Optimal. Leaf size=25 \[ -\frac {6 x}{7}-\frac {2+\frac {3 x (3+2 x)}{e^5}}{\log (x)} \]
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Rubi [F]
time = 0.23, 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 {14 e^5+63 x+42 x^2+\left (-63 x-84 x^2\right ) \log (x)-6 e^5 x \log ^2(x)}{7 e^5 x \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} &=\frac {\int \frac {14 e^5+63 x+42 x^2+\left (-63 x-84 x^2\right ) \log (x)-6 e^5 x \log ^2(x)}{x \log ^2(x)} \, dx}{7 e^5}\\ &=\frac {\int \left (-6 e^5+\frac {7 \left (2 e^5+9 x+6 x^2\right )}{x \log ^2(x)}-\frac {21 (3+4 x)}{\log (x)}\right ) \, dx}{7 e^5}\\ &=-\frac {6 x}{7}+\frac {\int \frac {2 e^5+9 x+6 x^2}{x \log ^2(x)} \, dx}{e^5}-\frac {3 \int \frac {3+4 x}{\log (x)} \, dx}{e^5}\\ &=-\frac {6 x}{7}+\frac {\int \frac {2 e^5+9 x+6 x^2}{x \log ^2(x)} \, dx}{e^5}-\frac {3 \int \left (\frac {3}{\log (x)}+\frac {4 x}{\log (x)}\right ) \, dx}{e^5}\\ &=-\frac {6 x}{7}+\frac {\int \frac {2 e^5+9 x+6 x^2}{x \log ^2(x)} \, dx}{e^5}-\frac {9 \int \frac {1}{\log (x)} \, dx}{e^5}-\frac {12 \int \frac {x}{\log (x)} \, dx}{e^5}\\ &=-\frac {6 x}{7}-\frac {9 \text {li}(x)}{e^5}+\frac {\int \frac {2 e^5+9 x+6 x^2}{x \log ^2(x)} \, dx}{e^5}-\frac {12 \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )}{e^5}\\ &=-\frac {6 x}{7}-\frac {12 \text {Ei}(2 \log (x))}{e^5}-\frac {9 \text {li}(x)}{e^5}+\frac {\int \frac {2 e^5+9 x+6 x^2}{x \log ^2(x)} \, dx}{e^5}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 28, normalized size = 1.12 \begin {gather*} -\frac {6 x}{7}+\frac {-2 e^5-9 x-6 x^2}{e^5 \log (x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 37, normalized size = 1.48
method | result | size |
risch | \(-\frac {6 x}{7}-\frac {{\mathrm e}^{-5} \left (6 x^{2}+2 \,{\mathrm e}^{5}+9 x \right )}{\ln \left (x \right )}\) | \(26\) |
norman | \(\frac {-2-9 x \,{\mathrm e}^{-5}-\frac {6 x \ln \left (x \right )}{7}-6 \,{\mathrm e}^{-5} x^{2}}{\ln \left (x \right )}\) | \(29\) |
default | \(\frac {{\mathrm e}^{-5} \left (-6 x \,{\mathrm e}^{5}-\frac {42 x^{2}}{\ln \left (x \right )}-\frac {14 \,{\mathrm e}^{5}}{\ln \left (x \right )}-\frac {63 x}{\ln \left (x \right )}\right )}{7}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.29, size = 46, normalized size = 1.84 \begin {gather*} -\frac {1}{7} \, {\left (6 \, x e^{5} + \frac {14 \, e^{5}}{\log \left (x\right )} + 84 \, {\rm Ei}\left (2 \, \log \left (x\right )\right ) + 63 \, {\rm Ei}\left (\log \left (x\right )\right ) - 63 \, \Gamma \left (-1, -\log \left (x\right )\right ) - 84 \, \Gamma \left (-1, -2 \, \log \left (x\right )\right )\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.57, size = 28, normalized size = 1.12 \begin {gather*} -\frac {{\left (6 \, x e^{5} \log \left (x\right ) + 42 \, x^{2} + 63 \, x + 14 \, e^{5}\right )} e^{\left (-5\right )}}{7 \, \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 26, normalized size = 1.04 \begin {gather*} - \frac {6 x}{7} + \frac {- 6 x^{2} - 9 x - 2 e^{5}}{e^{5} \log {\left (x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 28, normalized size = 1.12 \begin {gather*} -\frac {{\left (6 \, x e^{5} \log \left (x\right ) + 42 \, x^{2} + 63 \, x + 14 \, e^{5}\right )} e^{\left (-5\right )}}{7 \, \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 7.44, size = 24, normalized size = 0.96 \begin {gather*} -\frac {6\,x}{7}-\frac {6\,{\mathrm {e}}^{-5}\,x^2+9\,{\mathrm {e}}^{-5}\,x+2}{\ln \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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