3.26.31 \(\int \frac {-8 e^{2 x}+e^{e^{e^5}+2 x} (10-30 x+10 x^2)+(-16 e^{2 x}+e^{e^{e^5}+2 x} (70-80 x+20 x^2)) \log (\frac {1}{5} (4+e^{e^{e^5}} (-30+25 x-5 x^2)))+(-8 e^{2 x}+e^{e^{e^5}+2 x} (60-50 x+10 x^2)) \log ^2(\frac {1}{5} (4+e^{e^{e^5}} (-30+25 x-5 x^2)))}{-4+e^{e^{e^5}} (30-25 x+5 x^2)} \, dx\)

Optimal. Leaf size=31 \[ e^{2 x} \left (1+\log \left (\frac {4}{5}+e^{e^{e^5}} (2-x) (-3+x)\right )\right )^2 \]

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Rubi [F]  time = 50.57, 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 {-8 e^{2 x}+e^{e^{e^5}+2 x} \left (10-30 x+10 x^2\right )+\left (-16 e^{2 x}+e^{e^{e^5}+2 x} \left (70-80 x+20 x^2\right )\right ) \log \left (\frac {1}{5} \left (4+e^{e^{e^5}} \left (-30+25 x-5 x^2\right )\right )\right )+\left (-8 e^{2 x}+e^{e^{e^5}+2 x} \left (60-50 x+10 x^2\right )\right ) \log ^2\left (\frac {1}{5} \left (4+e^{e^{e^5}} \left (-30+25 x-5 x^2\right )\right )\right )}{-4+e^{e^{e^5}} \left (30-25 x+5 x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-8*E^(2*x) + E^(E^E^5 + 2*x)*(10 - 30*x + 10*x^2) + (-16*E^(2*x) + E^(E^E^5 + 2*x)*(70 - 80*x + 20*x^2))*
Log[(4 + E^E^E^5*(-30 + 25*x - 5*x^2))/5] + (-8*E^(2*x) + E^(E^E^5 + 2*x)*(60 - 50*x + 10*x^2))*Log[(4 + E^E^E
^5*(-30 + 25*x - 5*x^2))/5]^2)/(-4 + E^E^E^5*(30 - 25*x + 5*x^2)),x]

[Out]

