Optimal. Leaf size=30 \[ e^{1+e^{-2 x+2 e^{2 x} x^2 (9+\log (x))^2} x^4} \]
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Rubi [F]
time = 16.91, 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 \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) \left (4 x^3-2 x^4+e^{2 x} \left (360 x^5+324 x^6\right )+e^{2 x} \left (76 x^5+72 x^6\right ) \log (x)+e^{2 x} \left (4 x^5+4 x^6\right ) \log ^2(x)\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (4 \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^3-2 \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 (10+9 x)+4 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 (19+18 x) \log (x)+4 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 (1+x) \log ^2(x)\right ) \, dx\\ &=-\left (2 \int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4 \, dx\right )+4 \int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^3 \, dx+4 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 (19+18 x) \log (x) \, dx+4 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 (1+x) \log ^2(x) \, dx+36 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 (10+9 x) \, dx\\ &=-\left (2 \int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4 \, dx\right )+4 \int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^3 \, dx+4 \int \left (19 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 \log (x)+18 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^6 \log (x)\right ) \, dx+4 \int \left (\exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 \log ^2(x)+\exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^6 \log ^2(x)\right ) \, dx+36 \int \left (10 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5+9 \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^6\right ) \, dx\\ &=-\left (2 \int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4 \, dx\right )+4 \int \exp \left (1-2 x+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^3 \, dx+4 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 \log ^2(x) \, dx+4 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^6 \log ^2(x) \, dx+72 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^6 \log (x) \, dx+76 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 \log (x) \, dx+324 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^6 \, dx+360 \int \exp \left (1+162 e^{2 x} x^2+\exp \left (-2 x+162 e^{2 x} x^2+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^4+36 e^{2 x} x^2 \log (x)+2 e^{2 x} x^2 \log ^2(x)\right ) x^5 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.16, size = 39, normalized size = 1.30 \begin {gather*} e^{1+e^{2 x \left (-1+e^{2 x} x \left (81+\log ^2(x)\right )\right )} x^{4+36 e^{2 x} x^2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 44, normalized size = 1.47
method | result | size |
risch | \({\mathrm e}^{x^{4} x^{36 \,{\mathrm e}^{2 x} x^{2}} {\mathrm e}^{2 x \left (\ln \left (x \right )^{2} {\mathrm e}^{2 x} x +81 x \,{\mathrm e}^{2 x}-1\right )}+1}\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.62, size = 45, normalized size = 1.50 \begin {gather*} e^{\left (x^{4} e^{\left (2 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right )^{2} + 36 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right ) + 162 \, x^{2} e^{\left (2 \, x\right )} - 2 \, x\right )} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 45, normalized size = 1.50 \begin {gather*} e^{\left (x^{4} e^{\left (2 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right )^{2} + 36 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right ) + 162 \, x^{2} e^{\left (2 \, x\right )} - 2 \, x\right )} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 32.35, size = 49, normalized size = 1.63 \begin {gather*} e^{x^{4} e^{2 x^{2} e^{2 x} \log {\left (x \right )}^{2} + 36 x^{2} e^{2 x} \log {\left (x \right )} + 162 x^{2} e^{2 x} - 2 x} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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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.
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Mupad [B]
time = 1.19, size = 46, normalized size = 1.53 \begin {gather*} \mathrm {e}\,{\mathrm {e}}^{x^{36\,x^2\,{\mathrm {e}}^{2\,x}+4}\,{\mathrm {e}}^{2\,x^2\,{\mathrm {e}}^{2\,x}\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{162\,x^2\,{\mathrm {e}}^{2\,x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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