Optimal. Leaf size=26 \[ \frac {5 \left (-e^x+\left (e^3-e^x\right )^2\right ) \log (5)}{6 x^2} \]
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Rubi [A] time = 0.09, antiderivative size = 46, normalized size of antiderivative = 1.77, number of steps used = 5, number of rules used = 3, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {12, 14, 2197} \begin {gather*} \frac {5 e^{2 x} \log (5)}{6 x^2}-\frac {5 \left (1+2 e^3\right ) e^x \log (5)}{6 x^2}+\frac {5 e^6 \log (5)}{6 x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2197
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{6} \int \frac {-10 e^6 \log (5)+e^x \left (10+e^3 (20-10 x)-5 x\right ) \log (5)+e^{2 x} (-10+10 x) \log (5)}{x^3} \, dx\\ &=\frac {1}{6} \int \left (-\frac {10 e^6 \log (5)}{x^3}-\frac {5 e^x \left (1+2 e^3\right ) (-2+x) \log (5)}{x^3}+\frac {10 e^{2 x} (-1+x) \log (5)}{x^3}\right ) \, dx\\ &=\frac {5 e^6 \log (5)}{6 x^2}+\frac {1}{3} (5 \log (5)) \int \frac {e^{2 x} (-1+x)}{x^3} \, dx-\frac {1}{6} \left (5 \left (1+2 e^3\right ) \log (5)\right ) \int \frac {e^x (-2+x)}{x^3} \, dx\\ &=\frac {5 e^6 \log (5)}{6 x^2}+\frac {5 e^{2 x} \log (5)}{6 x^2}-\frac {5 e^x \left (1+2 e^3\right ) \log (5)}{6 x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 30, normalized size = 1.15 \begin {gather*} \frac {5 \left (e^6-e^x+e^{2 x}-2 e^{3+x}\right ) \log (5)}{6 x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 31, normalized size = 1.19 \begin {gather*} -\frac {5 \, {\left ({\left (2 \, e^{3} + 1\right )} e^{x} \log \relax (5) - e^{6} \log \relax (5) - e^{\left (2 \, x\right )} \log \relax (5)\right )}}{6 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 32, normalized size = 1.23 \begin {gather*} \frac {5 \, {\left (e^{6} \log \relax (5) + e^{\left (2 \, x\right )} \log \relax (5) - 2 \, e^{\left (x + 3\right )} \log \relax (5) - e^{x} \log \relax (5)\right )}}{6 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 36, normalized size = 1.38
method | result | size |
norman | \(\frac {\left (-\frac {5 \,{\mathrm e}^{3} \ln \relax (5)}{3}-\frac {5 \ln \relax (5)}{6}\right ) {\mathrm e}^{x}+\frac {5 \,{\mathrm e}^{6} \ln \relax (5)}{6}+\frac {5 \ln \relax (5) {\mathrm e}^{2 x}}{6}}{x^{2}}\) | \(36\) |
risch | \(\frac {5 \,{\mathrm e}^{6} \ln \relax (5)}{6 x^{2}}+\frac {5 \ln \relax (5) {\mathrm e}^{2 x}}{6 x^{2}}-\frac {5 \left (2 \,{\mathrm e}^{3}+1\right ) \ln \relax (5) {\mathrm e}^{x}}{6 x^{2}}\) | \(37\) |
default | \(\frac {5 \,{\mathrm e}^{6} \ln \relax (5)}{6 x^{2}}-\frac {5 \,{\mathrm e}^{x} \ln \relax (5)}{6 x^{2}}+\frac {5 \ln \relax (5) {\mathrm e}^{2 x}}{6 x^{2}}-\frac {5 \,{\mathrm e}^{x} \ln \relax (5) {\mathrm e}^{3}}{3 x^{2}}\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.42, size = 68, normalized size = 2.62 \begin {gather*} -\frac {5}{3} \, e^{3} \Gamma \left (-1, -x\right ) \log \relax (5) - \frac {10}{3} \, e^{3} \Gamma \left (-2, -x\right ) \log \relax (5) - \frac {5}{6} \, \Gamma \left (-1, -x\right ) \log \relax (5) + \frac {10}{3} \, \Gamma \left (-1, -2 \, x\right ) \log \relax (5) - \frac {5}{3} \, \Gamma \left (-2, -x\right ) \log \relax (5) + \frac {20}{3} \, \Gamma \left (-2, -2 \, x\right ) \log \relax (5) + \frac {5 \, e^{6} \log \relax (5)}{6 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 32, normalized size = 1.23 \begin {gather*} \frac {5\,{\mathrm {e}}^{2\,x}\,\ln \relax (5)+5\,{\mathrm {e}}^6\,\ln \relax (5)-5\,{\mathrm {e}}^x\,\ln \relax (5)\,\left (2\,{\mathrm {e}}^3+1\right )}{6\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.17, size = 56, normalized size = 2.15 \begin {gather*} \frac {5 e^{6} \log {\relax (5 )}}{6 x^{2}} + \frac {30 x^{2} e^{2 x} \log {\relax (5 )} + \left (- 60 x^{2} e^{3} \log {\relax (5 )} - 30 x^{2} \log {\relax (5 )}\right ) e^{x}}{36 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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