Optimal. Leaf size=21 \[ -9+e^{2 x} \left (x+x \left (6+x^{-3+6 x}\right )\right ) \]
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Rubi [F]
time = 0.29, 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 \left (e^{2 x} (7+14 x)+x^{-3+6 x} \left (e^{2 x} (-2+8 x)+6 e^{2 x} x \log (x)\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{2 x} (7+14 x) \, dx+\int x^{-3+6 x} \left (e^{2 x} (-2+8 x)+6 e^{2 x} x \log (x)\right ) \, dx\\ &=\frac {7}{2} e^{2 x} (1+2 x)-7 \int e^{2 x} \, dx+\int 2 e^{2 x} x^{-3+6 x} (-1+4 x+3 x \log (x)) \, dx\\ &=-\frac {7 e^{2 x}}{2}+\frac {7}{2} e^{2 x} (1+2 x)+2 \int e^{2 x} x^{-3+6 x} (-1+4 x+3 x \log (x)) \, dx\\ &=-\frac {7 e^{2 x}}{2}+\frac {7}{2} e^{2 x} (1+2 x)+2 \int \left (-e^{2 x} x^{-3+6 x}+4 e^{2 x} x^{-2+6 x}+3 e^{2 x} x^{-2+6 x} \log (x)\right ) \, dx\\ &=-\frac {7 e^{2 x}}{2}+\frac {7}{2} e^{2 x} (1+2 x)-2 \int e^{2 x} x^{-3+6 x} \, dx+6 \int e^{2 x} x^{-2+6 x} \log (x) \, dx+8 \int e^{2 x} x^{-2+6 x} \, dx\\ &=-\frac {7 e^{2 x}}{2}+\frac {7}{2} e^{2 x} (1+2 x)-2 \int e^{2 x} x^{-3+6 x} \, dx-6 \int \frac {\int e^{2 x} x^{-2+6 x} \, dx}{x} \, dx+8 \int e^{2 x} x^{-2+6 x} \, dx+(6 \log (x)) \int e^{2 x} x^{-2+6 x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.20, size = 20, normalized size = 0.95 \begin {gather*} \frac {e^{2 x} \left (7 x^3+x^{6 x}\right )}{x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 24, normalized size = 1.14
method | result | size |
risch | \({\mathrm e}^{2 x} x^{6 x -3} x +7 x \,{\mathrm e}^{2 x}\) | \(22\) |
default | \(7 x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x} {\mathrm e}^{\left (6 x -3\right ) \ln \left (x \right )} x\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 32, normalized size = 1.52 \begin {gather*} \frac {7}{2} \, {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} + \frac {e^{\left (6 \, x \log \left (x\right ) + 2 \, x\right )}}{x^{2}} + \frac {7}{2} \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 21, normalized size = 1.00 \begin {gather*} x x^{6 \, x - 3} e^{\left (2 \, x\right )} + 7 \, x e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 3.53, size = 24, normalized size = 1.14 \begin {gather*} x e^{2 x} e^{\left (6 x - 3\right ) \log {\left (x \right )}} + 7 x e^{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.46, size = 22, normalized size = 1.05 \begin {gather*} 7 \, x e^{\left (2 \, x\right )} + e^{\left (6 \, x \log \left (x\right ) + 2 \, x - 2 \, \log \left (x\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.01, size = 19, normalized size = 0.90 \begin {gather*} \frac {{\mathrm {e}}^{2\,x}\,\left (x^{6\,x}+7\,x^3\right )}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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