln \left (3\right )-3\,{\ln \left (3\right )}^2-9\,x^2+3\,x^3+18\,x^4\right )}{\left (6\,x+1\right )\,\left (24\,x-{\mathrm {e}}^{\frac {x}{3}-\frac {16}{3}}\,\left (6\,x+1\right )\right )\,\left (6\,x^2+x-3\right )} \]
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