Integrand size = 45, antiderivative size = 17 \[ \int \frac {15+e^{\frac {1}{15} \left (75+11 x+x^2\right )} (11+2 x)}{15 e^{\frac {1}{15} \left (75+11 x+x^2\right )}+15 x} \, dx=-1+\log \left (e^{5+\frac {1}{15} x (11+x)}+x\right ) \]
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Time = 0.04 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.12, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.022, Rules used = {6816} \[ \int \frac {15+e^{\frac {1}{15} \left (75+11 x+x^2\right )} (11+2 x)}{15 e^{\frac {1}{15} \left (75+11 x+x^2\right )}+15 x} \, dx=\log \left (e^{\frac {x^2}{15}+\frac {11 x}{15}+5}+x\right ) \]
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Rule 6816
Rubi steps \begin{align*} \text {integral}& = \log \left (e^{5+\frac {11 x}{15}+\frac {x^2}{15}}+x\right ) \\ \end{align*}
Time = 0.10 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \frac {15+e^{\frac {1}{15} \left (75+11 x+x^2\right )} (11+2 x)}{15 e^{\frac {1}{15} \left (75+11 x+x^2\right )}+15 x} \, dx=\log \left (e^{\frac {1}{15} \left (75+11 x+x^2\right )}+x\right ) \]
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Time = 0.09 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88
method | result | size |
parallelrisch | \(\ln \left ({\mathrm e}^{\frac {1}{15} x^{2}+\frac {11}{15} x +5}+x \right )\) | \(15\) |
risch | \(-5+\ln \left ({\mathrm e}^{\frac {1}{15} x^{2}+\frac {11}{15} x +5}+x \right )\) | \(17\) |
norman | \(\ln \left (15 \,{\mathrm e}^{\frac {1}{15} x^{2}+\frac {11}{15} x +5}+15 x \right )\) | \(19\) |
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none
Time = 0.45 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int \frac {15+e^{\frac {1}{15} \left (75+11 x+x^2\right )} (11+2 x)}{15 e^{\frac {1}{15} \left (75+11 x+x^2\right )}+15 x} \, dx=\log \left (x + e^{\left (\frac {1}{15} \, x^{2} + \frac {11}{15} \, x + 5\right )}\right ) \]
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Time = 0.08 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int \frac {15+e^{\frac {1}{15} \left (75+11 x+x^2\right )} (11+2 x)}{15 e^{\frac {1}{15} \left (75+11 x+x^2\right )}+15 x} \, dx=\log {\left (x + e^{\frac {x^{2}}{15} + \frac {11 x}{15} + 5} \right )} \]
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none
Time = 0.22 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.47 \[ \int \frac {15+e^{\frac {1}{15} \left (75+11 x+x^2\right )} (11+2 x)}{15 e^{\frac {1}{15} \left (75+11 x+x^2\right )}+15 x} \, dx=\frac {11}{15} \, x + \log \left ({\left (x + e^{\left (\frac {1}{15} \, x^{2} + \frac {11}{15} \, x + 5\right )}\right )} e^{\left (-\frac {11}{15} \, x - 5\right )}\right ) \]
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none
Time = 0.28 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int \frac {15+e^{\frac {1}{15} \left (75+11 x+x^2\right )} (11+2 x)}{15 e^{\frac {1}{15} \left (75+11 x+x^2\right )}+15 x} \, dx=\log \left (x + e^{\left (\frac {1}{15} \, x^{2} + \frac {11}{15} \, x + 5\right )}\right ) \]
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Time = 0.18 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int \frac {15+e^{\frac {1}{15} \left (75+11 x+x^2\right )} (11+2 x)}{15 e^{\frac {1}{15} \left (75+11 x+x^2\right )}+15 x} \, dx=\ln \left (x+{\mathrm {e}}^{\frac {x^2}{15}+\frac {11\,x}{15}+5}\right ) \]
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