Optimal. Leaf size=19 \[ \frac {16 e^{2+4 x+4 x^2} x}{\log ^8(x)} \]
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Rubi [F]
time = 0.37, 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 {16 e^{2+4 x+4 x^2} \left (-8+\left (1+4 x+8 x^2\right ) \log (x)\right )}{\log ^9(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=16 \int \frac {e^{2+4 x+4 x^2} \left (-8+\left (1+4 x+8 x^2\right ) \log (x)\right )}{\log ^9(x)} \, dx\\ &=16 \int \left (-\frac {8 e^{2+4 x+4 x^2}}{\log ^9(x)}+\frac {e^{2+4 x+4 x^2} \left (1+4 x+8 x^2\right )}{\log ^8(x)}\right ) \, dx\\ &=16 \int \frac {e^{2+4 x+4 x^2} \left (1+4 x+8 x^2\right )}{\log ^8(x)} \, dx-128 \int \frac {e^{2+4 x+4 x^2}}{\log ^9(x)} \, dx\\ &=16 \int \left (\frac {e^{2+4 x+4 x^2}}{\log ^8(x)}+\frac {4 e^{2+4 x+4 x^2} x}{\log ^8(x)}+\frac {8 e^{2+4 x+4 x^2} x^2}{\log ^8(x)}\right ) \, dx-128 \int \frac {e^{2+4 x+4 x^2}}{\log ^9(x)} \, dx\\ &=16 \int \frac {e^{2+4 x+4 x^2}}{\log ^8(x)} \, dx+64 \int \frac {e^{2+4 x+4 x^2} x}{\log ^8(x)} \, dx-128 \int \frac {e^{2+4 x+4 x^2}}{\log ^9(x)} \, dx+128 \int \frac {e^{2+4 x+4 x^2} x^2}{\log ^8(x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 19, normalized size = 1.00 \begin {gather*} \frac {16 e^{2+4 x+4 x^2} x}{\log ^8(x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.14, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (8 x^{2}+4 x +1\right ) \ln \left (x \right )-8\right ) {\mathrm e}^{-\ln \left (\frac {\ln \left (x \right )^{8} {\mathrm e}^{-4 x} {\mathrm e}^{-4 x^{2}}}{16}\right )+2}}{\ln \left (x \right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 18, normalized size = 0.95 \begin {gather*} \frac {16 \, x e^{\left (4 \, x^{2} + 4 \, x + 2\right )}}{\log \left (x\right )^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 18, normalized size = 0.95 \begin {gather*} \frac {16 \, x e^{\left (4 \, x^{2} + 4 \, x + 2\right )}}{\log \left (x\right )^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 22, normalized size = 1.16 \begin {gather*} \frac {16 x e^{2} e^{4 x} e^{4 x^{2}}}{\log {\left (x \right )}^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 18, normalized size = 0.95 \begin {gather*} \frac {16 \, x e^{\left (4 \, x^{2} + 4 \, x + 2\right )}}{\log \left (x\right )^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.52, size = 19, normalized size = 1.00 \begin {gather*} \frac {16\,x\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^2\,{\mathrm {e}}^{4\,x^2}}{{\ln \left (x\right )}^8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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