Optimal. Leaf size=32 \[ -5 x+\left (-4+\frac {e^{2 x}}{5}\right )^2 \left (1+x+x^2+\frac {x}{\log (x)}\right )^2 \]
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Rubi [F] time = 18.71, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-800 x+80 e^{2 x} x-2 e^{4 x} x+\left (-800+80 e^{2 x}-800 x^2+e^{4 x} \left (-2+2 x^2\right )\right ) \log (x)+\left (800+1600 x+2400 x^2+e^{2 x} \left (-80-320 x-400 x^2-160 x^3\right )+e^{4 x} \left (2+12 x+14 x^2+8 x^3\right )\right ) \log ^2(x)+\left (675+2400 x+2400 x^2+1600 x^3+e^{2 x} \left (-160-400 x-480 x^2-320 x^3-80 x^4\right )+e^{4 x} \left (6+14 x+18 x^2+12 x^3+4 x^4\right )\right ) \log ^3(x)}{25 \log ^3(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{25} \int \frac {-800 x+80 e^{2 x} x-2 e^{4 x} x+\left (-800+80 e^{2 x}-800 x^2+e^{4 x} \left (-2+2 x^2\right )\right ) \log (x)+\left (800+1600 x+2400 x^2+e^{2 x} \left (-80-320 x-400 x^2-160 x^3\right )+e^{4 x} \left (2+12 x+14 x^2+8 x^3\right )\right ) \log ^2(x)+\left (675+2400 x+2400 x^2+1600 x^3+e^{2 x} \left (-160-400 x-480 x^2-320 x^3-80 x^4\right )+e^{4 x} \left (6+14 x+18 x^2+12 x^3+4 x^4\right )\right ) \log ^3(x)}{\log ^3(x)} \, dx\\ &=\frac {1}{25} \int \left (\frac {25 \left (-32 x-32 \log (x)-32 x^2 \log (x)+32 \log ^2(x)+64 x \log ^2(x)+96 x^2 \log ^2(x)+27 \log ^3(x)+96 x \log ^3(x)+96 x^2 \log ^3(x)+64 x^3 \log ^3(x)\right )}{\log ^3(x)}-\frac {80 e^{2 x} \left (-x-\log (x)+\log ^2(x)+4 x \log ^2(x)+5 x^2 \log ^2(x)+2 x^3 \log ^2(x)+2 \log ^3(x)+5 x \log ^3(x)+6 x^2 \log ^3(x)+4 x^3 \log ^3(x)+x^4 \log ^3(x)\right )}{\log ^3(x)}+\frac {2 e^{4 x} \left (-x-\log (x)+x^2 \log (x)+\log ^2(x)+6 x \log ^2(x)+7 x^2 \log ^2(x)+4 x^3 \log ^2(x)+3 \log ^3(x)+7 x \log ^3(x)+9 x^2 \log ^3(x)+6 x^3 \log ^3(x)+2 x^4 \log ^3(x)\right )}{\log ^3(x)}\right ) \, dx\\ &=\frac {2}{25} \int \frac {e^{4 x} \left (-x-\log (x)+x^2 \log (x)+\log ^2(x)+6 x \log ^2(x)+7 x^2 \log ^2(x)+4 x^3 \log ^2(x)+3 \log ^3(x)+7 x \log ^3(x)+9 x^2 \log ^3(x)+6 x^3 \log ^3(x)+2 x^4 \log ^3(x)\right )}{\log ^3(x)} \, dx-\frac {16}{5} \int \frac {e^{2 x} \left (-x-\log (x)+\log ^2(x)+4 x \log ^2(x)+5 x^2 \log ^2(x)+2 x^3 \log ^2(x)+2 \log ^3(x)+5 x \log ^3(x)+6 x^2 \log ^3(x)+4 x^3 \log ^3(x)+x^4 \log ^3(x)\right )}{\log ^3(x)} \, dx+\int \frac {-32 x-32 \log (x)-32 x^2 \log (x)+32 \log ^2(x)+64 x \log ^2(x)+96 x^2 \log ^2(x)+27 \log ^3(x)+96 x \log ^3(x)+96 x^2 \log ^3(x)+64 x^3 \log ^3(x)}{\log ^3(x)} \, dx\\ &=\frac {2}{25} \int \frac {e^{4 x} \left (-x+\left (-1+x^2\right ) \log (x)+\left (1+6 x+7 x^2+4 x^3\right ) \log ^2(x)+\left (3+7 x+9 x^2+6 x^3+2 x^4\right ) \log ^3(x)\right )}{\log ^3(x)} \, dx-\frac {16}{5} \int \frac {e^{2 x} \left (-x-\log (x)+(1+x)^2 (1+2 x) \log ^2(x)+\left (2+5 x+6 x^2+4 x^3+x^4\right ) \log ^3(x)\right )}{\log ^3(x)} \, dx+\int \left (27+96 x+96 x^2+64 x^3-\frac {32 x}{\log ^3(x)}-\frac {32 \left (1+x^2\right )}{\log ^2(x)}+\frac {32 \left (1+2 x+3 x^2\right )}{\log (x)}\right ) \, dx\\ &=27 x+48 x^2+32 x^3+16 x^4+\frac {2}{25} \int \left (3 e^{4 x}+7 e^{4 x} x+9 e^{4 x} x^2+6 e^{4 x} x^3+2 e^{4 x} x^4-\frac {e^{4 x} x}{\log ^3(x)}+\frac {e^{4 x} \left (-1+x^2\right )}{\log ^2(x)}+\frac {e^{4 x} \left (1+6 x+7 x^2+4 x^3\right )}{\log (x)}\right ) \, dx-\frac {16}{5} \int \left (2 e^{2 x}+5 e^{2 x} x+6 e^{2 x} x^2+4 e^{2 x} x^3+e^{2 x} x^4-\frac {e^{2 x} x}{\log ^3(x)}-\frac {e^{2 x}}{\log ^2(x)}+\frac {e^{2 x} (1+x)^2 (1+2 x)}{\log (x)}\right ) \, dx-32 \int \frac {x}{\log ^3(x)} \, dx-32 \int \frac {1+x^2}{\log ^2(x)} \, dx+32 \int \frac {1+2 x+3 x^2}{\log (x)} \, dx\\ &=27 x+48 x^2+32 x^3+16 x^4+\frac {16 x^2}{\log ^2(x)}-\frac {2}{25} \int \frac {e^{4 x} x}{\log ^3(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x} \left (-1+x^2\right )}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x} \left (1+6 x+7 x^2+4 x^3\right )}{\log (x)} \, dx+\frac {4}{25} \int e^{4 x} x^4 \, dx+\frac {6}{25} \int e^{4 x} \, dx+\frac {12}{25} \int e^{4 x} x^3 \, dx+\frac {14}{25} \int e^{4 x} x \, dx+\frac {18}{25} \int e^{4 x} x^2 \, dx-\frac {16}{5} \int e^{2 x} x^4 \, dx+\frac {16}{5} \int \frac {e^{2 x} x}{\log ^3(x)} \, dx+\frac {16}{5} \int \frac {e^{2 x}}{\log ^2(x)} \, dx-\frac {16}{5} \int \frac {e^{2 x} (1+x)^2 (1+2 x)}{\log (x)} \, dx-\frac {32}{5} \int e^{2 x} \, dx-\frac {64}{5} \int e^{2 x} x^3 \, dx-16 \int e^{2 x} x \, dx-\frac {96}{5} \int e^{2 x} x^2 \, dx-32 \int \left (\frac {1}{\log ^2(x)}+\frac {x^2}{\log ^2(x)}\right ) \, dx+32 \int \left (\frac {1}{\log (x)}+\frac {2 x}{\log (x)}+\frac {3 x^2}{\log (x)}\right ) \, dx-32 \int \frac {x}{\log ^2(x)} \, dx\\ &=-\frac {16 e^{2 x}}{5}+\frac {3 e^{4 x}}{50}+27 x-8 e^{2 x} x+\frac {7}{50} e^{4 x} x+48 x^2-\frac {48}{5} e^{2 x} x^2+\frac {9}{50} e^{4 x} x^2+32 x^3-\frac {32}{5} e^{2 x} x^3+\frac {3}{25} e^{4 x} x^3+16 x^4-\frac {8}{5} e^{2 x} x^4+\frac {1}{25} e^{4 x} x^4+\frac {16 x^2}{\log ^2(x)}+\frac {32 x^2}{\log (x)}+\frac {2}{25} \int \left (-\frac {e^{4 x}}{\log ^2(x)}+\frac {e^{4 x} x^2}{\log ^2(x)}\right ) \, dx+\frac {2}{25} \int \left (\frac {e^{4 x}}{\log (x)}+\frac {6 e^{4 x} x}{\log (x)}+\frac {7 e^{4 x} x^2}{\log (x)}+\frac {4 e^{4 x} x^3}{\log (x)}\right ) \, dx-\frac {2}{25} \int \frac {e^{4 x} x}{\log ^3(x)} \, dx-\frac {7}{50} \int e^{4 x} \, dx-\frac {4}{25} \int e^{4 x} x^3 \, dx-\frac {9}{25} \int e^{4 x} x \, dx-\frac {9}{25} \int e^{4 x} x^2 \, dx-\frac {16}{5} \int \left (\frac {e^{2 x}}{\log (x)}+\frac {4 e^{2 x} x}{\log (x)}+\frac {5 e^{2 x} x^2}{\log (x)}+\frac {2 e^{2 x} x^3}{\log (x)}\right ) \, dx+\frac {16}{5} \int \frac {e^{2 x} x}{\log ^3(x)} \, dx+\frac {16}{5} \int \frac {e^{2 x}}{\log ^2(x)} \, dx+\frac {32}{5} \int e^{2 x} x^3 \, dx+8 \int e^{2 x} \, dx+\frac {96}{5} \int e^{2 x} x \, dx+\frac {96}{5} \int e^{2 x} x^2 \, dx-32 \int \frac {1}{\log ^2(x)} \, dx-32 \int \frac {x^2}{\log ^2(x)} \, dx+32 \int \frac {1}{\log (x)} \, dx+96 \int \frac {x^2}{\log (x)} \, dx\\ &=\frac {4 e^{2 x}}{5}+\frac {e^{4 x}}{40}+27 x+\frac {8}{5} e^{2 x} x+\frac {1}{20} e^{4 x} x+48 x^2+\frac {9}{100} e^{4 x} x^2+32 x^3-\frac {16}{5} e^{2 x} x^3+\frac {2}{25} e^{4 x} x^3+16 x^4-\frac {8}{5} e^{2 x} x^4+\frac {1}{25} e^{4 x} x^4+\frac {16 x^2}{\log ^2(x)}+\frac {32 x}{\log (x)}+\frac {32 x^2}{\log (x)}+\frac {32 x^3}{\log (x)}+32 \text {li}(x)-\frac {2}{25} \int \frac {e^{4 x} x}{\log ^3(x)} \, dx-\frac {2}{25} \int \frac {e^{4 x}}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x} x^2}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x}}{\log (x)} \, dx+\frac {9}{100} \int e^{4 x} \, dx+\frac {3}{25} \int e^{4 x} x^2 \, dx+\frac {9}{50} \int e^{4 x} x \, dx+\frac {8}{25} \int \frac {e^{4 x} x^3}{\log (x)} \, dx+\frac {12}{25} \int \frac {e^{4 x} x}{\log (x)} \, dx+\frac {14}{25} \int \frac {e^{4 x} x^2}{\log (x)} \, dx+\frac {16}{5} \int \frac {e^{2 x} x}{\log ^3(x)} \, dx+\frac {16}{5} \int \frac {e^{2 x}}{\log ^2(x)} \, dx-\frac {16}{5} \int \frac {e^{2 x}}{\log (x)} \, dx-\frac {32}{5} \int \frac {e^{2 x} x^3}{\log (x)} \, dx-\frac {48}{5} \int e^{2 x} \, dx-\frac {48}{5} \int e^{2 x} x^2 \, dx-\frac {64}{5} \int \frac {e^{2 x} x}{\log (x)} \, dx-16 \int \frac {e^{2 x} x^2}{\log (x)} \, dx-\frac {96}{5} \int e^{2 x} x \, dx-32 \int \frac {1}{\log (x)} \, dx-96 \int \frac {x^2}{\log (x)} \, dx+96 \operatorname {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right )\\ &=-4 e^{2 x}+\frac {19 e^{4 x}}{400}+27 x-8 e^{2 x} x+\frac {19}{200} e^{4 x} x+48 x^2-\frac {24}{5} e^{2 x} x^2+\frac {3}{25} e^{4 x} x^2+32 x^3-\frac {16}{5} e^{2 x} x^3+\frac {2}{25} e^{4 x} x^3+16 x^4-\frac {8}{5} e^{2 x} x^4+\frac {1}{25} e^{4 x} x^4+96 \text {Ei}(3 \log (x))+\frac {16 x^2}{\log ^2(x)}+\frac {32 x}{\log (x)}+\frac {32 x^2}{\log (x)}+\frac {32 x^3}{\log (x)}-\frac {9}{200} \int e^{4 x} \, dx-\frac {3}{50} \int e^{4 x} x \, dx-\frac {2}{25} \int \frac {e^{4 x} x}{\log ^3(x)} \, dx-\frac {2}{25} \int \frac {e^{4 x}}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x} x^2}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x}}{\log (x)} \, dx+\frac {8}{25} \int \frac {e^{4 x} x^3}{\log (x)} \, dx+\frac {12}{25} \int \frac {e^{4 x} x}{\log (x)} \, dx+\frac {14}{25} \int \frac {e^{4 x} x^2}{\log (x)} \, dx+\frac {16}{5} \int \frac {e^{2 x} x}{\log ^3(x)} \, dx+\frac {16}{5} \int \frac {e^{2 x}}{\log ^2(x)} \, dx-\frac {16}{5} \int \frac {e^{2 x}}{\log (x)} \, dx-\frac {32}{5} \int \frac {e^{2 x} x^3}{\log (x)} \, dx+\frac {48}{5} \int e^{2 x} \, dx+\frac {48}{5} \int e^{2 x} x \, dx-\frac {64}{5} \int \frac {e^{2 x} x}{\log (x)} \, dx-16 \int \frac {e^{2 x} x^2}{\log (x)} \, dx-96 \operatorname {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right )\\ &=\frac {4 e^{2 x}}{5}+\frac {29 e^{4 x}}{800}+27 x-\frac {16}{5} e^{2 x} x+\frac {2}{25} e^{4 x} x+48 x^2-\frac {24}{5} e^{2 x} x^2+\frac {3}{25} e^{4 x} x^2+32 x^3-\frac {16}{5} e^{2 x} x^3+\frac {2}{25} e^{4 x} x^3+16 x^4-\frac {8}{5} e^{2 x} x^4+\frac {1}{25} e^{4 x} x^4+\frac {16 x^2}{\log ^2(x)}+\frac {32 x}{\log (x)}+\frac {32 x^2}{\log (x)}+\frac {32 x^3}{\log (x)}+\frac {3}{200} \int e^{4 x} \, dx-\frac {2}{25} \int \frac {e^{4 x} x}{\log ^3(x)} \, dx-\frac {2}{25} \int \frac {e^{4 x}}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x} x^2}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x}}{\log (x)} \, dx+\frac {8}{25} \int \frac {e^{4 x} x^3}{\log (x)} \, dx+\frac {12}{25} \int \frac {e^{4 x} x}{\log (x)} \, dx+\frac {14}{25} \int \frac {e^{4 x} x^2}{\log (x)} \, dx+\frac {16}{5} \int \frac {e^{2 x} x}{\log ^3(x)} \, dx+\frac {16}{5} \int \frac {e^{2 x}}{\log ^2(x)} \, dx-\frac {16}{5} \int \frac {e^{2 x}}{\log (x)} \, dx-\frac {24}{5} \int e^{2 x} \, dx-\frac {32}{5} \int \frac {e^{2 x} x^3}{\log (x)} \, dx-\frac {64}{5} \int \frac {e^{2 x} x}{\log (x)} \, dx-16 \int \frac {e^{2 x} x^2}{\log (x)} \, dx\\ &=-\frac {8 e^{2 x}}{5}+\frac {e^{4 x}}{25}+27 x-\frac {16}{5} e^{2 x} x+\frac {2}{25} e^{4 x} x+48 x^2-\frac {24}{5} e^{2 x} x^2+\frac {3}{25} e^{4 x} x^2+32 x^3-\frac {16}{5} e^{2 x} x^3+\frac {2}{25} e^{4 x} x^3+16 x^4-\frac {8}{5} e^{2 x} x^4+\frac {1}{25} e^{4 x} x^4+\frac {16 x^2}{\log ^2(x)}+\frac {32 x}{\log (x)}+\frac {32 x^2}{\log (x)}+\frac {32 x^3}{\log (x)}-\frac {2}{25} \int \frac {e^{4 x} x}{\log ^3(x)} \, dx-\frac {2}{25} \int \frac {e^{4 x}}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x} x^2}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x}}{\log (x)} \, dx+\frac {8}{25} \int \frac {e^{4 x} x^3}{\log (x)} \, dx+\frac {12}{25} \int \frac {e^{4 x} x}{\log (x)} \, dx+\frac {14}{25} \int \frac {e^{4 x} x^2}{\log (x)} \, dx+\frac {16}{5} \int \frac {e^{2 x} x}{\log ^3(x)} \, dx+\frac {16}{5} \int \frac {e^{2 x}}{\log ^2(x)} \, dx-\frac {16}{5} \int \frac {e^{2 x}}{\log (x)} \, dx-\frac {32}{5} \int \frac {e^{2 x} x^3}{\log (x)} \, dx-\frac {64}{5} \int \frac {e^{2 x} x}{\log (x)} \, dx-16 \int \frac {e^{2 x} x^2}{\log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.16, size = 91, normalized size = 2.84 \begin {gather*} \frac {1}{25} \left (675 x+1200 x^2+800 x^3+400 x^4-40 e^{2 x} \left (1+x+x^2\right )^2+e^{4 x} \left (1+x+x^2\right )^2+\frac {\left (-20+e^{2 x}\right )^2 x^2}{\log ^2(x)}+\frac {2 \left (-20+e^{2 x}\right )^2 x \left (1+x+x^2\right )}{\log (x)}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.52, size = 145, normalized size = 4.53 \begin {gather*} \frac {x^{2} e^{\left (4 \, x\right )} - 40 \, x^{2} e^{\left (2 \, x\right )} + {\left (400 \, x^{4} + 800 \, x^{3} + 1200 \, x^{2} + {\left (x^{4} + 2 \, x^{3} + 3 \, x^{2} + 2 \, x + 1\right )} e^{\left (4 \, x\right )} - 40 \, {\left (x^{4} + 2 \, x^{3} + 3 \, x^{2} + 2 \, x + 1\right )} e^{\left (2 \, x\right )} + 675 \, x\right )} \log \relax (x)^{2} + 400 \, x^{2} + 2 \, {\left (400 \, x^{3} + 400 \, x^{2} + {\left (x^{3} + x^{2} + x\right )} e^{\left (4 \, x\right )} - 40 \, {\left (x^{3} + x^{2} + x\right )} e^{\left (2 \, x\right )} + 400 \, x\right )} \log \relax (x)}{25 \, \log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.27, size = 294, normalized size = 9.19 \begin {gather*} 16 \, x^{4} + 32 \, x^{3} + 48 \, x^{2} + \frac {1}{800} \, {\left (32 \, x^{4} - 32 \, x^{3} + 24 \, x^{2} - 12 \, x + 3\right )} e^{\left (4 \, x\right )} + \frac {3}{800} \, {\left (32 \, x^{3} - 24 \, x^{2} + 12 \, x - 3\right )} e^{\left (4 \, x\right )} + \frac {9}{400} \, {\left (8 \, x^{2} - 4 \, x + 1\right )} e^{\left (4 \, x\right )} + \frac {7}{200} \, {\left (4 \, x - 1\right )} e^{\left (4 \, x\right )} - \frac {4}{5} \, {\left (2 \, x^{4} - 4 \, x^{3} + 6 \, x^{2} - 6 \, x + 3\right )} e^{\left (2 \, x\right )} - \frac {8}{5} \, {\left (4 \, x^{3} - 6 \, x^{2} + 6 \, x - 3\right )} e^{\left (2 \, x\right )} - \frac {24}{5} \, {\left (2 \, x^{2} - 2 \, x + 1\right )} e^{\left (2 \, x\right )} - 4 \, {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} + 