Optimal. Leaf size=25 \[ \left (-\left (-2+e-e^{e^8}+x+x^2\right )^2+\log (1+x)\right )^2 \]
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Rubi [A] time = 1.24, antiderivative size = 29, normalized size of antiderivative = 1.16, number of steps used = 3, number of rules used = 3, integrand size = 279, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {6688, 12, 6686} \begin {gather*} \left (\left (-x^2-x+e^{e^8}-e+2\right )^2-\log (x+1)\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (5-2 e+2 e^{e^8}+2 \left (5-3 e+3 e^{e^8}\right ) x-4 \left (e-e^{e^8}\right ) x^2-10 x^3-4 x^4\right ) \left (-\left (-2+e-e^{e^8}+x+x^2\right )^2+\log (1+x)\right )}{1+x} \, dx\\ &=2 \int \frac {\left (5-2 e+2 e^{e^8}+2 \left (5-3 e+3 e^{e^8}\right ) x-4 \left (e-e^{e^8}\right ) x^2-10 x^3-4 x^4\right ) \left (-\left (-2+e-e^{e^8}+x+x^2\right )^2+\log (1+x)\right )}{1+x} \, dx\\ &=\left (\left (2-e+e^{e^8}-x-x^2\right )^2-\log (1+x)\right )^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 25, normalized size = 1.00 \begin {gather*} \left (\left (-2+e-e^{e^8}+x+x^2\right )^2-\log (1+x)\right )^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.64, size = 263, normalized size = 10.52 \begin {gather*} x^{8} + 4 \, x^{7} - 2 \, x^{6} - 20 \, x^{5} + x^{4} + 40 \, x^{3} - 8 \, x^{2} + 4 \, {\left (x^{2} + x\right )} e^{3} + 6 \, {\left (x^{4} + 2 \, x^{3} - 3 \, x^{2} - 4 \, x\right )} e^{2} + 4 \, {\left (x^{6} + 3 \, x^{5} - 3 \, x^{4} - 11 \, x^{3} + 6 \, x^{2} + 12 \, x\right )} e - 4 \, {\left (x^{2} + x\right )} e^{\left (3 \, e^{8}\right )} + 6 \, {\left (x^{4} + 2 \, x^{3} - 3 \, x^{2} + 2 \, {\left (x^{2} + x\right )} e - 4 \, x\right )} e^{\left (2 \, e^{8}\right )} - 4 \, {\left (x^{6} + 3 \, x^{5} - 3 \, x^{4} - 11 \, x^{3} + 6 \, x^{2} + 3 \, {\left (x^{2} + x\right )} e^{2} + 3 \, {\left (x^{4} + 2 \, x^{3} - 3 \, x^{2} - 4 \, x\right )} e + 12 \, x\right )} e^{\left (e^{8}\right )} - 2 \, {\left (x^{4} + 2 \, x^{3} - 3 \, x^{2} + 2 \, {\left (x^{2} + x - 2\right )} e - 2 \, {\left (x^{2} + x + e - 2\right )} e^{\left (e^{8}\right )} - 4 \, x + e^{2} + e^{\left (2 \, e^{8}\right )} + 4\right )} \log \left (x + 1\right ) + \log \left (x + 1\right )^{2} - 32 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.34, size = 428, normalized size = 17.12 \begin {gather*} x^{8} + 4 \, x^{7} + 4 \, x^{6} e - 4 \, x^{6} e^{\left (e^{8}\right )} - 2 \, x^{6} + 12 \, x^{5} e - 12 \, x^{5} e^{\left (e^{8}\right )} - 20 \, x^{5} + 6 \, x^{4} e^{2} - 12 \, x^{4} e + 6 \, x^{4} e^{\left (2 \, e^{8}\right )} - 12 \, x^{4} e^{\left (e^{8} + 1\right )} + 12 \, x^{4} e^{\left (e^{8}\right )} - 2 \, x^{4} \log \left (x + 1\right ) + x^{4} + 12 \, x^{3} e^{2} - 44 \, x^{3} e + 12 \, x^{3} e^{\left (2 \, e^{8}\right )} - 24 \, x^{3} e^{\left (e^{8} + 