E^(2*x) + 2*E^(2*x)*Log[(2*(2 - 15*E^E^E^5))/5 + 5*E^E^E^5*x - E^E^E^5*x^2] + 2*E^(5 - Sqrt[16/5 + E^E^E^5]/E^
(E^E^5/2))*ExpIntegralEi[-1/5*(25*E^E^E^5 - E^(E^E^5/2)*Sqrt[80 + 25*E^E^E^5] - 10*E^E^E^5*x)/E^E^E^5]*Log[(2*
(2 - 15*E^E^E^5))/5 + 5*E^E^E^5*x - E^E^E^5*x^2] + 2*E^(5 + Sqrt[16/5 + E^E^E^5]/E^(E^E^5/2))*ExpIntegralEi[-1
/5*(25*E^E^E^5 + E^(E^E^5/2)*Sqrt[80 + 25*E^E^E^5] - 10*E^E^E^5*x)/E^E^E^5]*Log[(2*(2 - 15*E^E^E^5))/5 + 5*E^E
^E^5*x - E^E^E^5*x^2] - (100*E^(5 + (3*E^E^5)/2 + Sqrt[16/5 + E^E^E^5]/E^(E^E^5/2))*Defer[Int][ExpIntegralEi[-
5 - Sqrt[16/5 + E^E^E^5]/E^(E^E^5/2) + 2*x]/(25*E^E^E^5 + E^(E^E^5/2)*Sqrt[5*(16 + 5*E^E^E^5)] - 10*E^E^E^5*x)
, x])/Sqrt[(16 + 5*E^E^E^5)/5] - 20*E^(5 + E^E^5 + Sqrt[16/5 + E^E^E^5]/E^(E^E^5/2))*(1 + (5*E^(E^E^5/2))/Sqrt
[16/5 + E^E^E^5])*Defer[Int][ExpIntegralEi[-5 - Sqrt[16/5 + E^E^E^5]/E^(E^E^5/2) + 2*x]/(-25*E^E^E^5 - E^(E^E^
5/2)*Sqrt[5*(16 + 5*E^E^E^5)] + 10*E^E^E^5*x), x] - (100*E^(5 + (3*E^E^5)/2 + Sqrt[16/5 + E^E^E^5]/E^(E^E^5/2)
)*Defer[Int][ExpIntegralEi[-5 - Sqrt[16/5 + E^E^E^5]/E^(E^E^5/2) + 2*x]/(-25*E^E^E^5 + E^(E^E^5/2)*Sqrt[5*(16
+ 5*E^E^E^5)] + 10*E^E^E^5*x), x])/Sqrt[(16 + 5*E^E^E^5)/5] - 20*E^(5 + E^E^5 + Sqrt[16/5 + E^E^E^5]/E^(E^E^5/
2))*(1 - (5*E^(E^E^5/2))/Sqrt[16/5 + E^E^E^5])*Defer[Int][ExpIntegralEi[-5 - Sqrt[16/5 + E^E^E^5]/E^(E^E^5/2)
+ 2*x]/(-25*E^E^E^5 + E^(E^E^5/2)*Sqrt[5*(16 + 5*E^E^E^5)] + 10*E^E^E^5*x), x] - (100*E^(5 + (3*E^E^5)/2 - Sqr
t[16/5 + E^E^E^5]/E^(E^E^5/2))*Defer[Int][ExpIntegralEi[-5 + Sqrt[16/5 + E^E^E^5]/E^(E^E^5/2) + 2*x]/(25*E^E^E
^5 + E^(E^E^5/2)*Sqrt[5*(16 + 5*E^E^E^5)] - 10*E^E^E^5*x), x])/Sqrt[(16 + 5*E^E^E^5)/5] - 20*E^(5 + E^E^5 - Sq
rt[16/5 + E^E^E^5]/E^(E^E^5/2))*(1 + (5*E^(E^E^5/2))/Sqrt[16/5 + E^E^E^5])*Defer[Int][ExpIntegralEi[-5 + Sqrt[
16/5 + E^E^E^5]/E^(E^E^5/2) + 2*x]/(-25*E^E^E^5 - E^(E^E^5/2)*Sqrt[5*(16 + 5*E^E^E^5)] + 10*E^E^E^5*x), x] - (
100*E^(5 + (3*E^E^5)/2 - Sqrt[16/5 + E^E^E^5]/E^(E^E^5/2))*Defer[Int][ExpIntegralEi[-5 + Sqrt[16/5 + E^E^E^5]/
E^(E^E^5/2) + 2*x]/(-25*E^E^E^5 + E^(E^E^5/2)*Sqrt[5*(16 + 5*E^E^E^5)] + 10*E^E^E^5*x), x])/Sqrt[(16 + 5*E^E^E
^5)/5] - 20*E^(5 + E^E^5 - Sqrt[16/5 + E^E^E^5]/E^(E^E^5/2))*(1 - (5*E^(E^E^5/2))/Sqrt[16/5 + E^E^E^5])*Defer[
Int][ExpIntegralEi[-5 + Sqrt[16/5 + E^E^E^5]/E^(E^E^5/2) + 2*x]/(-25*E^E^E^5 + E^(E^E^5/2)*Sqrt[5*(16 + 5*E^E^
E^5)] + 10*E^E^E^5*x), x] + 2*Defer[Int][E^(2*x)*Log[(2*(2 - 15*E^E^E^5))/5 + 5*E^E^E^5*x - E^E^E^5*x^2]^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {8 e^{2 x}-e^{e^{e^5}+2 x} \left (10-30 x+10 x^2\right )-\left (-16 e^{2 x}+e^{e^{e^5}+2 x} \left (70-80 x+20 x^2\right )\right ) \log \left (\frac {1}{5} \left (4+e^{e^{e^5}} \left (-30+25 x-5 x^2\right )\right )\right )-\left (-8 e^{2 x}+e^{e^{e^5}+2 x} \left (60-50 x+10 x^2\right )\right ) \log ^2\left (\frac {1}{5} \left (4+e^{e^{e^5}} \left (-30+25 x-5 x^2\right )\right )\right )}{2 \left (2-15 e^{e^{e^5}}\right )+25 e^{e^{e^5}} x-5 e^{e^{e^5}} x^2} \, dx\\ &=\int \frac {2 e^{2 x} \left (1+\log \left (\frac {4}{5}-e^{e^{e^5}} \left (6-5 x+x^2\right )\right )\right ) \left (4-5 e^{e^{e^5}} \left (1-3 x+x^2\right )-\left (-4+5 e^{e^{e^5}} \left (6-5 x+x^2\right )\right ) \log \left (\frac {4}{5}-e^{e^{e^5}} \left (6-5 x+x^2\right )\right )\right )}{2 \left (2-15 e^{e^{e^5}}\right )+25 e^{e^{e^5}} x-5 e^{e^{e^5}} x^2} \, dx\\ &=2 \int \frac {e^{2 x} \left (1+\log \left (\frac {4}{5}-e^{e^{e^5}} \left (6-5 x+x^2\right )\right )\right ) \left (4-5 e^{e^{e^5}} \left (1-3 x+x^2\right )-\left (-4+5 e^{e^{e^5}} \left (6-5 x+x^2\right )\right ) \log \left (\frac {4}{5}-e^{e^{e^5}} \left (6-5 x+x^2\right )\right )\right )}{2 \left (2-15 e^{e^{e^5}}\right )+25 e^{e^{e^5}} x-5 e^{e^{e^5}} x^2} \, dx\\ &=2 \int \left (\frac {e^{2 x} \left (4-5 e^{e^{e^5}}+15 e^{e^{e^5}} x-5 e^{e^{e^5}} x^2\right )}{2 \left (2-15 e^{e^{e^5}}\right )+25 