27 \, x + \frac {2 \, x^{3} e^{\left (4 \, x\right )} \log \relax (x) - 80 \, x^{3} e^{\left (2 \, x\right )} \log \relax (x) + 2 \, x^{2} e^{\left (4 \, x\right )} \log \relax (x) - 80 \, x^{2} e^{\left (2 \, x\right )} \log \relax (x) + x^{2} e^{\left (4 \, x\right )} - 40 \, x^{2} e^{\left (2 \, x\right )} + 2 \, x e^{\left (4 \, x\right )} \log \relax (x) - 80 \, x e^{\left (2 \, x\right )} \log \relax (x)}{25 \, \log \relax (x)^{2}} + \frac {16 \, {\left (2 \, x^{3} \log \relax (x) + 2 \, x^{2} \log \relax (x) + x^{2} + 2 \, x \log \relax (x)\right )}}{\log \relax (x)^{2}} + \frac {3}{50} \, e^{\left (4 \, x\right )} - \frac {16}{5} \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.07, size = 196, normalized size = 6.12
method | result | size |
risch | \(\frac {x^{4} {\mathrm e}^{4 x}}{25}+\frac {2 x^{3} {\mathrm e}^{4 x}}{25}-\frac {8 \,{\mathrm e}^{2 x} x^{4}}{5}+\frac {3 x^{2} {\mathrm e}^{4 x}}{25}-\frac {16 \,{\mathrm e}^{2 x} x^{3}}{5}+\frac {2 x \,{\mathrm e}^{4 x}}{25}+16 x^{4}-\frac {24 \,{\mathrm e}^{2 x} x^{2}}{5}+\frac {{\mathrm e}^{4 x}}{25}+32 x^{3}-\frac {16 x \,{\mathrm e}^{2 x}}{5}+48 x^{2}-\frac {8 \,{\mathrm e}^{2 x}}{5}+27 x +\frac {x \left (2 \ln \relax (x ) {\mathrm e}^{4 x} x^{2}+2 x \,{\mathrm e}^{4 x} \ln \relax (x )-80 x^{2} {\mathrm e}^{2 x} \ln \relax (x )+x \,{\mathrm e}^{4 x}+2 \ln \relax (x ) {\mathrm e}^{4 x}-80 x \,{\mathrm e}^{2 x} \ln \relax (x )+800 x^{2} \ln \relax (x )-40 x \,{\mathrm e}^{2 x}-80 \ln \relax (x ) {\mathrm e}^{2 x}+800 x \ln \relax (x )+400 x +800 \ln \relax (x )\right )}{25 \ln \relax (x )^{2}}\) | \(196\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} 16 \, x^{4} + 32 \, x^{3} + 48 \, x^{2} + \frac {1}{800} \, {\left (32 \, x^{4} - 32 \, x^{3} + 24 \, x^{2} - 12 \, x + 3\right )} e^{\left (4 \, x\right )} + \frac {3}{800} \, {\left (32 \, x^{3} - 24 \, x^{2} + 12 \, x - 3\right )} e^{\left (4 \, x\right )} + \frac {9}{400} \, {\left (8 \, x^{2} - 4 \, x + 1\right )} e^{\left (4 \, x\right )} + \frac {7}{200} \, {\left (4 \, x - 1\right )} e^{\left (4 \, x\right )} - \frac {4}{5} \, {\left (2 \, x^{4} - 4 \, x^{3} + 6 \, x^{2} - 6 \, x + 3\right )} e^{\left (2 \, x\right )} - \frac {8}{5} \, {\left (4 \, x^{3} - 6 \, x^{2} + 6 \, x - 3\right )} e^{\left (2 \, x\right )} - \frac {24}{5} \, {\left (2 \, x^{2} - 2 \, x + 1\right )} e^{\left (2 \, x\right )} - 4 \, {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} + 27 \, x + \frac {{\left (x^{2} + 2 \, {\left (x^{3} + x^{2} + x\right )} \log \relax (x)\right )} e^{\left (4 \, x\right )} - 40 \, {\left (x^{2} + 2 \, {\left (x^{3} + x^{2} + x\right )} \log \relax (x)\right )} e^{\left (2 \, x\right )} + 800 \, {\left (x^{3} + x\right )} \log \relax (x)}{25 \, \log \relax (x)^{2}} + \frac {3}{50} \, e^{\left (4 \, x\right )} - \frac {16}{5} \, e^{\left (2 \, x\right )} + 128 \, \Gamma \left (-2, -2 \, \log \relax (x)\right ) + 64 \, \int \frac {x}{\log \relax (x)}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.21, size = 233, normalized size = 7.28 \begin {gather*} 27\,x-\frac {8\,{\mathrm {e}}^{2\,x}}{5}+\frac {{\mathrm {e}}^{4\,x}}{25}-\frac {16\,x\,{\mathrm {e}}^{2\,x}}{5}+\frac {2\,x\,{\mathrm {e}}^{4\,x}}{25}+\frac {32\,x}{\ln \relax (x)}-\frac {24\,x^2\,{\mathrm {e}}^{2\,x}}{5}-\frac {16\,x^3\,{\mathrm {e}}^{2\,x}}{5}+\frac {3\,x^2\,{\mathrm {e}}^{4\,x}}{25}-\frac {8\,x^4\,{\mathrm {e}}^{2\,x}}{5}+\frac {2\,x^3\,{\mathrm {e}}^{4\,x}}{25}+\frac {x^4\,{\mathrm {e}}^{4\,x}}{25}+\frac {32\,x^2}{\ln \relax (x)}+\frac {16\,x^2}{{\ln \relax (x)}^2}+\frac {32\,x^3}{\ln \relax (x)}+48\,x^2+32\,x^3+16\,x^4-\frac {16\,x\,{\mathrm {e}}^{2\,x}}{5\,\ln \relax (x)}+\frac {2\,x\,{\mathrm {e}}^{4\,x}}{25\,\ln \relax (x)}-\frac {16\,x^2\,{\mathrm {e}}^{2\,x}}{5\,\ln \relax (x)}-\frac {8\,x^2\,{\mathrm {e}}^{2\,x}}{5\,{\ln \relax (x)}^2}-\frac {16\,x^3\,{\mathrm {e}}^{2\,x}}{5\,\ln \relax (x)}+\frac {2\,x^2\,{\mathrm {e}}^{4\,x}}{25\,\ln \relax (x)}+\frac {x^2\,{\mathrm {e}}^{4\,x}}{25\,{\ln \relax (x)}^2}+\frac {2\,x^3\,{\mathrm {e}}^{4\,x}}{25\,\ln \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.55, size = 233, normalized size = 7.28 \begin {gather*} 16 x^{4} + 32 x^{3} + 48 x^{2} + 27 x + \frac {16 x^{2} + \left (32 x^{3} + 32 x^{2} + 32 x\right ) \log {\relax (x )}}{\log {\relax (x )}^{2}} + \frac {\left (- 200 x^{4} \log {\relax (x )}^{4} - 400 x^{3} \log {\relax (x )}^{4} - 400 x^{3} \log {\relax (x )}^{3} - 600 x^{2} \log {\relax (x )}^{4} - 400 x^{2} \log {\relax (x )}^{3} - 200 x^{2} \log {\relax (x )}^{2} - 400 x \log {\relax (x )}^{4} - 400 x \log {\relax (x )}^{3} - 200 \log {\relax (x )}^{4}\right ) e^{2 x} + \left (5 x^{4} \log {\relax (x )}^{4} + 10 x^{3} \log {\relax (x )}^{4} + 10 x^{3} \log {\relax (x )}^{3} + 15 x^{2} \log {\relax (x )}^{4} + 10 x^{2} \log {\relax (x )}^{3} + 5 x^{2} \log {\relax (x )}^{2} + 10 x \log {\relax (x )}^{4} + 10 x \log {\relax (x )}^{3} + 5 \log {\relax (x )}^{4}\right ) e^{4 x}}{125 \log {\relax (x )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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