Integrand size = 66, antiderivative size = 18 \[ \int \frac {e^{\frac {49+1134 x^7+6561 e^x x^{12}+6561 x^{13}+6561 x^{14}}{6561 x^{12}}} \left (-196-1890 x^7+2187 x^{13}+2187 e^x x^{13}+4374 x^{14}\right )}{2187 x^{13}} \, dx=e^{e^x+x+\left (\frac {7}{81 x^6}+x\right )^2} \]
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Time = 0.81 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.89, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.030, Rules used = {12, 6838} \[ \int \frac {e^{\frac {49+1134 x^7+6561 e^x x^{12}+6561 x^{13}+6561 x^{14}}{6561 x^{12}}} \left (-196-1890 x^7+2187 x^{13}+2187 e^x x^{13}+4374 x^{14}\right )}{2187 x^{13}} \, dx=e^{\frac {6561 x^{14}+6561 x^{13}+6561 e^x x^{12}+1134 x^7+49}{6561 x^{12}}} \]
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Rule 12
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \frac {\int \frac {e^{\frac {49+1134 x^7+6561 e^x x^{12}+6561 x^{13}+6561 x^{14}}{6561 x^{12}}} \left (-196-1890 x^7+2187 x^{13}+2187 e^x x^{13}+4374 x^{14}\right )}{x^{13}} \, dx}{2187} \\ & = e^{\frac {49+1134 x^7+6561 e^x x^{12}+6561 x^{13}+6561 x^{14}}{6561 x^{12}}} \\ \end{align*}
Time = 0.78 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.33 \[ \int \frac {e^{\frac {49+1134 x^7+6561 e^x x^{12}+6561 x^{13}+6561 x^{14}}{6561 x^{12}}} \left (-196-1890 x^7+2187 x^{13}+2187 e^x x^{13}+4374 x^{14}\right )}{2187 x^{13}} \, dx=e^{e^x+\frac {49}{6561 x^{12}}+\frac {14}{81 x^5}+x+x^2} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(30\) vs. \(2(14)=28\).
Time = 3.80 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.72
method | result | size |
derivativedivides | \({\mathrm e}^{\frac {6561 x^{12} {\mathrm e}^{x}+6561 x^{14}+6561 x^{13}+1134 x^{7}+49}{6561 x^{12}}}\) | \(31\) |
default | \({\mathrm e}^{\frac {6561 x^{12} {\mathrm e}^{x}+6561 x^{14}+6561 x^{13}+1134 x^{7}+49}{6561 x^{12}}}\) | \(31\) |
risch | \({\mathrm e}^{\frac {6561 x^{12} {\mathrm e}^{x}+6561 x^{14}+6561 x^{13}+1134 x^{7}+49}{6561 x^{12}}}\) | \(31\) |
parallelrisch | \({\mathrm e}^{\frac {6561 x^{12} {\mathrm e}^{x}+6561 x^{14}+6561 x^{13}+1134 x^{7}+49}{6561 x^{12}}}\) | \(31\) |
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Time = 0.26 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.67 \[ \int \frac {e^{\frac {49+1134 x^7+6561 e^x x^{12}+6561 x^{13}+6561 x^{14}}{6561 x^{12}}} \left (-196-1890 x^7+2187 x^{13}+2187 e^x x^{13}+4374 x^{14}\right )}{2187 x^{13}} \, dx=e^{\left (\frac {6561 \, x^{14} + 6561 \, x^{13} + 6561 \, x^{12} e^{x} + 1134 \, x^{7} + 49}{6561 \, x^{12}}\right )} \]
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Time = 0.14 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.50 \[ \int \frac {e^{\frac {49+1134 x^7+6561 e^x x^{12}+6561 x^{13}+6561 x^{14}}{6561 x^{12}}} \left (-196-1890 x^7+2187 x^{13}+2187 e^x x^{13}+4374 x^{14}\right )}{2187 x^{13}} \, dx=e^{\frac {x^{14} + x^{13} + x^{12} e^{x} + \frac {14 x^{7}}{81} + \frac {49}{6561}}{x^{12}}} \]
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Time = 0.28 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {49+1134 x^7+6561 e^x x^{12}+6561 x^{13}+6561 x^{14}}{6561 x^{12}}} \left (-196-1890 x^7+2187 x^{13}+2187 e^x x^{13}+4374 x^{14}\right )}{2187 x^{13}} \, dx=e^{\left (x^{2} + x + \frac {14}{81 \, x^{5}} + \frac {49}{6561 \, x^{12}} + e^{x}\right )} \]
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Time = 0.27 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {49+1134 x^7+6561 e^x x^{12}+6561 x^{13}+6561 x^{14}}{6561 x^{12}}} \left (-196-1890 x^7+2187 x^{13}+2187 e^x x^{13}+4374 x^{14}\right )}{2187 x^{13}} \, dx=e^{\left (x^{2} + x + \frac {14}{81 \, x^{5}} + \frac {49}{6561 \, x^{12}} + e^{x}\right )} \]
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Time = 9.29 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {e^{\frac {49+1134 x^7+6561 e^x x^{12}+6561 x^{13}+6561 x^{14}}{6561 x^{12}}} \left (-196-1890 x^7+2187 x^{13}+2187 e^x x^{13}+4374 x^{14}\right )}{2187 x^{13}} \, dx={\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{\frac {14}{81\,x^5}}\,{\mathrm {e}}^{\frac {49}{6561\,x^{12}}}\,{\mathrm {e}}^x \]
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