Optimal. Leaf size=22 \[ \frac {e^{\frac {1+e^{21}+2 x}{x}}}{x \log (x)} \]
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Rubi [F]
time = 1.17, 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^{\frac {1+e^{21}+2 x}{x}} x+e^{\frac {1+e^{21}+2 x}{x}} \left (-1-e^{21}-x\right ) \log (x)}{x^3 \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{2+\frac {1+e^{21}}{x}} \left (-x-\left (1+e^{21}+x\right ) \log (x)\right )}{x^3 \log ^2(x)} \, dx\\ &=\int \left (-\frac {e^{2+\frac {1+e^{21}}{x}}}{x^2 \log ^2(x)}+\frac {e^{2+\frac {1+e^{21}}{x}} \left (-1-e^{21}-x\right )}{x^3 \log (x)}\right ) \, dx\\ &=-\int \frac {e^{2+\frac {1+e^{21}}{x}}}{x^2 \log ^2(x)} \, dx+\int \frac {e^{2+\frac {1+e^{21}}{x}} \left (-1-e^{21}-x\right )}{x^3 \log (x)} \, dx\\ &=\int \left (\frac {e^{2+\frac {1+e^{21}}{x}} \left (-1-e^{21}\right )}{x^3 \log (x)}-\frac {e^{2+\frac {1+e^{21}}{x}}}{x^2 \log (x)}\right ) \, dx-\int \frac {e^{2+\frac {1+e^{21}}{x}}}{x^2 \log ^2(x)} \, dx\\ &=\left (-1-e^{21}\right ) \int \frac {e^{2+\frac {1+e^{21}}{x}}}{x^3 \log (x)} \, dx-\int \frac {e^{2+\frac {1+e^{21}}{x}}}{x^2 \log ^2(x)} \, dx-\int \frac {e^{2+\frac {1+e^{21}}{x}}}{x^2 \log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.10, size = 21, normalized size = 0.95 \begin {gather*} \frac {e^{2+\frac {1+e^{21}}{x}}}{x \log (x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.43, size = 21, normalized size = 0.95
method | result | size |
risch | \(\frac {{\mathrm e}^{\frac {{\mathrm e}^{21}+2 x +1}{x}}}{x \ln \left (x \right )}\) | \(21\) |
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 = 20, normalized size = 0.91 \begin {gather*} \frac {e^{\left (\frac {2 \, x + e^{21} + 1}{x}\right )}}{x \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 15, normalized size = 0.68 \begin {gather*} \frac {e^{\frac {2 x + 1 + e^{21}}{x}}}{x \log {\left (x \right )}} \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 = 7.52, size = 21, normalized size = 0.95 \begin {gather*} \frac {{\mathrm {e}}^{\frac {{\mathrm {e}}^{21}}{x}}\,{\mathrm {e}}^{1/x}\,{\mathrm {e}}^2}{x\,\ln \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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