Integrand size = 39, antiderivative size = 18 \[ \int \frac {e^{4 x} (-2+x)+1944 x^{14}+e^{2 x} \left (18 x^7-36 x^8\right )}{324 x^9} \, dx=\left (-\frac {e^{2 x}}{36 x^4}+x^3\right )^2 \]
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Time = 0.05 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.56, number of steps used = 5, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12, 14, 2228} \[ \int \frac {e^{4 x} (-2+x)+1944 x^{14}+e^{2 x} \left (18 x^7-36 x^8\right )}{324 x^9} \, dx=\frac {e^{4 x}}{1296 x^8}+x^6-\frac {e^{2 x}}{18 x} \]
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Rule 12
Rule 14
Rule 2228
Rubi steps \begin{align*} \text {integral}& = \frac {1}{324} \int \frac {e^{4 x} (-2+x)+1944 x^{14}+e^{2 x} \left (18 x^7-36 x^8\right )}{x^9} \, dx \\ & = \frac {1}{324} \int \left (\frac {e^{4 x} (-2+x)}{x^9}+1944 x^5-\frac {18 e^{2 x} (-1+2 x)}{x^2}\right ) \, dx \\ & = x^6+\frac {1}{324} \int \frac {e^{4 x} (-2+x)}{x^9} \, dx-\frac {1}{18} \int \frac {e^{2 x} (-1+2 x)}{x^2} \, dx \\ & = \frac {e^{4 x}}{1296 x^8}-\frac {e^{2 x}}{18 x}+x^6 \\ \end{align*}
Time = 0.07 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.56 \[ \int \frac {e^{4 x} (-2+x)+1944 x^{14}+e^{2 x} \left (18 x^7-36 x^8\right )}{324 x^9} \, dx=\frac {e^{4 x}}{1296 x^8}-\frac {e^{2 x}}{18 x}+x^6 \]
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Time = 0.08 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.28
method | result | size |
default | \(x^{6}+\frac {{\mathrm e}^{4 x}}{1296 x^{8}}-\frac {{\mathrm e}^{2 x}}{18 x}\) | \(23\) |
risch | \(x^{6}+\frac {{\mathrm e}^{4 x}}{1296 x^{8}}-\frac {{\mathrm e}^{2 x}}{18 x}\) | \(23\) |
parts | \(x^{6}+\frac {{\mathrm e}^{4 x}}{1296 x^{8}}-\frac {{\mathrm e}^{2 x}}{18 x}\) | \(23\) |
parallelrisch | \(\frac {1296 x^{14}-72 \,{\mathrm e}^{2 x} x^{7}+{\mathrm e}^{4 x}}{1296 x^{8}}\) | \(25\) |
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none
Time = 0.24 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.33 \[ \int \frac {e^{4 x} (-2+x)+1944 x^{14}+e^{2 x} \left (18 x^7-36 x^8\right )}{324 x^9} \, dx=\frac {1296 \, x^{14} - 72 \, x^{7} e^{\left (2 \, x\right )} + e^{\left (4 \, x\right )}}{1296 \, x^{8}} \]
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Time = 0.06 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.44 \[ \int \frac {e^{4 x} (-2+x)+1944 x^{14}+e^{2 x} \left (18 x^7-36 x^8\right )}{324 x^9} \, dx=x^{6} + \frac {- 1296 x^{8} e^{2 x} + 18 x e^{4 x}}{23328 x^{9}} \]
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Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.22 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.72 \[ \int \frac {e^{4 x} (-2+x)+1944 x^{14}+e^{2 x} \left (18 x^7-36 x^8\right )}{324 x^9} \, dx=x^{6} - \frac {1}{9} \, {\rm Ei}\left (2 \, x\right ) + \frac {1}{9} \, \Gamma \left (-1, -2 \, x\right ) + \frac {4096}{81} \, \Gamma \left (-7, -4 \, x\right ) + \frac {32768}{81} \, \Gamma \left (-8, -4 \, x\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.33 \[ \int \frac {e^{4 x} (-2+x)+1944 x^{14}+e^{2 x} \left (18 x^7-36 x^8\right )}{324 x^9} \, dx=\frac {1296 \, x^{14} - 72 \, x^{7} e^{\left (2 \, x\right )} + e^{\left (4 \, x\right )}}{1296 \, x^{8}} \]
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Time = 8.08 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \frac {e^{4 x} (-2+x)+1944 x^{14}+e^{2 x} \left (18 x^7-36 x^8\right )}{324 x^9} \, dx=\frac {{\left ({\mathrm {e}}^{2\,x}-36\,x^7\right )}^2}{1296\,x^8} \]
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