e^{e^{e^5}} x-5 e^{e^{e^5}} x^2}+\frac {e^{2 x} \left (8-35 e^{e^{e^5}}+40 e^{e^{e^5}} x-10 e^{e^{e^5}} x^2\right ) \log \left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right )}{2 \left (2-15 e^{e^{e^5}}\right )+25 e^{e^{e^5}} x-5 e^{e^{e^5}} x^2}+e^{2 x} \log ^2\left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right )\right ) \, dx\\ &=2 \int \frac {e^{2 x} \left (4-5 e^{e^{e^5}}+15 e^{e^{e^5}} x-5 e^{e^{e^5}} x^2\right )}{2 \left (2-15 e^{e^{e^5}}\right )+25 e^{e^{e^5}} x-5 e^{e^{e^5}} x^2} \, dx+2 \int \frac {e^{2 x} \left (8-35 e^{e^{e^5}}+40 e^{e^{e^5}} x-10 e^{e^{e^5}} x^2\right ) \log \left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right )}{2 \left (2-15 e^{e^{e^5}}\right )+25 e^{e^{e^5}} x-5 e^{e^{e^5}} x^2} \, dx+2 \int e^{2 x} \log ^2\left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right ) \, dx\\ &=2 e^{2 x} \log \left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right )+2 e^{5-e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}} \text {Ei}\left (-\frac {1}{5} e^{-e^{e^5}} \left (25 e^{e^{e^5}}-e^{\frac {e^{e^5}}{2}} \sqrt {80+25 e^{e^{e^5}}}-10 e^{e^{e^5}} x\right )\right ) \log \left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right )+2 e^{5+e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}} \text {Ei}\left (-\frac {1}{5} e^{-e^{e^5}} \left (25 e^{e^{e^5}}+e^{\frac {e^{e^5}}{2}} \sqrt {80+25 e^{e^{e^5}}}-10 e^{e^{e^5}} x\right )\right ) \log \left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right )+2 \int \left (e^{2 x}+\frac {5 e^{e^{e^5}+2 x} (5-2 x)}{2 \left (2-15 e^{e^{e^5}}\right )+25 e^{e^{e^5}} x-5 e^{e^{e^5}} x^2}\right ) \, dx-2 \int \frac {5 e^{e^{e^5}-e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}} (5-2 x) \left (e^{e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}+2 x}+e^{5+2 e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}} \text {Ei}\left (-5-e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}+2 x\right )+e^5 \text {Ei}\left (-5+e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}+2 x\right )\right )}{2 \left (2-15 e^{e^{e^5}}\right )+25 e^{e^{e^5}} x-5 e^{e^{e^5}} x^2} \, dx+2 \int e^{2 x} \log ^2\left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right ) \, dx\\ &=2 e^{2 x} \log \left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right )+2 e^{5-e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}} \text {Ei}\left (-\frac {1}{5} e^{-e^{e^5}} \left (25 e^{e^{e^5}}-e^{\frac {e^{e^5}}{2}} \sqrt {80+25 e^{e^{e^5}}}-10 e^{e^{e^5}} x\right )\right ) \log \left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right )+2 e^{5+e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}} \text {Ei}\left (-\frac {1}{5} e^{-e^{e^5}} \left (25 e^{e^{e^5}}+e^{\frac {e^{e^5}}{2}} \sqrt {80+25 e^{e^{e^5}}}-10 e^{e^{e^5}} x\right )\right ) \log \left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right )+2 \int e^{2 x} \, dx+2 \int e^{2 x} \log ^2\left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right ) \, dx+10 \int \frac {e^{e^{e^5}+2 x} (5-2 x)}{2 \left (2-15 e^{e^{e^5}}\right )+25 e^{e^{e^5}} x-5 e^{e^{e^5}} x^2} \, dx-\left (10 e^{e^{e^5}-e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}}\right ) \int \frac {(5-2 x) \left (e^{e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}+2 x}+e^{5+2 e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}} \text {Ei}\left (-5-e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}+2 x\right )+e^5 \text {Ei}\left (-5+e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}+2 x\right )\right )}{2 \left (2-15 e^{e^{e^5}}\right )+25 e^{e^{e^5}} x-5 e^{e^{e^5}} x^2} \, dx\\ &=e^{2 x}+2 e^{2 x} \log \left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right )+2 e^{5-e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}} \text {Ei}\left (-\frac {1}{5} e^{-e^{e^5}} \left (25 e^{e^{e^5}}-e^{\frac {e^{e^5}}{2}} \sqrt {80+25 e^{e^{e^5}}}-10 e^{e^{e^5}} x\right )\right ) \log \left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right )+2 e^{5+e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}} \text {Ei}\left (-\frac {1}{5} e^{-e^{e^5}} \left (25 e^{e^{e^5}}+e^{\frac {e^{e^5}}{2}} \sqrt {80+25 e^{e^{e^5}}}-10 e^{e^{e^5}} x\right )\right ) \log \left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right )+2 \int e^{2 x} \log ^2\left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right ) \, dx+10 \int \left (-\frac {2 e^{e^{e^5}+2 x}}{25 e^{e^{e^5}}-e^{\frac {e^{e^5}}{2}} \sqrt {5 \left (16+5 e^{e^{e^5}}\right )}-10 e^{e^{e^5}} x}-\frac {2 e^{e^{e^5}+2 x}}{25 e^{e^{e^5}}+e^{\frac {e^{e^5}}{2}} \sqrt {5 \left (16+5 e^{e^{e^5}}\right )}-10 e^{e^{e^5}} x}\right ) \, dx-\left (10 e^{e^{e^5}-e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}}\right ) \int \left (\frac {e^{e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {1}{5} \left (16+5 e^{e^{e^5}}\right )}+2 x} (5-2 x)}{2 \left (2-15 e^{e^{e^5}}\right )+25 e^{e^{e^5}} x-5 e^{e^{e^5}} x^2}+\frac {e^5 (5-2 x) \left (e^{2 e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {1}{5} \left (16+5 e^{e^{e^5}}\right )}} \text {Ei}\left (-5-e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}+2 x\right )+\text {Ei}\left (-5+e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}+2 x\right )\right )}{2 \left (2-15 e^{e^{e^5}}\right )+25 e^{e^{e^5}} x-5 e^{e^{e^5}} x^2}\right ) \, dx\\ &=e^{2 x}+2 e^{2 x} \log \left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right )+2 e^{5-e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}} \text {Ei}\left (-\frac {1}{5} e^{-e^{e^5}} \left (25 e^{e^{e^5}}-e^{\frac {e^{e^5}}{2}} \sqrt {80+25 e^{e^{e^5}}}-10 e^{e^{e^5}} x\right )\right ) \log \left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right )+2 e^{5+e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}} \text {Ei}\left (-\frac {1}{5} e^{-e^{e^5}} \left (25 e^{e^{e^5}}+e^{\frac {e^{e^5}}{2}} \sqrt {80+25 e^{e^{e^5}}}-10 e^{e^{e^5}} x\right )\right ) \log \left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right )+2 \int e^{2 x} \log ^2\left (\frac {2}{5} \left (2-15 e^{e^{e^5}}\right )+5 e^{e^{e^5}} x-e^{e^{e^5}} x^2\right ) \, dx-20 \int \frac {e^{e^{e^5}+2 x}}{25 e^{e^{e^5}}-e^{\frac {e^{e^5}}{2}} \sqrt {5 \left (16+5 e^{e^{e^5}}\right )}-10 e^{e^{e^5}} x} \, dx-20 \int \frac {e^{e^{e^5}+2 x}}{25 e^{e^{e^5}}+e^{\frac {e^{e^5}}{2}} \sqrt {5 \left (16+5 e^{e^{e^5}}\right )}-10 e^{e^{e^5}} x} \, dx-\left (10 e^{e^{e^5}-e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}}\right ) \int \frac {e^{e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {1}{5} \left (16+5 e^{e^{e^5}}\right )}+2 x} (5-2 x)}{2 \left (2-15 e^{e^{e^5}}\right )+25 e^{e^{e^5}} x-5 e^{e^{e^5}} x^2} \, dx-\left (10 e^{5+e^{e^5}-e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}}\right ) \int \frac {(5-2 x) \left (e^{2 e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {1}{5} \left (16+5 e^{e^{e^5}}\right )}} \text {Ei}\left (-5-e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}+2 x\right )+\text {Ei}\left (-5+e^{-\frac {e^{e^5}}{2}} \sqrt {\frac {16}{5}+e^{e^{e^5}}}+2 x\right )\right )}{2 \left (2-15 e^{e^{e^5}}\right )+25 e^{e^{e^5}} x-5 e^{e^{e^5}} x^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.14, size = 32, normalized size = 1.03 \begin {gather*} e^{2 x} \left (1+\log \left (\frac {4}{5}-e^{e^{e^5}} \left (6-5 x+x^2\right )\right )\right )^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-8*E^(2*x) + E^(E^E^5 + 2*x)*(10 - 30*x + 10*x^2) + (-16*E^(2*x) + E^(E^E^5 + 2*x)*(70 - 80*x + 20*
x^2))*Log[(4 + E^E^E^5*(-30 + 25*x - 5*x^2))/5] + (-8*E^(2*x) + E^(E^E^5 + 2*x)*(60 - 50*x + 10*x^2))*Log[(4 +
E^E^E^5*(-30 + 25*x - 5*x^2))/5]^2)/(-4 + E^E^E^5*(30 - 25*x + 5*x^2)),x]

