Optimal. Leaf size=28 \[ \left (16+\log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right )\right )^2 \]
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Rubi [C] time = 3.02, antiderivative size = 902, normalized size of antiderivative = 32.21, number of steps used = 46, number of rules used = 16, integrand size = 108, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.148, Rules used = {6, 1594, 6728, 1628, 628, 2528, 2524, 2357, 2301, 2317, 2391, 2418, 2394, 2315, 2390, 2393} \begin {gather*} -\log ^2\left (-2 \left (-x-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2\right )\right )-\log ^2\left (-2 \left (-x+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2\right )\right )-\log ^2(x)-32 \log (x)-2 \log (x) \log \left (x-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}\right )-2 \log \left (-\frac {i \left (-x+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2\right )}{2 \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right ) \log \left (2 x-2 \left (2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )\right )+2 \log \left (\frac {x}{2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right ) \log \left (2 x-2 \left (2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )\right )+2 \log \left (x-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}\right ) \log \left (2 x-2 \left (2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )\right )-2 \log \left (\frac {i \left (-x-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2\right )}{2 \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right ) \log \left (2 x-2 \left (2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )\right )+2 \log \left (\frac {x}{2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right ) \log \left (2 x-2 \left (2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )\right )+2 \log \left (x-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}\right ) \log \left (2 x-2 \left (2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )\right )+2 \log (x) \log \left (1-\frac {x}{2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )+2 \log (x) \log \left (1-\frac {x}{2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )+32 \log \left (x^2-4 x-e^{\frac {e^3}{15}}+e^3+1\right )-2 \text {Li}_2\left (-\frac {-i x-\sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 i}{2 \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )-2 \text {Li}_2\left (\frac {-i x+\sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 i}{2 \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )+2 \text {Li}_2\left (\frac {x}{2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )+2 \text {Li}_2\left (\frac {x}{2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )+2 \text {Li}_2\left (1-\frac {x}{2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )+2 \text {Li}_2\left (1-\frac {x}{2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 628
Rule 1594
Rule 1628
Rule 2301
Rule 2315
Rule 2317
Rule 2357
Rule 2390
Rule 2391
Rule 2393
Rule 2394
Rule 2418
Rule 2524
Rule 2528
Rule 6728
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {32+32 e^3-32 e^{\frac {e^3}{15}}-32 x^2+\left (2+2 e^3-2 e^{\frac {e^3}{15}}-2 x^2\right ) \log \left (\frac {1+e^3-e^{\frac {e^3}{15}}-4 x+x^2}{x}\right )}{e^{\frac {e^3}{15}} x+\left (-1-e^3\right ) x+4 x^2-x^3} \, dx\\ &=\int \frac {32+32 e^3-32 e^{\frac {e^3}{15}}-32 x^2+\left (2+2 e^3-2 e^{\frac {e^3}{15}}-2 x^2\right ) \log \left (\frac {1+e^3-e^{\frac {e^3}{15}}-4 x+x^2}{x}\right )}{\left (-1-e^3+e^{\frac {e^3}{15}}\right ) x+4 x^2-x^3} \, dx\\ &=\int \frac {32+32 e^3-32 e^{\frac {e^3}{15}}-32 x^2+\left (2+2 e^3-2 e^{\frac {e^3}{15}}-2 x^2\right ) \log \left (\frac {1+e^3-e^{\frac {e^3}{15}}-4 x+x^2}{x}\right )}{x \left (-1-e^3+e^{\frac {e^3}{15}}+4 x-x^2\right )} \, dx\\ &=\int \left (\frac {32 \left (-1-e^3+e^{\frac {e^3}{15}}+x^2\right )}{x \left (1+e^3-e^{\frac {e^3}{15}}-4 x+x^2\right )}+\frac {2 \left (-1-e^3+e^{\frac {e^3}{15}}+x^2\right ) \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right )}{x \left (1+e^3-e^{\frac {e^3}{15}}-4 x+x^2\right )}\right ) \, dx\\ &=2 \int \frac {\left (-1-e^3+e^{\frac {e^3}{15}}+x^2\right ) \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right )}{x \left (1+e^3-e^{\frac {e^3}{15}}-4 x+x^2\right )} \, dx+32 \int \frac {-1-e^3+e^{\frac {e^3}{15}}+x^2}{x \left (1+e^3-e^{\frac {e^3}{15}}-4 x+x^2\right )} \, dx\\ &=2 \int \left (-\frac {\log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right )}{x}+\frac {2 (-2+x) \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right )}{1+e^3-e^{\frac {e^3}{15}}-4 x+x^2}\right ) \, dx+32 \int \left (-\frac {1}{x}+\frac {2 (-2+x)}{1+e^3-e^{\frac {e^3}{15}}-4 x+x^2}\right ) \, dx\\ &=-32 \log (x)-2 \int \frac {\log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right )}{x} \, dx+4 \int \frac {(-2+x) \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right )}{1+e^3-e^{\frac {e^3}{15}}-4 x+x^2} \, dx+64 \int \frac {-2+x}{1+e^3-e^{\frac {e^3}{15}}-4 x+x^2} \, dx\\ &=-32 \log (x)-2 \log (x) \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right )+32 \log \left (1+e^3-e^{\frac {e^3}{15}}-4 x+x^2\right )+2 \int \frac {\left (1-\frac {1+e^3-e^{\frac {e^3}{15}}}{x^2}\right ) \log (x)}{-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x} \, dx+4 \int \left (\frac {\log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right )}{-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x}+\frac {\log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right )}{-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x}\right ) \, dx\\ &=-32 \log (x)-2 \log (x) \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right )+32 \log \left (1+e^3-e^{\frac {e^3}{15}}-4 x+x^2\right )+2 \int \left (-\frac {\log (x)}{x}+\frac {2 (-2+x) \log (x)}{1+e^3-e^{\frac {e^3}{15}}-4 x+x^2}\right ) \, dx+4 \int \frac {\log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right )}{-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x} \, dx+4 \int \frac {\log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right )}{-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x} \, dx\\ &=-32 \log (x)-2 \log (x) \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right )+2 \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right ) \log \left (-2 \left (2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )+2 x\right )+2 \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right ) \log \left (-2 \left (2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )+2 x\right )+32 \log \left (1+e^3-e^{\frac {e^3}{15}}-4 x+x^2\right )-2 \int \frac {\log (x)}{x} \, dx-2 \int \frac {\left (1-\frac {1+e^3-e^{\frac {e^3}{15}}}{x^2}\right ) \log \left (-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x\right )}{-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x} \, dx-2 \int \frac {\left (1-\frac {1+e^3-e^{\frac {e^3}{15}}}{x^2}\right ) \log \left (-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x\right )}{-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x} \, dx+4 \int \frac {(-2+x) \log (x)}{1+e^3-e^{\frac {e^3}{15}}-4 x+x^2} \, dx\\ &=-32 \log (x)-\log ^2(x)-2 \log (x) \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right )+2 \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right ) \log \left (-2 \left (2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )+2 x\right )+2 \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right ) \log \left (-2 \left (2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )+2 x\right )+32 \log \left (1+e^3-e^{\frac {e^3}{15}}-4 x+x^2\right )-2 \int \left (-\frac {\log \left (-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x\right )}{x}+\frac {2 (-2+x) \log \left (-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x\right )}{1+e^3-e^{\frac {e^3}{15}}-4 x+x^2}\right ) \, dx-2 \int \left (-\frac {\log \left (-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x\right )}{x}+\frac {2 (-2+x) \log \left (-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x\right )}{1+e^3-e^{\frac {e^3}{15}}-4 x+x^2}\right ) \, dx+4 \int \left (\frac {\log (x)}{-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x}+\frac {\log (x)}{-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x}\right ) \, dx\\ &=-32 \log (x)-\log ^2(x)-2 \log (x) \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right )+2 \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right ) \log \left (-2 \left (2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )+2 x\right )+2 \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right ) \log \left (-2 \left (2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )+2 x\right )+32 \log \left (1+e^3-e^{\frac {e^3}{15}}-4 x+x^2\right )+2 \int \frac {\log \left (-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x\right )}{x} \, dx+2 \int \frac {\log \left (-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x\right )}{x} \, dx+4 \int \frac {\log (x)}{-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x} \, dx+4 \int \frac {\log (x)}{-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x} \, dx-4 \int \frac {(-2+x) \log \left (-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x\right )}{1+e^3-e^{\frac {e^3}{15}}-4 x+x^2} \, dx-4 \int \frac {(-2+x) \log \left (-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x\right )}{1+e^3-e^{\frac {e^3}{15}}-4 x+x^2} \, dx\\ &=-32 \log (x)-\log ^2(x)-2 \log (x) \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right )+2 \log \left (\frac {x}{2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right ) \log \left (-2 \left (2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )+2 x\right )+2 \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right ) \log \left (-2 \left (2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )+2 x\right )+2 \log \left (\frac {x}{2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right ) \log \left (-2 \left (2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )+2 x\right )+2 \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right ) \log \left (-2 \left (2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )+2 x\right )+2 \log (x) \log \left (1-\frac {x}{2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )+2 \log (x) \log \left (1-\frac {x}{2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )+32 \log \left (1+e^3-e^{\frac {e^3}{15}}-4 x+x^2\right )-2 \int \frac {\log \left (1+\frac {2 x}{-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )}{x} \, dx-2 \int \frac {\log \left (1+\frac {2 x}{-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )}{x} \, dx-4 \int \frac {\log \left (\frac {2 x}{4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )}{-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x} \, dx-4 \int \frac {\log \left (\frac {2 x}{4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )}{-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x} \, dx-4 \int \left (\frac {\log \left (-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x\right )}{-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x}+\frac {\log \left (-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x\right )}{-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x}\right ) \, dx-4 \int \left (\frac {\log \left (-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x\right )}{-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x}+\frac {\log \left (-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x\right )}{-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x}\right ) \, dx\\ &=-32 \log (x)-\log ^2(x)-2 \log (x) \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right )+2 \log \left (\frac {x}{2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right ) \log \left (-2 \left (2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )+2 x\right )+2 \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right ) \log \left (-2 \left (2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )+2 x\right )+2 \log \left (\frac {x}{2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right ) \log \left (-2 \left (2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )+2 x\right )+2 \log \left (-4+\frac {1+e^3-e^{\frac {e^3}{15}}}{x}+x\right ) \log \left (-2 \left (2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}\right )+2 x\right )+2 \log (x) \log \left (1-\frac {x}{2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )+2 \log (x) \log \left (1-\frac {x}{2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )+32 \log \left (1+e^3-e^{\frac {e^3}{15}}-4 x+x^2\right )+2 \text {Li}_2\left (\frac {x}{2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )+2 \text {Li}_2\left (\frac {x}{2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )+2 \text {Li}_2\left (1-\frac {x}{2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )+2 \text {Li}_2\left (1-\frac {x}{2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )-4 \int \frac {\log \left (-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x\right )}{-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x} \, dx-4 \int \frac {\log \left (-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x\right )}{-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x} \, dx-4 \int \frac {\log \left (-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x\right )}{-4-2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x} \, dx-4 \int \frac {\log \left (-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x\right )}{-4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+2 x} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [C] time = 0.37, size = 949, normalized size = 33.89 \begin {gather*} 2 \left (\log \left (\frac {2 i+\sqrt {-3+e^3-e^{\frac {e^3}{15}}}-i x}{2 i+\sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right ) \log (x)+\log \left (\frac {-2 i+\sqrt {-3+e^3-e^{\frac {e^3}{15}}}+i x}{-2 i+\sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right ) \log (x)-\frac {\log ^2(x)}{2}-\log \left (\frac {2 i+\sqrt {-3+e^3-e^{\frac {e^3}{15}}}-i x}{2 \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right ) \log \left (2 \left (-2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+x\right )\right )+\log \left (\frac {2 x}{4+2 i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right ) \log \left (2 \left (-2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+x\right )\right )-\frac {1}{2} \log ^2\left (2 \left (-2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+x\right )\right )-\log \left (\frac {-2 i+\sqrt {-3+e^3-e^{\frac {e^3}{15}}}+i x}{2 \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right ) \log \left (2 \left (-2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+x\right )\right )+\log \left (\frac {i x}{2 i+\sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right ) \log \left (2 \left (-2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+x\right )\right )-\frac {1}{2} \log ^2\left (2 \left (-2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+x\right )\right )-\log (x) \left (16+\log \left (\frac {1+e^3-e^{\frac {e^3}{15}}-4 x+x^2}{x}\right )\right )+\log \left (2 \left (-2-i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+x\right )\right ) \left (16+\log \left (\frac {1+e^3-e^{\frac {e^3}{15}}-4 x+x^2}{x}\right )\right )+\log \left (2 \left (-2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}+x\right )\right ) \left (16+\log \left (\frac {1+e^3-e^{\frac {e^3}{15}}-4 x+x^2}{x}\right )\right )-\text {Li}_2\left (\frac {2 i+\sqrt {-3+e^3-e^{\frac {e^3}{15}}}-i x}{2 \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )+\text {Li}_2\left (\frac {2 i+\sqrt {-3+e^3-e^{\frac {e^3}{15}}}-i x}{2 i+\sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )-\text {Li}_2\left (\frac {-2 i+\sqrt {-3+e^3-e^{\frac {e^3}{15}}}+i x}{2 \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )+\text {Li}_2\left (\frac {-2 i+\sqrt {-3+e^3-e^{\frac {e^3}{15}}}+i x}{-2 i+\sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )+\text {Li}_2\left (\frac {x}{2+i \sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )+\text {Li}_2\left (\frac {i x}{2 i+\sqrt {-3+e^3-e^{\frac {e^3}{15}}}}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.60, size = 49, normalized size = 1.75 \begin {gather*} \log \left (\frac {x^{2} - 4 \, x + e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} + 1}{x}\right )^{2} + 32 \, \log \left (\frac {x^{2} - 4 \, x + e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} + 1}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, {\left (16 \, x^{2} + {\left (x^{2} - e^{3} + e^{\left (\frac {1}{15} \, e^{3}\right )} - 1\right )} \log \left (\frac {x^{2} - 4 \, x + e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} + 1}{x}\right ) - 16 \, e^{3} + 16 \, e^{\left (\frac {1}{15} \, e^{3}\right )} - 16\right )}}{x^{3} - 4 \, x^{2} + x e^{3} - x e^{\left (\frac {1}{15} \, e^{3}\right )} + x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.53, size = 50, normalized size = 1.79
method | result | size |
norman | \(\ln \left (\frac {-{\mathrm e}^{\frac {{\mathrm e}^{3}}{15}}+{\mathrm e}^{3}+x^{2}-4 x +1}{x}\right )^{2}+32 \ln \left (\frac {-{\mathrm e}^{\frac {{\mathrm e}^{3}}{15}}+{\mathrm e}^{3}+x^{2}-4 x +1}{x}\right )\) | \(50\) |
default | error in gcdex: invalid arguments\ | N/A |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 3.55, size = 399, normalized size = 14.25 \begin {gather*} 16 \, {\left (\frac {\log \left (x^{2} - 4 \, x + e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} + 1\right )}{e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} + 1} - \frac {2 \, \log \relax (x)}{e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} + 1} - \frac {4 \, \arctan \left (\frac {x - 2}{\sqrt {e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} - 3}}\right )}{{\left (e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} + 1\right )} \sqrt {e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} - 3}}\right )} e^{3} - 16 \, {\left (\frac {\log \left (x^{2} - 4 \, x + e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} + 1\right )}{e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} + 1} - \frac {2 \, \log \relax (x)}{e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} + 1} - \frac {4 \, \arctan \left (\frac {x - 2}{\sqrt {e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} - 3}}\right )}{{\left (e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} + 1\right )} \sqrt {e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} - 3}}\right )} e^{\left (\frac {1}{15} \, e^{3}\right )} + \log \left (x^{2} - 4 \, x + e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} + 1\right )^{2} - 2 \, \log \left (x^{2} - 4 \, x + e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} + 1\right ) \log \relax (x) + \log \relax (x)^{2} + \frac {64 \, \arctan \left (\frac {x - 2}{\sqrt {e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} - 3}}\right )}{\sqrt {e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} - 3}} + \frac {16 \, \log \left (x^{2} - 4 \, x + e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} + 1\right )}{e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} + 1} - \frac {32 \, \log \relax (x)}{e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} + 1} - \frac {64 \, \arctan \left (\frac {x - 2}{\sqrt {e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} - 3}}\right )}{{\left (e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} + 1\right )} \sqrt {e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} - 3}} + 16 \, \log \left (x^{2} - 4 \, x + e^{3} - e^{\left (\frac {1}{15} \, e^{3}\right )} + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 33.35, size = 49, normalized size = 1.75 \begin {gather*} {\ln \left (\frac {x^2-4\,x+{\mathrm {e}}^3-{\left ({\mathrm {e}}^{{\mathrm {e}}^3}\right )}^{1/15}+1}{x}\right )}^2+32\,\ln \left (x^2-4\,x-{\mathrm {e}}^{\frac {{\mathrm {e}}^3}{15}}+{\mathrm {e}}^3+1\right )-32\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 49.07, size = 49, normalized size = 1.75 \begin {gather*} - 32 \log {\relax (x )} + \log {\left (\frac {x^{2} - 4 x - e^{\frac {e^{3}}{15}} + 1 + e^{3}}{x} \right )}^{2} + 32 \log {\left (x^{2} - 4 x - e^{\frac {e^{3}}{15}} + 1 + e^{3} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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