Integrand size = 39, antiderivative size = 31 \[ \int \frac {2 x^4+e^{\frac {5+e^{e^5}}{x}} \left (165+33 e^{e^5}+33 x\right )}{11 x^3} \, dx=\frac {x^2}{11}+\frac {x-3 \left (e^{\frac {5+e^{e^5}}{x}}+x\right )}{x} \]
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Time = 0.06 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.84, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12, 14, 2326} \[ \int \frac {2 x^4+e^{\frac {5+e^{e^5}}{x}} \left (165+33 e^{e^5}+33 x\right )}{11 x^3} \, dx=\frac {x^2}{11}-\frac {3 e^{\frac {5+e^{e^5}}{x}}}{x} \]
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Rule 12
Rule 14
Rule 2326
Rubi steps \begin{align*} \text {integral}& = \frac {1}{11} \int \frac {2 x^4+e^{\frac {5+e^{e^5}}{x}} \left (165+33 e^{e^5}+33 x\right )}{x^3} \, dx \\ & = \frac {1}{11} \int \left (2 x+\frac {33 e^{\frac {5+e^{e^5}}{x}} \left (5+e^{e^5}+x\right )}{x^3}\right ) \, dx \\ & = \frac {x^2}{11}+3 \int \frac {e^{\frac {5+e^{e^5}}{x}} \left (5+e^{e^5}+x\right )}{x^3} \, dx \\ & = -\frac {3 e^{\frac {5+e^{e^5}}{x}}}{x}+\frac {x^2}{11} \\ \end{align*}
Time = 0.05 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.84 \[ \int \frac {2 x^4+e^{\frac {5+e^{e^5}}{x}} \left (165+33 e^{e^5}+33 x\right )}{11 x^3} \, dx=-\frac {3 e^{\frac {5+e^{e^5}}{x}}}{x}+\frac {x^2}{11} \]
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Time = 0.22 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.71
method | result | size |
risch | \(\frac {x^{2}}{11}-\frac {3 \,{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}}}{x}\) | \(22\) |
parallelrisch | \(\frac {x^{3}-33 \,{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}}}{11 x}\) | \(22\) |
norman | \(\frac {\frac {x^{4}}{11}-3 \,{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}} x}{x^{2}}\) | \(24\) |
parts | \(\frac {x^{2}}{11}-\frac {3 \left ({\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}} {\mathrm e}^{{\mathrm e}^{5}}+{\mathrm e}^{{\mathrm e}^{5}} \left (\frac {\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right ) {\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}}}{x}-{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}}\right )+\frac {5 \left ({\mathrm e}^{{\mathrm e}^{5}}+5\right ) {\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}}}{x}\right )}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}\) | \(87\) |
derivativedivides | \(-\frac {-\frac {625 x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}-\frac {500 \,{\mathrm e}^{{\mathrm e}^{5}} x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}-\frac {150 \,{\mathrm e}^{2 \,{\mathrm e}^{5}} x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}-\frac {20 \,{\mathrm e}^{3 \,{\mathrm e}^{5}} x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}-\frac {{\mathrm e}^{4 \,{\mathrm e}^{5}} x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}+\frac {165 \left ({\mathrm e}^{{\mathrm e}^{5}}+5\right ) {\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}}}{x}+33 \,{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}} {\mathrm e}^{{\mathrm e}^{5}}+33 \,{\mathrm e}^{{\mathrm e}^{5}} \left (\frac {\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right ) {\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}}}{x}-{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}}\right )}{11 \left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}\) | \(161\) |
default | \(-\frac {-\frac {625 x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}-\frac {500 \,{\mathrm e}^{{\mathrm e}^{5}} x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}-\frac {150 \,{\mathrm e}^{2 \,{\mathrm e}^{5}} x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}-\frac {20 \,{\mathrm e}^{3 \,{\mathrm e}^{5}} x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}-\frac {{\mathrm e}^{4 \,{\mathrm e}^{5}} x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}+\frac {165 \left ({\mathrm e}^{{\mathrm e}^{5}}+5\right ) {\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}}}{x}+33 \,{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}} {\mathrm e}^{{\mathrm e}^{5}}+33 \,{\mathrm e}^{{\mathrm e}^{5}} \left (\frac {\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right ) {\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}}}{x}-{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}}\right )}{11 \left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}\) | \(161\) |
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Time = 0.25 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.68 \[ \int \frac {2 x^4+e^{\frac {5+e^{e^5}}{x}} \left (165+33 e^{e^5}+33 x\right )}{11 x^3} \, dx=\frac {x^{3} - 33 \, e^{\left (\frac {e^{\left (e^{5}\right )} + 5}{x}\right )}}{11 \, x} \]
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Time = 0.07 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.55 \[ \int \frac {2 x^4+e^{\frac {5+e^{e^5}}{x}} \left (165+33 e^{e^5}+33 x\right )}{11 x^3} \, dx=\frac {x^{2}}{11} - \frac {3 e^{\frac {5 + e^{e^{5}}}{x}}}{x} \]
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\[ \int \frac {2 x^4+e^{\frac {5+e^{e^5}}{x}} \left (165+33 e^{e^5}+33 x\right )}{11 x^3} \, dx=\int { \frac {2 \, x^{4} + 33 \, {\left (x + e^{\left (e^{5}\right )} + 5\right )} e^{\left (\frac {e^{\left (e^{5}\right )} + 5}{x}\right )}}{11 \, x^{3}} \,d x } \]
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Leaf count of result is larger than twice the leaf count of optimal. 55 vs. \(2 (27) = 54\).
Time = 0.28 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.77 \[ \int \frac {2 x^4+e^{\frac {5+e^{e^5}}{x}} \left (165+33 e^{e^5}+33 x\right )}{11 x^3} \, dx=-\frac {x^{2} {\left (\frac {33 \, {\left (e^{\left (e^{5}\right )} + 5\right )}^{3} e^{\left (\frac {e^{\left (e^{5}\right )} + 5}{x}\right )}}{x^{3}} - e^{\left (3 \, e^{5}\right )} - 15 \, e^{\left (2 \, e^{5}\right )} - 75 \, e^{\left (e^{5}\right )} - 125\right )}}{11 \, {\left (e^{\left (e^{5}\right )} + 5\right )}^{3}} \]
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Time = 8.64 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.81 \[ \int \frac {2 x^4+e^{\frac {5+e^{e^5}}{x}} \left (165+33 e^{e^5}+33 x\right )}{11 x^3} \, dx=\frac {x^2}{11}-\frac {3\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{{\mathrm {e}}^5}}{x}}\,{\mathrm {e}}^{5/x}}{x} \]
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