[Out]

E^(2*x)*(1 + Log[4/5 - E^E^E^5*(6 - 5*x + x^2)])^2

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fricas [B]  time = 0.60, size = 52, normalized size = 1.68 \begin {gather*} e^{\left (2 \, x\right )} \log \left (-{\left (x^{2} - 5 \, x + 6\right )} e^{\left (e^{\left (e^{5}\right )}\right )} + \frac {4}{5}\right )^{2} + 2 \, e^{\left (2 \, x\right )} \log \left (-{\left (x^{2} - 5 \, x + 6\right )} e^{\left (e^{\left (e^{5}\right )}\right )} + \frac {4}{5}\right ) + e^{\left (2 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((10*x^2-50*x+60)*exp(x)^2*exp(exp(exp(5)))-8*exp(x)^2)*log(1/5*(-5*x^2+25*x-30)*exp(exp(exp(5)))+4
/5)^2+((20*x^2-80*x+70)*exp(x)^2*exp(exp(exp(5)))-16*exp(x)^2)*log(1/5*(-5*x^2+25*x-30)*exp(exp(exp(5)))+4/5)+
(10*x^2-30*x+10)*exp(x)^2*exp(exp(exp(5)))-8*exp(x)^2)/((5*x^2-25*x+30)*exp(exp(exp(5)))-4),x, algorithm="fric
as")

