Optimal. Leaf size=17 \[ -1+\log \left (e^{5+\frac {1}{15} x (11+x)}+x\right ) \]
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Rubi [A] time = 0.06, antiderivative size = 19, normalized size of antiderivative = 1.12, number of steps used = 1, number of rules used = 1, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.022, Rules used = {6684} \begin {gather*} \log \left (e^{\frac {x^2}{15}+\frac {11 x}{15}+5}+x\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (e^{5+\frac {11 x}{15}+\frac {x^2}{15}}+x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.16, size = 19, normalized size = 1.12 \begin {gather*} \log \left (e^{5+\frac {11 x}{15}+\frac {x^2}{15}}+x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 14, normalized size = 0.82 \begin {gather*} \log \left (x + e^{\left (\frac {1}{15} \, x^{2} + \frac {11}{15} \, x + 5\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 14, normalized size = 0.82 \begin {gather*} \log \left (x + e^{\left (\frac {1}{15} \, x^{2} + \frac {11}{15} \, x + 5\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 17, normalized size = 1.00
method | result | size |
risch | \(-5+\ln \left ({\mathrm e}^{\frac {1}{15} x^{2}+\frac {11}{15} x +5}+x \right )\) | \(17\) |
norman | \(\ln \left (15 \,{\mathrm e}^{\frac {1}{15} x^{2}+\frac {11}{15} x +5}+15 x \right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 25, normalized size = 1.47 \begin {gather*} \frac {11}{15} \, x + \log \left ({\left (x + e^{\left (\frac {1}{15} \, x^{2} + \frac {11}{15} \, x + 5\right )}\right )} e^{\left (-\frac {11}{15} \, x - 5\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.16, size = 14, normalized size = 0.82 \begin {gather*} \ln \left (x+{\mathrm {e}}^{\frac {x^2}{15}+\frac {11\,x}{15}+5}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 29, normalized size = 1.71 \begin {gather*} \frac {14 x^{2}}{225} + \frac {154 x}{225} + \frac {\log {\left (x + e^{\frac {x^{2}}{15} + \frac {11 x}{15} + 5} \right )}}{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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