Optimal. Leaf size=24 \[ (-3+x) \left (-e^{\frac {1-\frac {1}{\log (25)}}{x^2}}+2 x\right ) \]
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Rubi [A]
time = 0.14, antiderivative size = 32, normalized size of antiderivative = 1.33, number of steps
used = 4, number of rules used = 3, integrand size = 56, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.054, Rules used = {12, 14, 2326}
\begin {gather*} (3-x) e^{\frac {1-\frac {1}{\log (25)}}{x^2}}+\frac {1}{2} (3-2 x)^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {\left (-6 x^3+4 x^4\right ) \log (25)+e^{\frac {-1+\log (25)}{x^2 \log (25)}} \left (6-2 x+\left (-6+2 x-x^3\right ) \log (25)\right )}{x^3} \, dx}{\log (25)}\\ &=\frac {\int \left (2 (-3+2 x) \log (25)+\frac {e^{\frac {1-\frac {1}{\log (25)}}{x^2}} \left (6 (1-\log (25))-2 x (1-\log (25))-x^3 \log (25)\right )}{x^3}\right ) \, dx}{\log (25)}\\ &=\frac {1}{2} (3-2 x)^2+\frac {\int \frac {e^{\frac {1-\frac {1}{\log (25)}}{x^2}} \left (6 (1-\log (25))-2 x (1-\log (25))-x^3 \log (25)\right )}{x^3} \, dx}{\log (25)}\\ &=\frac {1}{2} (3-2 x)^2+e^{\frac {1-\frac {1}{\log (25)}}{x^2}} (3-x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.25, size = 38, normalized size = 1.58 \begin {gather*} -6 x+2 x^2+\frac {e^{\frac {-1+\log (25)}{x^2 \log (25)}} (3 \log (25)-x \log (25))}{\log (25)} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(89\) vs.
\(2(23)=46\).
time = 4.57, size = 90, normalized size = 3.75
method | result | size |
risch | \(2 x^{2}-6 x +\frac {\left (-2 x \ln \left (5\right )+6 \ln \left (5\right )\right ) {\mathrm e}^{\frac {2 \ln \left (5\right )-1}{2 x^{2} \ln \left (5\right )}}}{2 \ln \left (5\right )}\) | \(42\) |
norman | \(\frac {-6 x^{3}+2 x^{4}+3 x^{2} {\mathrm e}^{\frac {2 \ln \left (5\right )-1}{2 x^{2} \ln \left (5\right )}}-x^{3} {\mathrm e}^{\frac {2 \ln \left (5\right )-1}{2 x^{2} \ln \left (5\right )}}}{x^{2}}\) | \(58\) |
derivativedivides | \(-\frac {-4 x^{2} \ln \left (5\right )+12 x \ln \left (5\right )+\frac {3 \,{\mathrm e}^{\frac {1-\frac {1}{2 \ln \left (5\right )}}{x^{2}}}}{1-\frac {1}{2 \ln \left (5\right )}}-\frac {6 \ln \left (5\right ) {\mathrm e}^{\frac {1-\frac {1}{2 \ln \left (5\right )}}{x^{2}}}}{1-\frac {1}{2 \ln \left (5\right )}}+2 \ln \left (5\right ) x \,{\mathrm e}^{\frac {1-\frac {1}{2 \ln \left (5\right )}}{x^{2}}}}{2 \ln \left (5\right )}\) | \(90\) |
default | \(\frac {4 x^{2} \ln \left (5\right )-12 x \ln \left (5\right )-\frac {3 \,{\mathrm e}^{\frac {1-\frac {1}{2 \ln \left (5\right )}}{x^{2}}}}{1-\frac {1}{2 \ln \left (5\right )}}+\frac {6 \ln \left (5\right ) {\mathrm e}^{\frac {1-\frac {1}{2 \ln \left (5\right )}}{x^{2}}}}{1-\frac {1}{2 \ln \left (5\right )}}-2 \ln \left (5\right ) x \,{\mathrm e}^{\frac {1-\frac {1}{2 \ln \left (5\right )}}{x^{2}}}}{2 \ln \left (5\right )}\) | \(90\) |
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 = 0.38, size = 30, normalized size = 1.25 \begin {gather*} 2 \, x^{2} - {\left (x - 3\right )} e^{\left (\frac {2 \, \log \left (5\right ) - 1}{2 \, x^{2} \log \left (5\right )}\right )} - 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 26, normalized size = 1.08 \begin {gather*} 2 x^{2} - 6 x + \left (3 - x\right ) e^{\frac {- \frac {1}{2} + \log {\left (5 \right )}}{x^{2} \log {\left (5 \right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 59 vs.
\(2 (22) = 44\).
time = 0.43, size = 59, normalized size = 2.46 \begin {gather*} \frac {2 \, x^{2} \log \left (5\right ) - x e^{\left (\frac {2 \, \log \left (5\right ) - 1}{2 \, x^{2} \log \left (5\right )}\right )} \log \left (5\right ) - 6 \, x \log \left (5\right ) + 3 \, e^{\left (\frac {2 \, \log \left (5\right ) - 1}{2 \, x^{2} \log \left (5\right )}\right )} \log \left (5\right )}{\log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 7.19, size = 52, normalized size = 2.17 \begin {gather*} \frac {{\mathrm {e}}^{\frac {1}{x^2}-\frac {1}{2\,x^2\,\ln \left (5\right )}}\,\ln \left (125\right )}{\ln \left (5\right )}-x\,{\mathrm {e}}^{\frac {1}{x^2}-\frac {1}{2\,x^2\,\ln \left (5\right )}}-6\,x+\frac {x^2\,\ln \left (25\right )}{\ln \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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