Optimal. Leaf size=28 \[ 3+\frac {1}{4} \left (4-5 \left (e^{\frac {3 x}{\log (5)}+x (x+\log (5))}+x\right )\right ) \]
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Rubi [A]
time = 0.08, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 50, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.060, Rules used = {12, 2276, 2268}
\begin {gather*} -\frac {5}{4} e^{x^2+\frac {x \left (3+\log ^2(5)\right )}{\log (5)}}-\frac {5 x}{4} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2268
Rule 2276
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (-5 \log (5)+e^{\frac {3 x+x^2 \log (5)+x \log ^2(5)}{\log (5)}} \left (-15-10 x \log (5)-5 \log ^2(5)\right )\right ) \, dx}{4 \log (5)}\\ &=-\frac {5 x}{4}+\frac {\int e^{\frac {3 x+x^2 \log (5)+x \log ^2(5)}{\log (5)}} \left (-15-10 x \log (5)-5 \log ^2(5)\right ) \, dx}{4 \log (5)}\\ &=-\frac {5 x}{4}+\frac {\int e^{x^2+\frac {x \left (3+\log ^2(5)\right )}{\log (5)}} \left (-10 x \log (5)-5 \left (3+\log ^2(5)\right )\right ) \, dx}{4 \log (5)}\\ &=-\frac {5}{4} e^{x^2+\frac {x \left (3+\log ^2(5)\right )}{\log (5)}}-\frac {5 x}{4}\\ \end {aligned} \end {gather*}
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Mathematica [C] Result contains higher order function than in optimal. Order 4 vs. order 3 in
optimal.
time = 0.66, size = 140, normalized size = 5.00 \begin {gather*} -\frac {5 \left (x \log (5)+\frac {1}{2} e^{-\frac {\left (3+\log ^2(5)\right )^2}{4 \log ^2(5)}} \sqrt {\pi } \text {Erfi}\left (\frac {3+\log ^2(5)+x \log (25)}{\log (25)}\right ) \left (3+\log ^2(5)\right )\right )}{\log (625)}-\frac {e^{-\frac {\left (3+\log ^2(5)\right )^2}{4 \log ^2(5)}} \left (-5 \sqrt {\pi } \text {Erfi}\left (\frac {3+\log ^2(5)+x \log (25)}{\log (25)}\right ) \left (3+\log ^2(5)\right )+5 e^{\frac {\left (3+\log ^2(5)+x \log (25)\right )^2}{\log ^2(25)}} \log (25)\right )}{2 \log (625)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.50, size = 34, normalized size = 1.21
method | result | size |
risch | \(-\frac {5 x}{4}-\frac {5 \,5^{x} {\mathrm e}^{\frac {x \left (x \ln \left (5\right )+3\right )}{\ln \left (5\right )}}}{4}\) | \(23\) |
norman | \(-\frac {5 x}{4}-\frac {5 \,{\mathrm e}^{\frac {x \ln \left (5\right )^{2}+x^{2} \ln \left (5\right )+3 x}{\ln \left (5\right )}}}{4}\) | \(29\) |
default | \(\frac {-5 \ln \left (5\right ) {\mathrm e}^{x^{2}+\frac {\left (\ln \left (5\right )^{2}+3\right ) x}{\ln \left (5\right )}}-5 x \ln \left (5\right )}{4 \ln \left (5\right )}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 36, normalized size = 1.29 \begin {gather*} -\frac {5 \, {\left (x \log \left (5\right ) + e^{\left (\frac {x^{2} \log \left (5\right ) + x \log \left (5\right )^{2} + 3 \, x}{\log \left (5\right )}\right )} \log \left (5\right )\right )}}{4 \, \log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 28, normalized size = 1.00 \begin {gather*} -\frac {5}{4} \, x - \frac {5}{4} \, e^{\left (\frac {x^{2} \log \left (5\right ) + x \log \left (5\right )^{2} + 3 \, x}{\log \left (5\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 31, normalized size = 1.11 \begin {gather*} - \frac {5 x}{4} - \frac {5 e^{\frac {x^{2} \log {\left (5 \right )} + x \log {\left (5 \right )}^{2} + 3 x}{\log {\left (5 \right )}}}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 30, normalized size = 1.07 \begin {gather*} -\frac {5 \, {\left (x \log \left (5\right ) + e^{\left (x^{2} + x \log \left (5\right ) + \frac {3 \, x}{\log \left (5\right )}\right )} \log \left (5\right )\right )}}{4 \, \log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.16, size = 21, normalized size = 0.75 \begin {gather*} -\frac {5\,x}{4}-\frac {5\,5^x\,{\mathrm {e}}^{\frac {3\,x}{\ln \left (5\right )}}\,{\mathrm {e}}^{x^2}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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