Optimal. Leaf size=22 \[ \left (5+e^{9+4 (1+x)-\frac {10}{x \log (4)}}\right )^2 \]
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Rubi [F]
time = 0.81, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {\exp \left (\frac {2 \left (-10+\left (13 x+4 x^2\right ) \log (4)\right )}{x \log (4)}\right ) \left (20+8 x^2 \log (4)\right )+e^{\frac {-10+\left (13 x+4 x^2\right ) \log (4)}{x \log (4)}} \left (100+40 x^2 \log (4)\right )}{x^2 \log (4)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {\exp \left (\frac {2 \left (-10+\left (13 x+4 x^2\right ) \log (4)\right )}{x \log (4)}\right ) \left (20+8 x^2 \log (4)\right )+e^{\frac {-10+\left (13 x+4 x^2\right ) \log (4)}{x \log (4)}} \left (100+40 x^2 \log (4)\right )}{x^2} \, dx}{\log (4)}\\ &=\frac {\int \left (\frac {4 e^{26+8 x-\frac {20}{x \log (4)}} \left (5+x^2 \log (16)\right )}{x^2}+\frac {20 e^{13+4 x-\frac {10}{x \log (4)}} \left (5+x^2 \log (16)\right )}{x^2}\right ) \, dx}{\log (4)}\\ &=\frac {4 \int \frac {e^{26+8 x-\frac {20}{x \log (4)}} \left (5+x^2 \log (16)\right )}{x^2} \, dx}{\log (4)}+\frac {20 \int \frac {e^{13+4 x-\frac {10}{x \log (4)}} \left (5+x^2 \log (16)\right )}{x^2} \, dx}{\log (4)}\\ &=\frac {4 \int \left (\frac {5 e^{26+8 x-\frac {20}{x \log (4)}}}{x^2}+e^{26+8 x-\frac {20}{x \log (4)}} \log (16)\right ) \, dx}{\log (4)}+\frac {20 \int \left (\frac {5 e^{13+4 x-\frac {10}{x \log (4)}}}{x^2}+e^{13+4 x-\frac {10}{x \log (4)}} \log (16)\right ) \, dx}{\log (4)}\\ &=\frac {20 \int \frac {e^{26+8 x-\frac {20}{x \log (4)}}}{x^2} \, dx}{\log (4)}+\frac {100 \int \frac {e^{13+4 x-\frac {10}{x \log (4)}}}{x^2} \, dx}{\log (4)}+\frac {(4 \log (16)) \int e^{26+8 x-\frac {20}{x \log (4)}} \, dx}{\log (4)}+\frac {(20 \log (16)) \int e^{13+4 x-\frac {10}{x \log (4)}} \, dx}{\log (4)}\\ \end {aligned} \end {gather*}
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Mathematica [F] Contains unresolved integral.
time = 0.31, size = 81, normalized size = 3.68 \begin {gather*} \frac {\int \frac {e^{\frac {2 \left (-10+\left (13 x+4 x^2\right ) \log (4)\right )}{x \log (4)}} \left (20+8 x^2 \log (4)\right )+e^{\frac {-10+\left (13 x+4 x^2\right ) \log (4)}{x \log (4)}} \left (100+40 x^2 \log (4)\right )}{x^2} \, dx}{\log (4)} \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. \(50\) vs.
\(2(19)=38\).
time = 1.08, size = 51, normalized size = 2.32
method | result | size |
risch | \({\mathrm e}^{\frac {8 x^{2} \ln \left (2\right )+26 x \ln \left (2\right )-10}{x \ln \left (2\right )}}+10 \,{\mathrm e}^{\frac {4 x^{2} \ln \left (2\right )+13 x \ln \left (2\right )-5}{x \ln \left (2\right )}}\) | \(51\) |
norman | \(\frac {x \,{\mathrm e}^{\frac {2 \left (4 x^{2}+13 x \right ) \ln \left (2\right )-10}{x \ln \left (2\right )}}+10 x \,{\mathrm e}^{\frac {2 \left (4 x^{2}+13 x \right ) \ln \left (2\right )-10}{2 x \ln \left (2\right )}}}{x}\) | \(63\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 43 vs.
\(2 (19) = 38\).
time = 0.53, size = 43, normalized size = 1.95 \begin {gather*} \frac {e^{\left (8 \, x - \frac {10}{x \log \left (2\right )} + 26\right )} \log \left (2\right ) + 10 \, e^{\left (4 \, x - \frac {5}{x \log \left (2\right )} + 13\right )} \log \left (2\right )}{\log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 50 vs.
\(2 (19) = 38\).
time = 0.42, size = 50, normalized size = 2.27 \begin {gather*} e^{\left (\frac {2 \, {\left ({\left (4 \, x^{2} + 13 \, x\right )} \log \left (2\right ) - 5\right )}}{x \log \left (2\right )}\right )} + 10 \, e^{\left (\frac {{\left (4 \, x^{2} + 13 \, x\right )} \log \left (2\right ) - 5}{x \log \left (2\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 42 vs.
\(2 (15) = 30\).
time = 0.09, size = 42, normalized size = 1.91 \begin {gather*} e^{\frac {2 \left (\frac {\left (8 x^{2} + 26 x\right ) \log {\left (2 \right )}}{2} - 5\right )}{x \log {\left (2 \right )}}} + 10 e^{\frac {\frac {\left (8 x^{2} + 26 x\right ) \log {\left (2 \right )}}{2} - 5}{x \log {\left (2 \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. 60 vs.
\(2 (19) = 38\).
time = 0.42, size = 60, normalized size = 2.73 \begin {gather*} \frac {e^{\left (\frac {2 \, {\left (4 \, x^{2} \log \left (2\right ) + 13 \, x \log \left (2\right ) - 5\right )}}{x \log \left (2\right )}\right )} \log \left (2\right ) + 10 \, e^{\left (\frac {4 \, x^{2} \log \left (2\right ) + 13 \, x \log \left (2\right ) - 5}{x \log \left (2\right )}\right )} \log \left (2\right )}{\log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.35, size = 37, normalized size = 1.68 \begin {gather*} {\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{13}\,{\mathrm {e}}^{-\frac {10}{x\,\ln \left (2\right )}}\,\left (10\,{\mathrm {e}}^{\frac {5}{x\,\ln \left (2\right )}}+{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{13}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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