Optimal. Leaf size=20 \[ e^x+e^{(4+\log (28 x))^2}+\log (3-x) \]
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Rubi [A]
time = 0.60, antiderivative size = 25, normalized size of antiderivative = 1.25, number of steps
used = 5, number of rules used = 4, integrand size = 53, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.075, Rules used = {1607, 6820,
2225, 2326} \begin {gather*} 377801998336 x^8 e^{\log ^2(28 x)+16}+e^x+\log (3-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 1607
Rule 2225
Rule 2326
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x+e^x \left (-3 x+x^2\right )+377801998336 e^{16+\log ^2(28 x)} x^8 (-24+8 x+(-6+2 x) \log (28 x))}{(-3+x) x} \, dx\\ &=\int \left (e^x+\frac {1}{-3+x}+755603996672 e^{16+\log ^2(28 x)} x^7 (4+\log (28 x))\right ) \, dx\\ &=\log (3-x)+755603996672 \int e^{16+\log ^2(28 x)} x^7 (4+\log (28 x)) \, dx+\int e^x \, dx\\ &=e^x+377801998336 e^{16+\log ^2(28 x)} x^8+\log (3-x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 23, normalized size = 1.15 \begin {gather*} e^x+377801998336 e^{16+\log ^2(28 x)} x^8+\log (-3+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.39, size = 23, normalized size = 1.15
method | result | size |
risch | \(\ln \left (x -3\right )+377801998336 x^{8} {\mathrm e}^{\ln \left (28 x \right )^{2}+16}+{\mathrm e}^{x}\) | \(22\) |
default | \(\ln \left (x -3\right )+{\mathrm e}^{\ln \left (28 x \right )^{2}+8 \ln \left (28 x \right )+16}+{\mathrm e}^{x}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 22, normalized size = 1.10 \begin {gather*} e^{\left (\log \left (28 \, x\right )^{2} + 8 \, \log \left (28 \, x\right ) + 16\right )} + e^{x} + \log \left (x - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.17, size = 22, normalized size = 1.10 \begin {gather*} 377801998336 x^{8} e^{\log {\left (28 x \right )}^{2} + 16} + e^{x} + \log {\left (x - 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 21, normalized size = 1.05 \begin {gather*} 377801998336 \, x^{8} e^{\left (\log \left (28 \, x\right )^{2} + 16\right )} + e^{x} + \log \left (x - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.09, size = 30, normalized size = 1.50 \begin {gather*} \ln \left (x-3\right )+{\mathrm {e}}^x+377801998336\,x^{2\,\ln \left (28\right )}\,x^8\,{\mathrm {e}}^{{\ln \left (28\right )}^2}\,{\mathrm {e}}^{16}\,{\mathrm {e}}^{{\ln \left (x\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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