Optimal. Leaf size=27 \[ e^{\frac {4}{3} e^{-e^x} x^2 (3+25 x) (x-\log (4))} \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 7.25, 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 {1}{3} \exp \left (-e^x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) \left (36 x^2+400 x^3+\left (-24 x-300 x^2\right ) \log (4)+e^x \left (-12 x^3-100 x^4+\left (12 x^2+100 x^3\right ) \log (4)\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \exp \left (-e^x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) \left (36 x^2+400 x^3+\left (-24 x-300 x^2\right ) \log (4)+e^x \left (-12 x^3-100 x^4+\left (12 x^2+100 x^3\right ) \log (4)\right )\right ) \, dx\\ &=\frac {1}{3} \int \left (36 \exp \left (-e^x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x^2+400 \exp \left (-e^x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x^3-4 \exp \left (-e^x+x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x^2 (3+25 x) (x-\log (4))-12 \exp \left (-e^x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x (2+25 x) \log (4)\right ) \, dx\\ &=-\left (\frac {4}{3} \int \exp \left (-e^x+x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x^2 (3+25 x) (x-\log (4)) \, dx\right )+12 \int \exp \left (-e^x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x^2 \, dx+\frac {400}{3} \int \exp \left (-e^x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x^3 \, dx-(4 \log (4)) \int \exp \left (-e^x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x (2+25 x) \, dx\\ &=-\left (\frac {4}{3} \int \left (25 \exp \left (-e^x+x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x^4-3 \exp \left (-e^x+x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x^2 \log (4)-\exp \left (-e^x+x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x^3 (-3+25 \log (4))\right ) \, dx\right )+12 \int \exp \left (-e^x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x^2 \, dx+\frac {400}{3} \int \exp \left (-e^x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x^3 \, dx-(4 \log (4)) \int \left (2 \exp \left (-e^x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x+25 \exp \left (-e^x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x^2\right ) \, dx\\ &=12 \int \exp \left (-e^x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x^2 \, dx-\frac {100}{3} \int \exp \left (-e^x+x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x^4 \, dx+\frac {400}{3} \int \exp \left (-e^x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x^3 \, dx-\frac {1}{3} (4 (3-25 \log (4))) \int \exp \left (-e^x+x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x^3 \, dx+(4 \log (4)) \int \exp \left (-e^x+x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x^2 \, dx-(8 \log (4)) \int \exp \left (-e^x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x \, dx-(100 \log (4)) \int \exp \left (-e^x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )\right ) x^2 \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [F] Contains unresolved integral.
time = 2.06, size = 103, normalized size = 3.81 \begin {gather*} \frac {1}{3} \int e^{-e^x+\frac {1}{3} e^{-e^x} \left (12 x^3+100 x^4+\left (-12 x^2-100 x^3\right ) \log (4)\right )} \left (36 x^2+400 x^3+\left (-24 x-300 x^2\right ) \log (4)+e^x \left (-12 x^3-100 x^4+\left (12 x^2+100 x^3\right ) \log (4)\right )\right ) \, dx \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.17, size = 25, normalized size = 0.93
method | result | size |
risch | \({\mathrm e}^{-\frac {4 x^{2} \left (3+25 x \right ) \left (2 \ln \left (2\right )-x \right ) {\mathrm e}^{-{\mathrm e}^{x}}}{3}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 46 vs.
\(2 (22) = 44\).
time = 0.70, size = 46, normalized size = 1.70 \begin {gather*} e^{\left (\frac {100}{3} \, x^{4} e^{\left (-e^{x}\right )} - \frac {200}{3} \, x^{3} e^{\left (-e^{x}\right )} \log \left (2\right ) + 4 \, x^{3} e^{\left (-e^{x}\right )} - 8 \, x^{2} e^{\left (-e^{x}\right )} \log \left (2\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.57, size = 34, normalized size = 1.26 \begin {gather*} e^{\left (\frac {4}{3} \, {\left (25 \, x^{4} + 3 \, x^{3} - 2 \, {\left (25 \, x^{3} + 3 \, x^{2}\right )} \log \left (2\right )\right )} e^{\left (-e^{x}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.39, size = 34, normalized size = 1.26 \begin {gather*} e^{\left (\frac {100 x^{4}}{3} + 4 x^{3} + \frac {\left (- 200 x^{3} - 24 x^{2}\right ) \log {\left (2 \right )}}{3}\right ) e^{- e^{x}}} \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*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [F]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {{\mathrm {e}}^{-{\mathrm {e}}^x}\,{\mathrm {e}}^{{\mathrm {e}}^{-{\mathrm {e}}^x}\,\left (4\,x^3-\frac {2\,\ln \left (2\right )\,\left (100\,x^3+12\,x^2\right )}{3}+\frac {100\,x^4}{3}\right )}\,\left (2\,\ln \left (2\right )\,\left (300\,x^2+24\,x\right )+{\mathrm {e}}^x\,\left (12\,x^3-2\,\ln \left (2\right )\,\left (100\,x^3+12\,x^2\right )+100\,x^4\right )-36\,x^2-400\,x^3\right )}{3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________