Optimal. Leaf size=22 \[ 5 e^x \log \left (-e^{2 x}-\frac {3}{x}+10 x\right ) \]
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Rubi [A]
time = 0.19, antiderivative size = 25, normalized size of antiderivative = 1.14, number of steps
used = 1, number of rules used = 1, integrand size = 81, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {2326}
\begin {gather*} 5 e^x \log \left (-\frac {-10 x^2+e^{2 x} x+3}{x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=5 e^x \log \left (-\frac {3+e^{2 x} x-10 x^2}{x}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.09, size = 22, normalized size = 1.00 \begin {gather*} 5 e^x \log \left (-e^{2 x}-\frac {3}{x}+10 x\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 1.13, size = 189, normalized size = 8.59
method | result | size |
risch | \(5 \,{\mathrm e}^{x} \ln \left (-\frac {x \,{\mathrm e}^{2 x}}{10}+x^{2}-\frac {3}{10}\right )-5 \,{\mathrm e}^{x} \ln \left (x \right )+\frac {5 i \pi \,\mathrm {csgn}\left (i \left (-\frac {x \,{\mathrm e}^{2 x}}{10}+x^{2}-\frac {3}{10}\right )\right ) \mathrm {csgn}\left (\frac {i \left (-\frac {x \,{\mathrm e}^{2 x}}{10}+x^{2}-\frac {3}{10}\right )}{x}\right )^{2} {\mathrm e}^{x}}{2}-\frac {5 i \pi \,\mathrm {csgn}\left (i \left (-\frac {x \,{\mathrm e}^{2 x}}{10}+x^{2}-\frac {3}{10}\right )\right ) \mathrm {csgn}\left (\frac {i \left (-\frac {x \,{\mathrm e}^{2 x}}{10}+x^{2}-\frac {3}{10}\right )}{x}\right ) \mathrm {csgn}\left (\frac {i}{x}\right ) {\mathrm e}^{x}}{2}+\frac {5 i \pi \mathrm {csgn}\left (\frac {i \left (-\frac {x \,{\mathrm e}^{2 x}}{10}+x^{2}-\frac {3}{10}\right )}{x}\right )^{2} \mathrm {csgn}\left (\frac {i}{x}\right ) {\mathrm e}^{x}}{2}-\frac {5 i \pi \mathrm {csgn}\left (\frac {i \left (-\frac {x \,{\mathrm e}^{2 x}}{10}+x^{2}-\frac {3}{10}\right )}{x}\right )^{3} {\mathrm e}^{x}}{2}+5 \,{\mathrm e}^{x} \ln \left (2\right )+5 \,{\mathrm e}^{x} \ln \left (5\right )\) | \(189\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 26, normalized size = 1.18 \begin {gather*} 5 \, e^{x} \log \left (10 \, x^{2} - x e^{\left (2 \, x\right )} - 3\right ) - 5 \, e^{x} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 23, normalized size = 1.05 \begin {gather*} 5 \, e^{x} \log \left (\frac {10 \, x^{2} - x e^{\left (2 \, x\right )} - 3}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 26, normalized size = 1.18 \begin {gather*} 5 \, e^{x} \log \left (10 \, x^{2} - x e^{\left (2 \, x\right )} - 3\right ) - 5 \, e^{x} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.60, size = 20, normalized size = 0.91 \begin {gather*} 5\,{\mathrm {e}}^x\,\ln \left (10\,x-{\mathrm {e}}^{2\,x}-\frac {3}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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