[Out]

e^(2*x)*log(-(x^2 - 5*x + 6)*e^(e^(e^5)) + 4/5)^2 + 2*e^(2*x)*log(-(x^2 - 5*x + 6)*e^(e^(e^5)) + 4/5) + e^(2*x
)

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giac [B]  time = 0.40, size = 118, normalized size = 3.81 \begin {gather*} e^{\left (2 \, x\right )} \log \relax (5)^{2} - 2 \, e^{\left (2 \, x\right )} \log \relax (5) \log \left (-5 \, x^{2} e^{\left (e^{\left (e^{5}\right )}\right )} + 25 \, x e^{\left (e^{\left (e^{5}\right )}\right )} - 30 \, e^{\left (e^{\left (e^{5}\right )}\right )} + 4\right ) + e^{\left (2 \, x\right )} \log \left (-5 \, x^{2} e^{\left (e^{\left (e^{5}\right )}\right )} + 25 \, x e^{\left (e^{\left (e^{5}\right )}\right )} - 30 \, e^{\left (e^{\left (e^{5}\right )}\right )} + 4\right )^{2} - 2 \, e^{\left (2 \, x\right )} \log \relax (5) + 2 \, e^{\left (2 \, x\right )} \log \left (-5 \, x^{2} e^{\left (e^{\left (e^{5}\right )}\right )} + 25 \, x e^{\left (e^{\left (e^{5}\right )}\right )} - 30 \, e^{\left (e^{\left (e^{5}\right )}\right )} + 4\right ) + e^{\left (2 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((10*x^2-50*x+60)*exp(x)^2*exp(exp(exp(5)))-8*exp(x)^2)*log(1/5*(-5*x^2+25*x-30)*exp(exp(exp(5)))+4
/5)^2+((20*x^2-80*x+70)*exp(x)^2*exp(exp(exp(5)))-16*exp(x)^2)*log(1/5*(-5*x^2+25*x-30)*exp(exp(exp(5)))+4/5)+
(10*x^2-30*x+10)*exp(x)^2*exp(exp(exp(5)))-8*exp(x)^2)/((5*x^2-25*x+30)*exp(exp(exp(5)))-4),x, algorithm="giac
")

[Out]

e^(2*x)*log(5)^2 - 2*e^(2*x)*log(5)*log(-5*x^2*e^(e^(e^5)) + 25*x*e^(e^(e^5)) - 30*e^(e^(e^5)) + 4) + e^(2*x)*
log(-5*x^2*e^(e^(e^5)) + 25*x*e^(e^(e^5)) - 30*e^(e^(e^5)) + 4)^2 - 2*e^(2*x)*log(5) + 2*e^(2*x)*log(-5*x^2*e^
(e^(e^5)) + 25*x*e^(e^(e^5)) - 30*e^(e^(e^5)) + 4) + e^(2*x)

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maple [B]  time = 4.30, size = 57, normalized size = 1.84

method	result	size
risch	\({\mathrm e}^{2 x} \ln \left (\frac {\left (-5 x^{2}+25 x -30\right ) {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{5}}}}{5}+\frac {4}{5}\right )^{2}+2 \,{\mathrm e}^{2 x} \ln \left (\frac {\left (-5 x^{2}+25 x -30\right ) {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{5}}}}{5}+\frac {4}{5}\right )+{\mathrm e}^{2 x}\)	\(57\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((10*x^2-50*x+60)*exp(x)^2*exp(exp(exp(5)))-8*exp(x)^2)*ln(1/5*(-5*x^2+25*x-30)*exp(exp(exp(5)))+4/5)^2+(
(20*x^2-80*x+70)*exp(x)^2*exp(exp(exp(5)))-16*exp(x)^2)*ln(1/5*(-5*x^2+25*x-30)*exp(exp(exp(5)))+4/5)+(10*x^2-
30*x+10)*exp(x)^2*exp(exp(exp(5)))-8*exp(x)^2)/((5*x^2-25*x+30)*exp(exp(exp(5)))-4),x,method=_RETURNVERBOSE)

