Optimal. Leaf size=33 \[ 2 \left (e^{e^{e^{e^x}}}-x\right ) x \left (-x+x^2+3 (-x+\log (x))^2\right ) \]
________________________________________________________________________________________
Rubi [B] time = 0.25, antiderivative size = 89, normalized size of antiderivative = 2.70, number of steps used = 9, number of rules used = 7, integrand size = 111, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.063, Rules used = {1593, 43, 2334, 12, 2305, 2304, 2288} \begin {gather*} -8 x^4+2 x^3-6 x^2 \log ^2(x)+6 x^2 \log (x)-2 e^{e^{e^{e^x}}-x} \left (6 e^x x^2 \log (x)+e^x \left (x^2-4 x^3\right )-3 e^x x \log ^2(x)\right )-6 \left (x^2-2 x^3\right ) \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 43
Rule 1593
Rule 2288
Rule 2304
Rule 2305
Rule 2334
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=6 x^3-8 x^4-12 \int x \log ^2(x) \, dx+\int \left (-12 x+36 x^2\right ) \log (x) \, dx+\int e^{e^{e^{e^x}}} \left (-16 x+24 x^2+(12-24 x) \log (x)+6 \log ^2(x)+e^{e^{e^x}+e^x} \left (e^x \left (-2 x^2+8 x^3\right )-12 e^x x^2 \log (x)+6 e^x x \log ^2(x)\right )\right ) \, dx\\ &=6 x^3-8 x^4-6 x^2 \log ^2(x)-2 e^{e^{e^{e^x}}-x} \left (e^x \left (x^2-4 x^3\right )+6 e^x x^2 \log (x)-3 e^x x \log ^2(x)\right )+12 \int x \log (x) \, dx+\int x (-12+36 x) \log (x) \, dx\\ &=-3 x^2+6 x^3-8 x^4+6 x^2 \log (x)-6 \left (x^2-2 x^3\right ) \log (x)-6 x^2 \log ^2(x)-2 e^{e^{e^{e^x}}-x} \left (e^x \left (x^2-4 x^3\right )+6 e^x x^2 \log (x)-3 e^x x \log ^2(x)\right )-\int 6 x (-1+2 x) \, dx\\ &=-3 x^2+6 x^3-8 x^4+6 x^2 \log (x)-6 \left (x^2-2 x^3\right ) \log (x)-6 x^2 \log ^2(x)-2 e^{e^{e^{e^x}}-x} \left (e^x \left (x^2-4 x^3\right )+6 e^x x^2 \log (x)-3 e^x x \log ^2(x)\right )-6 \int x (-1+2 x) \, dx\\ &=-3 x^2+6 x^3-8 x^4+6 x^2 \log (x)-6 \left (x^2-2 x^3\right ) \log (x)-6 x^2 \log ^2(x)-2 e^{e^{e^{e^x}}-x} \left (e^x \left (x^2-4 x^3\right )+6 e^x x^2 \log (x)-3 e^x x \log ^2(x)\right )-6 \int \left (-x+2 x^2\right ) \, dx\\ &=2 x^3-8 x^4+6 x^2 \log (x)-6 \left (x^2-2 x^3\right ) \log (x)-6 x^2 \log ^2(x)-2 e^{e^{e^{e^x}}-x} \left (e^x \left (x^2-4 x^3\right )+6 e^x x^2 \log (x)-3 e^x x \log ^2(x)\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.25, size = 35, normalized size = 1.06 \begin {gather*} 2 \left (e^{e^{e^{e^x}}}-x\right ) x \left (x (-1+4 x)-6 x \log (x)+3 \log ^2(x)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.52, size = 59, normalized size = 1.79 \begin {gather*} -8 \, x^{4} + 12 \, x^{3} \log \relax (x) - 6 \, x^{2} \log \relax (x)^{2} + 2 \, x^{3} + 2 \, {\left (4 \, x^{3} - 6 \, x^{2} \log \relax (x) + 3 \, x \log \relax (x)^{2} - x^{2}\right )} e^{\left (e^{\left (e^{\left (e^{x}\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -32 \, x^{3} - 12 \, x \log \relax (x)^{2} + 18 \, x^{2} + 2 \, {\left (12 \, x^{2} - {\left (6 \, x^{2} e^{x} \log \relax (x) - 3 \, x e^{x} \log \relax (x)^{2} - {\left (4 \, x^{3} - x^{2}\right )} e^{x}\right )} e^{\left (e^{x} + e^{\left (e^{x}\right )}\right )} - 6 \, {\left (2 \, x - 1\right )} \log \relax (x) + 3 \, \log \relax (x)^{2} - 8 \, x\right )} e^{\left (e^{\left (e^{\left (e^{x}\right )}\right )}\right )} + 12 \, {\left (3 \, x^{2} - x\right )} \log \relax (x)\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.09, size = 70, normalized size = 2.12
method | result | size |
risch | \(2 x \left (4 x^{2}-6 x \ln \relax (x )+3 \ln \relax (x )^{2}-x \right ) {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}}-6 x^{2} \ln \relax (x )^{2}+6 x^{2} \ln \relax (x )+\left (12 x^{3}-6 x^{2}\right ) \ln \relax (x )+2 x^{3}-8 x^{4}\) | \(70\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.37, size = 80, normalized size = 2.42 \begin {gather*} -8 \, x^{4} - 3 \, {\left (2 \, \log \relax (x)^{2} - 2 \, \log \relax (x) + 1\right )} x^{2} + 2 \, x^{3} + 3 \, x^{2} + 2 \, {\left (4 \, x^{3} - 6 \, x^{2} \log \relax (x) + 3 \, x \log \relax (x)^{2} - x^{2}\right )} e^{\left (e^{\left (e^{\left (e^{x}\right )}\right )}\right )} + 6 \, {\left (2 \, x^{3} - x^{2}\right )} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.54, size = 58, normalized size = 1.76 \begin {gather*} 12\,x^3\,\ln \relax (x)+{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}\,\left (8\,x^3-12\,x^2\,\ln \relax (x)-2\,x^2+6\,x\,{\ln \relax (x)}^2\right )-6\,x^2\,{\ln \relax (x)}^2+2\,x^3-8\,x^4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 13.56, size = 63, normalized size = 1.91 \begin {gather*} - 8 x^{4} + 12 x^{3} \log {\relax (x )} + 2 x^{3} - 6 x^{2} \log {\relax (x )}^{2} + \left (8 x^{3} - 12 x^{2} \log {\relax (x )} - 2 x^{2} + 6 x \log {\relax (x )}^{2}\right ) e^{e^{e^{e^{x}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________