Optimal. Leaf size=18 \[ \log \left (-16+\frac {e^{\frac {6 (9+x)}{31}}+x}{x}\right ) \]
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Rubi [A] time = 0.73, antiderivative size = 19, normalized size of antiderivative = 1.06, number of steps used = 4, number of rules used = 4, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {6741, 12, 6712, 31} \begin {gather*} \log \left (15-\frac {e^{\frac {6 x}{31}+\frac {54}{31}}}{x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 31
Rule 6712
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {54}{31}+\frac {6 x}{31}} (-31+6 x)}{31 \left (e^{\frac {54}{31}+\frac {6 x}{31}}-15 x\right ) x} \, dx\\ &=\frac {1}{31} \int \frac {e^{\frac {54}{31}+\frac {6 x}{31}} (-31+6 x)}{\left (e^{\frac {54}{31}+\frac {6 x}{31}}-15 x\right ) x} \, dx\\ &=\operatorname {Subst}\left (\int \frac {1}{-15+x} \, dx,x,\frac {e^{\frac {54}{31}+\frac {6 x}{31}}}{x}\right )\\ &=\log \left (15-\frac {e^{\frac {54}{31}+\frac {6 x}{31}}}{x}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.19, size = 27, normalized size = 1.50 \begin {gather*} \frac {1}{31} \left (31 \log \left (e^{\frac {54}{31}+\frac {6 x}{31}}-15 x\right )-31 \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 16, normalized size = 0.89 \begin {gather*} -\log \relax (x) + \log \left (-15 \, x + e^{\left (\frac {6}{31} \, x + \frac {54}{31}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.32, size = 18, normalized size = 1.00 \begin {gather*} \log \left (15 \, x - e^{\left (\frac {6}{31} \, x + \frac {54}{31}\right )}\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, size = 18, normalized size = 1.00
method | result | size |
risch | \(-\ln \relax (x )-\frac {54}{31}+\ln \left ({\mathrm e}^{\frac {6 x}{31}+\frac {54}{31}}-15 x \right )\) | \(18\) |
norman | \(-\ln \relax (x )+\ln \left (15 x -{\mathrm e}^{\frac {6 x}{31}+\frac {54}{31}}\right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 24, normalized size = 1.33 \begin {gather*} \log \left (-{\left (15 \, x e^{\frac {8}{31}} - e^{\left (\frac {6}{31} \, x + 2\right )}\right )} e^{\left (-2\right )}\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.43, size = 16, normalized size = 0.89 \begin {gather*} \ln \left (x-\frac {{\mathrm {e}}^{54/31}\,{\left ({\mathrm {e}}^x\right )}^{6/31}}{15}\right )-\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 17, normalized size = 0.94 \begin {gather*} - \log {\relax (x )} + \log {\left (- 15 x + e^{\frac {6 x}{31} + \frac {54}{31}} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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