Optimal. Leaf size=28 \[ x+\frac {(9+x) \left (-x+e^2 \left (-e^5+x\right )\right )}{x \log (5)} \]
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Rubi [A]
time = 0.02, antiderivative size = 31, normalized size of antiderivative = 1.11, number of steps
used = 5, number of rules used = 3, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.094, Rules used = {6, 12, 14}
\begin {gather*} -\frac {x \left (1-e^2-\log (5)\right )}{\log (5)}-\frac {9 e^7}{x \log (5)} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {9 e^7+\left (-1+e^2\right ) x^2+x^2 \log (5)}{x^2 \log (5)} \, dx\\ &=\int \frac {9 e^7+x^2 \left (-1+e^2+\log (5)\right )}{x^2 \log (5)} \, dx\\ &=\frac {\int \frac {9 e^7+x^2 \left (-1+e^2+\log (5)\right )}{x^2} \, dx}{\log (5)}\\ &=\frac {\int \left (-1+e^2+\frac {9 e^7}{x^2}+\log (5)\right ) \, dx}{\log (5)}\\ &=-\frac {9 e^7}{x \log (5)}-\frac {x \left (1-e^2-\log (5)\right )}{\log (5)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 23, normalized size = 0.82 \begin {gather*} \frac {-\frac {9 e^7}{x}+x \left (-1+e^2+\log (5)\right )}{\log (5)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 25, normalized size = 0.89
method | result | size |
default | \(\frac {{\mathrm e}^{2} x +x \ln \left (5\right )-x -\frac {9 \,{\mathrm e}^{7}}{x}}{\ln \left (5\right )}\) | \(25\) |
risch | \(\frac {x \,{\mathrm e}^{2}}{\ln \left (5\right )}+x -\frac {x}{\ln \left (5\right )}-\frac {9 \,{\mathrm e}^{7}}{\ln \left (5\right ) x}\) | \(29\) |
norman | \(\frac {\frac {\left ({\mathrm e}^{2}+\ln \left (5\right )-1\right ) x^{2}}{\ln \left (5\right )}-\frac {9 \,{\mathrm e}^{2} {\mathrm e}^{5}}{\ln \left (5\right )}}{x}\) | \(34\) |
gosper | \(-\frac {-x^{2} {\mathrm e}^{2}+9 \,{\mathrm e}^{2} {\mathrm e}^{5}-x^{2} \ln \left (5\right )+x^{2}}{x \ln \left (5\right )}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 21, normalized size = 0.75 \begin {gather*} \frac {x {\left (e^{2} + \log \left (5\right ) - 1\right )} - \frac {9 \, e^{7}}{x}}{\log \left (5\right )} \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 = 1.07 \begin {gather*} \frac {x^{2} e^{2} + x^{2} \log \left (5\right ) - x^{2} - 9 \, e^{7}}{x \log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 19, normalized size = 0.68 \begin {gather*} \frac {x \left (-1 + \log {\left (5 \right )} + e^{2}\right ) - \frac {9 e^{7}}{x}}{\log {\left (5 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 24, normalized size = 0.86 \begin {gather*} \frac {x e^{2} + x \log \left (5\right ) - x - \frac {9 \, e^{7}}{x}}{\log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.09, size = 24, normalized size = 0.86 \begin {gather*} \frac {x\,\left ({\mathrm {e}}^2+\ln \left (5\right )-1\right )}{\ln \left (5\right )}-\frac {9\,{\mathrm {e}}^7}{x\,\ln \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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