1\right )} + 44 \, x^{3} e^{\left (e^{8}\right )} - 4 \, x^{3} \log \left (x + 1\right ) - 4 \, x^{2} e \log \left (x + 1\right ) + 4 \, x^{2} e^{\left (e^{8}\right )} \log \left (x + 1\right ) + 40 \, x^{3} + 4 \, x^{2} e^{3} - 18 \, x^{2} e^{2} + 24 \, x^{2} e - 4 \, x^{2} e^{\left (3 \, e^{8}\right )} - 18 \, x^{2} e^{\left (2 \, e^{8}\right )} + 12 \, x^{2} e^{\left (2 \, e^{8} + 1\right )} - 12 \, x^{2} e^{\left (e^{8} + 2\right )} + 36 \, x^{2} e^{\left (e^{8} + 1\right )} - 24 \, x^{2} e^{\left (e^{8}\right )} + 6 \, x^{2} \log \left (x + 1\right ) - 4 \, x e \log \left (x + 1\right ) + 4 \, x e^{\left (e^{8}\right )} \log \left (x + 1\right ) - 8 \, x^{2} + 4 \, x e^{3} - 24 \, x e^{2} + 48 \, x e - 4 \, x e^{\left (3 \, e^{8}\right )} - 24 \, x e^{\left (2 \, e^{8}\right )} + 12 \, x e^{\left (2 \, e^{8} + 1\right )} - 12 \, x e^{\left (e^{8} + 2\right )} + 48 \, x e^{\left (e^{8} + 1\right )} - 48 \, x e^{\left (e^{8}\right )} + 8 \, x \log \left (x + 1\right ) - 2 \, e^{2} \log \left (x + 1\right ) + 8 \, e \log \left (x + 1\right ) - 2 \, e^{\left (2 \, e^{8}\right )} \log \left (x + 1\right ) + 4 \, e^{\left (e^{8} + 1\right )} \log \left (x + 1\right ) - 8 \, e^{\left (e^{8}\right )} \log \left (x + 1\right ) + \log \left (x + 1\right )^{2} - 32 \, x - 8 \, \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.29, size = 386, normalized size = 15.44
method | result | size |
norman | \(x^{8}+\ln \left (x +1\right )^{2}+\left (-20+12 \,{\mathrm e}-12 \,{\mathrm e}^{{\mathrm e}^{8}}\right ) x^{5}+\left (-2+4 \,{\mathrm e}-4 \,{\mathrm e}^{{\mathrm e}^{8}}\right ) x^{6}+\left (1-12 \,{\mathrm e}+12 \,{\mathrm e}^{{\mathrm e}^{8}}+6 \,{\mathrm e}^{2}+6 \,{\mathrm e}^{2 \,{\mathrm e}^{8}}-12 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}}\right ) x^{4}+\left (40-44 \,{\mathrm e}+44 \,{\mathrm e}^{{\mathrm e}^{8}}+12 \,{\mathrm e}^{2}+12 \,{\mathrm e}^{2 \,{\mathrm e}^{8}}-24 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}}\right ) x^{3}+\left (-2 \,{\mathrm e}^{2}+4 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}}-2 \,{\mathrm e}^{2 \,{\mathrm e}^{8}}+8 \,{\mathrm e}-8 \,{\mathrm e}^{{\mathrm e}^{8}}-8\right ) \ln \left (x +1\right )+\left (-32+48 \,{\mathrm e}-48 \,{\mathrm e}^{{\mathrm e}^{8}}-24 \,{\mathrm e}^{2}-24 \,{\mathrm e}^{2 \,{\mathrm e}^{8}}+48 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}}-4 \,{\mathrm e}^{3 \,{\mathrm e}^{8}}+4 \,{\mathrm e}^{3}-12 \,{\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{8}}+12 \,{\mathrm e} \,{\mathrm e}^{2 \,{\mathrm e}^{8}}\right ) x +\left (-8+24 \,{\mathrm e}-24 \,{\mathrm e}^{{\mathrm e}^{8}}-18 \,{\mathrm e}^{2}-18 \,{\mathrm e}^{2 \,{\mathrm e}^{8}}+36 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}}-4 \,{\mathrm e}^{3 \,{\mathrm