Integrand size = 51, antiderivative size = 15 \[ \int \frac {-7680000+e^{4 x} (-3+2 x)+e^{3 x} (-480+240 x)+e^{2 x} (-28800+9600 x)+e^x (-768000+128000 x)}{5000 x^7} \, dx=\frac {\left (-4-\frac {e^x}{10}\right )^4}{x^6} \]
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Leaf count is larger than twice the leaf count of optimal. \(52\) vs. \(2(15)=30\).
Time = 0.09 (sec) , antiderivative size = 52, normalized size of antiderivative = 3.47, number of steps used = 7, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {12, 14, 2228} \[ \int \frac {-7680000+e^{4 x} (-3+2 x)+e^{3 x} (-480+240 x)+e^{2 x} (-28800+9600 x)+e^x (-768000+128000 x)}{5000 x^7} \, dx=\frac {128 e^x}{5 x^6}+\frac {24 e^{2 x}}{25 x^6}+\frac {2 e^{3 x}}{125 x^6}+\frac {e^{4 x}}{10000 x^6}+\frac {256}{x^6} \]
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Rule 12
Rule 14
Rule 2228
Rubi steps \begin{align*} \text {integral}& = \frac {\int \frac {-7680000+e^{4 x} (-3+2 x)+e^{3 x} (-480+240 x)+e^{2 x} (-28800+9600 x)+e^x (-768000+128000 x)}{x^7} \, dx}{5000} \\ & = \frac {\int \left (-\frac {7680000}{x^7}+\frac {128000 e^x (-6+x)}{x^7}+\frac {9600 e^{2 x} (-3+x)}{x^7}+\frac {240 e^{3 x} (-2+x)}{x^7}+\frac {e^{4 x} (-3+2 x)}{x^7}\right ) \, dx}{5000} \\ & = \frac {256}{x^6}+\frac {\int \frac {e^{4 x} (-3+2 x)}{x^7} \, dx}{5000}+\frac {6}{125} \int \frac {e^{3 x} (-2+x)}{x^7} \, dx+\frac {48}{25} \int \frac {e^{2 x} (-3+x)}{x^7} \, dx+\frac {128}{5} \int \frac {e^x (-6+x)}{x^7} \, dx \\ & = \frac {256}{x^6}+\frac {128 e^x}{5 x^6}+\frac {24 e^{2 x}}{25 x^6}+\frac {2 e^{3 x}}{125 x^6}+\frac {e^{4 x}}{10000 x^6} \\ \end{align*}
Time = 0.21 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {-7680000+e^{4 x} (-3+2 x)+e^{3 x} (-480+240 x)+e^{2 x} (-28800+9600 x)+e^x (-768000+128000 x)}{5000 x^7} \, dx=\frac {\left (40+e^x\right )^4}{10000 x^6} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(27\) vs. \(2(12)=24\).
Time = 0.08 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.87
method | result | size |
parallelrisch | \(\frac {{\mathrm e}^{4 x}+160 \,{\mathrm e}^{3 x}+2560000+9600 \,{\mathrm e}^{2 x}+256000 \,{\mathrm e}^{x}}{10000 x^{6}}\) | \(28\) |
default | \(\frac {{\mathrm e}^{4 x}}{10000 x^{6}}+\frac {2 \,{\mathrm e}^{3 x}}{125 x^{6}}+\frac {256}{x^{6}}+\frac {24 \,{\mathrm e}^{2 x}}{25 x^{6}}+\frac {128 \,{\mathrm e}^{x}}{5 x^{6}}\) | \(41\) |
risch | \(\frac {{\mathrm e}^{4 x}}{10000 x^{6}}+\frac {2 \,{\mathrm e}^{3 x}}{125 x^{6}}+\frac {256}{x^{6}}+\frac {24 \,{\mathrm e}^{2 x}}{25 x^{6}}+\frac {128 \,{\mathrm e}^{x}}{5 x^{6}}\) | \(41\) |
parts | \(\frac {{\mathrm e}^{4 x}}{10000 x^{6}}+\frac {2 \,{\mathrm e}^{3 x}}{125 x^{6}}+\frac {256}{x^{6}}+\frac {24 \,{\mathrm e}^{2 x}}{25 x^{6}}+\frac {128 \,{\mathrm e}^{x}}{5 x^{6}}\) | \(41\) |
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Leaf count of result is larger than twice the leaf count of optimal. 27 vs. \(2 (11) = 22\).
Time = 0.25 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.80 \[ \int \frac {-7680000+e^{4 x} (-3+2 x)+e^{3 x} (-480+240 x)+e^{2 x} (-28800+9600 x)+e^x (-768000+128000 x)}{5000 x^7} \, dx=\frac {e^{\left (4 \, x\right )} + 160 \, e^{\left (3 \, x\right )} + 9600 \, e^{\left (2 \, x\right )} + 256000 \, e^{x} + 2560000}{10000 \, x^{6}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 48 vs. \(2 (12) = 24\).
Time = 0.10 (sec) , antiderivative size = 48, normalized size of antiderivative = 3.20 \[ \int \frac {-7680000+e^{4 x} (-3+2 x)+e^{3 x} (-480+240 x)+e^{2 x} (-28800+9600 x)+e^x (-768000+128000 x)}{5000 x^7} \, dx=\frac {256}{x^{6}} + \frac {15625 x^{18} e^{4 x} + 2500000 x^{18} e^{3 x} + 150000000 x^{18} e^{2 x} + 4000000000 x^{18} e^{x}}{156250000 x^{24}} \]
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Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.24 (sec) , antiderivative size = 62, normalized size of antiderivative = 4.13 \[ \int \frac {-7680000+e^{4 x} (-3+2 x)+e^{3 x} (-480+240 x)+e^{2 x} (-28800+9600 x)+e^x (-768000+128000 x)}{5000 x^7} \, dx=\frac {256}{x^{6}} + \frac {128}{5} \, \Gamma \left (-5, -x\right ) + \frac {1536}{25} \, \Gamma \left (-5, -2 \, x\right ) + \frac {1458}{125} \, \Gamma \left (-5, -3 \, x\right ) + \frac {256}{625} \, \Gamma \left (-5, -4 \, x\right ) + \frac {768}{5} \, \Gamma \left (-6, -x\right ) + \frac {9216}{25} \, \Gamma \left (-6, -2 \, x\right ) + \frac {8748}{125} \, \Gamma \left (-6, -3 \, x\right ) + \frac {1536}{625} \, \Gamma \left (-6, -4 \, x\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 27 vs. \(2 (11) = 22\).
Time = 0.27 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.80 \[ \int \frac {-7680000+e^{4 x} (-3+2 x)+e^{3 x} (-480+240 x)+e^{2 x} (-28800+9600 x)+e^x (-768000+128000 x)}{5000 x^7} \, dx=\frac {e^{\left (4 \, x\right )} + 160 \, e^{\left (3 \, x\right )} + 9600 \, e^{\left (2 \, x\right )} + 256000 \, e^{x} + 2560000}{10000 \, x^{6}} \]
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Time = 0.11 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int \frac {-7680000+e^{4 x} (-3+2 x)+e^{3 x} (-480+240 x)+e^{2 x} (-28800+9600 x)+e^x (-768000+128000 x)}{5000 x^7} \, dx=\frac {{\left ({\mathrm {e}}^x+40\right )}^4}{10000\,x^6} \]
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