Optimal. Leaf size=33 \[ \frac {x^2+\frac {5-x+\frac {4^{2 e^{-6+2 x}}}{\log ^2(2)}}{x}}{x} \]
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Rubi [F]
time = 0.66, 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 {e^{-6+2 x} \left (e^{6-2 x} \left (-10+x+x^3\right ) \log ^2(2)+4^{2 e^{-6+2 x}} \left (-2 e^{6-2 x}+4 x \log (4)\right )\right )}{x^3 \log ^2(2)} \, 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 {e^{-6+2 x} \left (e^{6-2 x} \left (-10+x+x^3\right ) \log ^2(2)+4^{2 e^{-6+2 x}} \left (-2 e^{6-2 x}+4 x \log (4)\right )\right )}{x^3} \, dx}{\log ^2(2)}\\ &=\frac {\int \left (\frac {-2^{1+4 e^{-6+2 x}}-10 \log ^2(2)+x \log ^2(2)+x^3 \log ^2(2)}{x^3}+\frac {4^{1+2 e^{-6+2 x}} e^{-6+2 x} \log (4)}{x^2}\right ) \, dx}{\log ^2(2)}\\ &=\frac {\int \frac {-2^{1+4 e^{-6+2 x}}-10 \log ^2(2)+x \log ^2(2)+x^3 \log ^2(2)}{x^3} \, dx}{\log ^2(2)}+\frac {\log (4) \int \frac {4^{1+2 e^{-6+2 x}} e^{-6+2 x}}{x^2} \, dx}{\log ^2(2)}\\ &=\frac {\int \left (-\frac {2^{1+4 e^{-6+2 x}}}{x^3}+\frac {\left (-10+x+x^3\right ) \log ^2(2)}{x^3}\right ) \, dx}{\log ^2(2)}+\frac {\log (4) \int \frac {4^{1+2 e^{-6+2 x}} e^{-6+2 x}}{x^2} \, dx}{\log ^2(2)}\\ &=-\frac {\int \frac {2^{1+4 e^{-6+2 x}}}{x^3} \, dx}{\log ^2(2)}+\frac {\log (4) \int \frac {4^{1+2 e^{-6+2 x}} e^{-6+2 x}}{x^2} \, dx}{\log ^2(2)}+\int \frac {-10+x+x^3}{x^3} \, dx\\ &=-\frac {\int \frac {2^{1+4 e^{-6+2 x}}}{x^3} \, dx}{\log ^2(2)}+\frac {\log (4) \int \frac {4^{1+2 e^{-6+2 x}} e^{-6+2 x}}{x^2} \, dx}{\log ^2(2)}+\int \left (1-\frac {10}{x^3}+\frac {1}{x^2}\right ) \, dx\\ &=\frac {5}{x^2}-\frac {1}{x}+x-\frac {\int \frac {2^{1+4 e^{-6+2 x}}}{x^3} \, dx}{\log ^2(2)}+\frac {\log (4) \int \frac {4^{1+2 e^{-6+2 x}} e^{-6+2 x}}{x^2} \, dx}{\log ^2(2)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.11, size = 35, normalized size = 1.06 \begin {gather*} \frac {5}{x^2}-\frac {1}{x}+x+\frac {2^{-1+4 e^{-6+2 x}} \log (4)}{x^2 \log ^3(2)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.42, size = 43, normalized size = 1.30
method | result | size |
risch | \(x +\frac {-x \ln \left (2\right )^{2}+5 \ln \left (2\right )^{2}}{\ln \left (2\right )^{2} x^{2}}+\frac {4^{2 \,{\mathrm e}^{2 x -6}}}{\ln \left (2\right )^{2} x^{2}}\) | \(43\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.53, size = 44, normalized size = 1.33 \begin {gather*} \frac {x \log \left (2\right )^{2} - \frac {\log \left (2\right )^{2}}{x} + \frac {5 \, \log \left (2\right )^{2}}{x^{2}} + \frac {2^{4 \, e^{\left (2 \, x - 6\right )}}}{x^{2}}}{\log \left (2\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 32, normalized size = 0.97 \begin {gather*} \frac {{\left (x^{3} - x + 5\right )} \log \left (2\right )^{2} + 2^{4 \, e^{\left (2 \, x - 6\right )}}}{x^{2} \log \left (2\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 29, normalized size = 0.88 \begin {gather*} x + \frac {5 - x}{x^{2}} + \frac {e^{4 e^{2 x - 6} \log {\left (2 \right )}}}{x^{2} \log {\left (2 \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.40, size = 34, normalized size = 1.03 \begin {gather*} x+\frac {2^{4\,{\mathrm {e}}^{2\,x-6}}-x\,{\ln \left (2\right )}^2+5\,{\ln \left (2\right )}^2}{x^2\,{\ln \left (2\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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