e}^{8}}+4 \,{\mathrm e}^{3}-12 \,{\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{8}}+12 \,{\mathrm e} \,{\mathrm e}^{2 \,{\mathrm e}^{8}}\right ) x^{2}+\left (6-4 \,{\mathrm e}+4 \,{\mathrm e}^{{\mathrm e}^{8}}\right ) x^{2} \ln \left (x +1\right )+\left (8-4 \,{\mathrm e}+4 \,{\mathrm e}^{{\mathrm e}^{8}}\right ) x \ln \left (x +1\right )+4 x^{7}-4 \ln \left (x +1\right ) x^{3}-2 \ln \left (x +1\right ) x^{4}\) | \(386\) |
risch | \(-32 x -24 \,{\mathrm e}^{2} x +\ln \left (x +1\right )^{2}-8 \ln \left (x +1\right )+4 x^{7}+x^{8}-2 x^{6}-20 x^{5}+x^{4}+40 x^{3}-8 x^{2}+12 x^{5} {\mathrm e}+12 x^{3} {\mathrm e}^{2}-18 x^{2} {\mathrm e}^{2}+6 x^{4} {\mathrm e}^{2}+48 x \,{\mathrm e}+4 x \,{\mathrm e}^{3}+24 x^{2} {\mathrm e}-44 x^{3} {\mathrm e}+4 x^{2} {\mathrm e}^{3}-12 x^{4} {\mathrm e}+48 x \,{\mathrm e}^{1+{\mathrm e}^{8}}+36 x^{2} {\mathrm e}^{1+{\mathrm e}^{8}}+4 \ln \left (x +1\right ) {\mathrm e}^{1+{\mathrm e}^{8}}-24 x^{3} {\mathrm e}^{1+{\mathrm e}^{8}}-12 x \,{\mathrm e}^{2+{\mathrm e}^{8}}+12 x \,{\mathrm e}^{1+2 \,{\mathrm e}^{8}}-12 x^{2} {\mathrm e}^{2+{\mathrm e}^{8}}+12 x^{2} {\mathrm e}^{1+2 \,{\mathrm e}^{8}}-12 x^{4} {\mathrm e}^{1+{\mathrm e}^{8}}-2 \,{\mathrm e}^{2} \ln \left (x +1\right )-2 \ln \left (x +1\right ) {\mathrm e}^{2 \,{\mathrm e}^{8}}-8 \ln \left (x +1\right ) {\mathrm e}^{{\mathrm e}^{8}}-48 \,{\mathrm e}^{{\mathrm e}^{8}} x -24 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} x +\left (-2 x^{4}-4 x^{2} {\mathrm e}+4 \,{\mathrm e}^{{\mathrm e}^{8}} x^{2}-4 x^{3}-4 x \,{\mathrm e}+4 \,{\mathrm e}^{{\mathrm e}^{8}} x +6 x^{2}+8 x \right ) \ln \left (x +1\right )-24 \,{\mathrm e}^{{\mathrm e}^{8}} x^{2}-4 \,{\mathrm e}^{3 \,{\mathrm e}^{8}} x +44 \,{\mathrm e}^{{\mathrm e}^{8}} x^{3}+12 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} x^{3}+12 \,{\mathrm e}^{{\mathrm e}^{8}} x^{4}-12 \,{\mathrm e}^{{\mathrm e}^{8}} x^{5}-4 \,{\mathrm e}^{3 \,{\mathrm e}^{8}} x^{2}-4 \,{\mathrm e}^{{\mathrm e}^{8}} x^{6}+6 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} x^{4}-18 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} x^{2}+8 \,{\mathrm e} \ln \left (x +1\right )+4 x^{6} {\mathrm e}\) | \(403\) |
derivativedivides | \(32+32 x +\ln \left (x +1\right )^{2}+\left (x +1\right )^{4}-8 \left (x +1\right )^{2}-8 \ln \left (x +1\right )-2 \,{\mathrm e}^{2} \ln \left (x +1\right )-2 \ln \left (x +1\right ) {\mathrm e}^{2 \,{\mathrm e}^{8}}-8 \ln \left (x +1\right ) {\mathrm e}^{{\mathrm e}^{8}}+4 \ln \left (x +1\right ) \left (x +1\right )^{3}+22 \,{\mathrm e} \left (x +1\right )^{2}+4 \,{\mathrm e} \left (\left (x +1\right ) \ln \left (x +1\right )-x -1\right )+6 \ln \left (x +1\right ) \left (x +1\right )^{2}-8 \,{\mathrm e} \left (\frac {\ln \left (x +1\right ) \left (x +1\right )^{2}}{2}-\frac {\left (x +1\right )^{2}}{4}\right )+4 \,{\mathrm e} \left (x +1\right )^{6}-12 \,{\mathrm e} \left (x +1\right )^{5}-12 \,{\mathrm e} \left (x +1\right )^{4}-2 \ln \left (x +1\right ) \left (x +1\right )^{4}+44 \,{\mathrm e} \left (x +1\right )^{3}+8 \,{\mathrm e} \ln \left (x +1\right )-44 \left (x +1\right ) {\mathrm e}-8 \left (x +1\right ) \ln \left (x +1\right )+24 \left (x +1\right ) {\mathrm e}^{2}-4 \left (x +1\right ) {\mathrm e}^{3}+\left (x +1\right )^{8}-4 \left (x +1\right )^{7}-2 \left (x +1\right )^{6}+20 \left (x +1\right )^{5}-40 \left (x +1\right )^{3}-18 \,{\mathrm e}^{2} \left (x +1\right )^{2}+4 \,{\mathrm e}^{3 \,{\mathrm e}^{8}} \left (x +1\right )-18 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )^{2}-44 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{3}+24 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )-22 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{2}+44 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )-4 \,{\mathrm e}^{{\mathrm e}^{8}} \left (\left (x +1\right ) \ln \left (x +1\right )-x -1\right )+8 \,{\mathrm e}^{{\mathrm e}^{8}} \left (\frac {\ln \left (x +1\right ) \left (x +1\right )^{2}}{2}-\frac {\left (x +1\right )^{2}}{4}\right )-4 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{6}+6 \,{\mathrm e}^{2} \left (x +1\right )^{4}+6 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )^{4}+12 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{5}+4 \,{\mathrm e}^{3} \left (x +1\right )^{2}-12 \,{\mathrm e}^{2} \left (x +1\right )^{3}-4 \,{\mathrm e}^{3 \,{\mathrm e}^{8}} \left (x +1\right )^{2}-12 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )^{3}+12 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{4}-12 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{4}-12 \,{\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{2}+12 \,{\mathrm e} \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )^{2}+24 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{3}+12 \,{\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )-12 \,{\mathrm e} \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )+36 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{2}-48 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )+4 \,{\mathrm e} \ln \left (x +1\right ) {\mathrm e}^{{\mathrm e}^{8}}\) | \(624\) |
default | \(32+32 x +\ln \left (x +1\right )^{2}+\left (x +1\right )^{4}-8 \left (x +1\right )^{2}-8 \ln \left (x +1\right )-2 \,{\mathrm e}^{2} \ln \left (x +1\right )-2 \ln \left (x +1\right ) {\mathrm e}^{2 \,{\mathrm e}^{8}}-8 \ln \left (x +1\right ) {\mathrm e}^{{\mathrm e}^{8}}+4 \ln \left (x +1\right ) \left (x +1\right )^{3}+22 \,{\mathrm e} \left (x +1\right )^{2}+4 \,{\mathrm e} \left (\left (x +1\right ) \ln \left (x +1\right )-x -1\right )+6 \ln \left (x +1\right ) \left (x +1\right )^{2}-8 \,{\mathrm e} \left (\frac {\ln \left (x +1\right ) \left (x +1\right )^{2}}{2}-\frac {\left (x +1\right )^{2}}{4}\right )+4 \,{\mathrm e} \left (x +1\right )^{6}-12 \,{\mathrm e} \left (x +1\right )^{5}-12 \,{\mathrm e} \left (x +1\right )^{4}-2 \ln \left (x +1\right ) \left (x +1\right )^{4}+44 \,{\mathrm e} \left (x +1\right )^{3}+8 \,{\mathrm e} \ln \left (x +1\right )-44 \left (x +1\right ) {\mathrm e}-8 \left (x +1\right ) \ln \left (x +1\right )+24 \left (x +1\right ) {\mathrm e}^{2}-4 \left (x +1\right ) {\mathrm e}^{3}+\left (x +1\right )^{8}-4 \left (x +1\right )^{7}-2 \left (x +1\right )^{6}+20 \left (x +1\right )^{5}-40 \left (x +1\right )^{3}-18 \,{\mathrm e}^{2} \left (x +1\right )^{2}+4 \,{\mathrm e}^{3 \,{\mathrm e}^{8}} \left (x +1\right )-18 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )^{2}-44 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{3}+24 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )-22 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{2}+44 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )-4 \,{\mathrm e}^{{\mathrm e}^{8}} \left (\left (x +1\right ) \ln \left (x +1\right )-x -1\right )+8 \,{\mathrm e}^{{\mathrm e}^{8}} \left (\frac {\ln \left (x +1\right ) \left (x +1\right )^{2}}{2}-\frac {\left (x +1\right )^{2}}{4}\right )-4 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{6}+6 \,{\mathrm e}^{2} \left (x +1\right )^{4}+6 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )^{4}+12 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{5}+4 \,{\mathrm e}^{3} \left (x +1\right )^{2}-12 \,{\mathrm e}^{2} \left (x +1\right )^{3}-4 \,{\mathrm e}^{3 \,{\mathrm e}^{8}} \left (x +1\right )^{2}-12 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )^{3}+12 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{4}-12 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{4}-12 \,{\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{2}+12 \,{\mathrm e} \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )^{2}+24 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{3}+12 \,{\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )-12 \,{\mathrm e} \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )+36 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{2}-48 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )+4 \,{\mathrm e} \ln \left (x +1\right ) {\mathrm e}^{{\mathrm e}^{8}}\) | \(624\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.59, size = 1065, normalized size = 42.60 result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.72, size = 428, normalized size = 17.12 \begin {gather*} 48\,x\,{\mathrm {e}}^{{\mathrm {e}}^8+1}-8\,\ln \left (x+1\right )-24\,x\,{\mathrm {e}}^{2\,{\mathrm {e}}^8}-4\,x\,{\mathrm {e}}^{3\,{\mathrm {e}}^8}-32\,x-12\,x\,{\mathrm {e}}^{{\mathrm {e}}^8+2}-24\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^8}+44\,x^3\,{\mathrm {e}}^{{\mathrm {e}}^8}+12\,x^4\,{\mathrm {e}}^{{\mathrm {e}}^8}-12\,x^5\,{\mathrm {e}}^{{\mathrm {e}}^8}-4\,x^6\,{\mathrm {e}}^{{\mathrm {e}}^8}+8\,\ln \left (x+1\right )\,\mathrm {e}-2\,\ln \left (x+1\right )\,{\mathrm {e}}^2+8\,x\,\ln \left (x+1\right )+48\,x\,\mathrm {e}-24\,x\,{\mathrm {e}}^2+4\,x\,{\mathrm {e}}^3+12\,x\,{\mathrm {e}}^{2\,{\mathrm {e}}^8+1}-18\,x^2\,{\mathrm {e}}^{2\,{\mathrm {e}}^8}-4\,x^2\,{\mathrm {e}}^{3\,{\mathrm {e}}^8}+12\,x^3\,{\mathrm {e}}^{2\,{\mathrm {e}}^8}+6\,x^4\,{\mathrm {e}}^{2\,{\mathrm {e}}^8}+36\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^8+1}-12\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^8+2}-24\,x^3\,{\mathrm {e}}^{{\mathrm {e}}^8+1}-12\,x^4\,{\mathrm {e}}^{{\mathrm {e}}^8+1}-8\,\ln \left (x+1\right )\,{\mathrm {e}}^{{\mathrm {e}}^8}+6\,x^2\,\ln \left (x+1\right )-4\,x^3\,\ln \left (x+1\right )-2\,x^4\,\ln \left (x+1\right )+24\,x^2\,\mathrm {e}-18\,x^2\,{\mathrm {e}}^2-44\,x^3\,\mathrm {e}+4\,x^2\,{\mathrm {e}}^3+12\,x^3\,{\mathrm {e}}^2-12\,x^4\,\mathrm {e}+6\,x^4\,{\mathrm {e}}^2+12\,x^5\,\mathrm {e}+4\,x^6\,\mathrm {e}-48\,x\,{\mathrm {e}}^{{\mathrm {e}}^8}+{\ln \left (x+1\right )}^2+12\,x^2\,{\mathrm {e}}^{2\,{\mathrm {e}}^8+1}-2\,\ln \left (x+1\right )\,{\mathrm {e}}^{2\,{\mathrm {e}}^8}+4\,\ln \left (x+1\right )\,{\mathrm {e}}^{{\mathrm {e}}^8+1}-8\,x^2+40\,x^3+x^4-20\,x^5-2\,x^6+4\,x^7+x^8+4\,x^2\,\ln \left (x+1\right )\,{\mathrm {e}}^{{\mathrm {e}}^8}-4\,x\,\ln \left (x+1\right )\,\mathrm {e}-4\,x^2\,\ln \left (x+1\right )\,\mathrm {e}+4\,x\,\ln \left (x+1\right )\,{\mathrm {e}}^{{\mathrm {e}}^8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.97, size = 357, normalized size = 14.28 \begin {gather*} x^{8} + 4 x^{7} + x^{6} \left (-2 + 4 e - 4 e^{e^{8}}\right ) + x^{5} \left (-20 + 12 e - 12 e^{e^{8}}\right ) + x^{4} \left (- 12 e + 1 + 6 e^{2} + 6 e^{2 e^{8}} + 12 e^{e^{8}} - 12 e e^{e^{8}}\right ) + x^{3} \left (- 44 e + 40 + 12 e^{2} + 12 e^{2 e^{8}} + 44 e^{e^{8}} - 24 e e^{e^{8}}\right ) + x^{2} \left (- 18 e^{2} - 8 + 24 e + 4 e^{3} - 24 e^{e^{8}} - 18 e^{2 e^{8}} - 4 e^{3 e^{8}} - 12 e^{2} e^{e^{8}} + 12 e e^{2 e^{8}} + 36 e e^{e^{8}}\right ) + x \left (- 24 e^{2} - 32 + 4 e^{3} + 48 e - 48 e^{e^{8}} - 24 e^{2 e^{8}} - 4 e^{3 e^{8}} - 12 e^{2} e^{e^{8}} + 12 e e^{2 e^{8}} + 48 e e^{e^{8}}\right ) + \left (- 2 x^{4} - 4 x^{3} - 4 e x^{2} + 6 x^{2} + 4 x^{2} e^{e^{8}} - 4 e x + 8 x + 4 x e^{e^{8}}\right ) \log {\left (x + 1 \right )} + \log {\left (x + 1 \right )}^{2} - 2 \left (-2 + e - e^{e^{8}}\right )^{2} \log {\left (x + 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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