[Out]

exp(2*x)*ln(1/5*(-5*x^2+25*x-30)*exp(exp(exp(5)))+4/5)^2+2*exp(2*x)*ln(1/5*(-5*x^2+25*x-30)*exp(exp(exp(5)))+4
/5)+exp(2*x)

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maxima [B]  time = 0.60, size = 83, normalized size = 2.68 \begin {gather*} -2 \, {\left (\log \relax (5) - 1\right )} e^{\left (2 \, x\right )} \log \left (-5 \, x^{2} e^{\left (e^{\left (e^{5}\right )}\right )} + 25 \, x e^{\left (e^{\left (e^{5}\right )}\right )} - 30 \, e^{\left (e^{\left (e^{5}\right )}\right )} + 4\right ) + e^{\left (2 \, x\right )} \log \left (-5 \, x^{2} e^{\left (e^{\left (e^{5}\right )}\right )} + 25 \, x e^{\left (e^{\left (e^{5}\right )}\right )} - 30 \, e^{\left (e^{\left (e^{5}\right )}\right )} + 4\right )^{2} + {\left (\log \relax (5)^{2} - 2 \, \log \relax (5) + 1\right )} e^{\left (2 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((10*x^2-50*x+60)*exp(x)^2*exp(exp(exp(5)))-8*exp(x)^2)*log(1/5*(-5*x^2+25*x-30)*exp(exp(exp(5)))+4
/5)^2+((20*x^2-80*x+70)*exp(x)^2*exp(exp(exp(5)))-16*exp(x)^2)*log(1/5*(-5*x^2+25*x-30)*exp(exp(exp(5)))+4/5)+
(10*x^2-30*x+10)*exp(x)^2*exp(exp(exp(5)))-8*exp(x)^2)/((5*x^2-25*x+30)*exp(exp(exp(5)))-4),x, algorithm="maxi
ma")

[Out]

-2*(log(5) - 1)*e^(2*x)*log(-5*x^2*e^(e^(e^5)) + 25*x*e^(e^(e^5)) - 30*e^(e^(e^5)) + 4) + e^(2*x)*log(-5*x^2*e
^(e^(e^5)) + 25*x*e^(e^(e^5)) - 30*e^(e^(e^5)) + 4)^2 + (log(5)^2 - 2*log(5) + 1)*e^(2*x)

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mupad [B]  time = 2.01, size = 28, normalized size = 0.90 \begin {gather*} {\mathrm {e}}^{2\,x}\,{\left (\ln \left (\frac {4}{5}-\frac {{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^5}}\,\left (5\,x^2-25\,x+30\right )}{5}\right )+1\right )}^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(8*exp(2*x) + log(4/5 - (exp(exp(exp(5)))*(5*x^2 - 25*x + 30))/5)*(16*exp(2*x) - exp(exp(exp(5)))*exp(2*x
)*(20*x^2 - 80*x + 70)) + log(4/5 - (exp(exp(exp(5)))*(5*x^2 - 25*x + 30))/5)^2*(8*exp(2*x) - exp(exp(exp(5)))
*exp(2*x)*(10*x^2 - 50*x + 60)) - exp(exp(exp(5)))*exp(2*x)*(10*x^2 - 30*x + 10))/(exp(exp(exp(5)))*(5*x^2 - 2
5*x + 30) - 4),x)

[Out]

exp(2*x)*(log(4/5 - (exp(exp(exp(5)))*(5*x^2 - 25*x + 30))/5) + 1)^2

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((10*x**2-50*x+60)*exp(x)**2*exp(exp(exp(5)))-8*exp(x)**2)*ln(1/5*(-5*x**2+25*x-30)*exp(exp(exp(5))
)+4/5)**2+((20*x**2-80*x+70)*exp(x)**2*exp(exp(exp(5)))-16*exp(x)**2)*ln(1/5*(-5*x**2+25*x-30)*exp(exp(exp(5))
)+4/5)+(10*x**2-30*x+10)*exp(x)**2*exp(exp(exp(5)))-8*exp(x)**2)/((5*x**2-25*x+30)*exp(exp(exp(5)))-4),x)

[Out]

Timed out

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