Integrand size = 56, antiderivative size = 26 \[ \int \left (-1+486 x^5+e^{7 x} \left (2430 x^4+4374 x^5+1134 x^6\right )+e^{14 x} \left (2916 x^3+12636 x^4+7290 x^5+1134 x^6\right )\right ) \, dx=-1-x+81 x^4 \left (-e^{7 x} (-3-x)+x\right )^2 \]
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Leaf count is larger than twice the leaf count of optimal. \(59\) vs. \(2(26)=52\).
Time = 0.30 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.27, number of steps used = 46, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {1608, 2227, 2207, 2225} \[ \int \left (-1+486 x^5+e^{7 x} \left (2430 x^4+4374 x^5+1134 x^6\right )+e^{14 x} \left (2916 x^3+12636 x^4+7290 x^5+1134 x^6\right )\right ) \, dx=162 e^{7 x} x^6+81 e^{14 x} x^6+81 x^6+486 e^{7 x} x^5+486 e^{14 x} x^5+729 e^{14 x} x^4-x \]
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Rule 1608
Rule 2207
Rule 2225
Rule 2227
Rubi steps \begin{align*} \text {integral}& = -x+81 x^6+\int e^{7 x} \left (2430 x^4+4374 x^5+1134 x^6\right ) \, dx+\int e^{14 x} \left (2916 x^3+12636 x^4+7290 x^5+1134 x^6\right ) \, dx \\ & = -x+81 x^6+\int e^{7 x} x^4 \left (2430+4374 x+1134 x^2\right ) \, dx+\int \left (2916 e^{14 x} x^3+12636 e^{14 x} x^4+7290 e^{14 x} x^5+1134 e^{14 x} x^6\right ) \, dx \\ & = -x+81 x^6+1134 \int e^{14 x} x^6 \, dx+2916 \int e^{14 x} x^3 \, dx+7290 \int e^{14 x} x^5 \, dx+12636 \int e^{14 x} x^4 \, dx+\int \left (2430 e^{7 x} x^4+4374 e^{7 x} x^5+1134 e^{7 x} x^6\right ) \, dx \\ & = -x+\frac {1458}{7} e^{14 x} x^3+\frac {6318}{7} e^{14 x} x^4+\frac {3645}{7} e^{14 x} x^5+81 x^6+81 e^{14 x} x^6-486 \int e^{14 x} x^5 \, dx-\frac {4374}{7} \int e^{14 x} x^2 \, dx+1134 \int e^{7 x} x^6 \, dx+2430 \int e^{7 x} x^4 \, dx-\frac {18225}{7} \int e^{14 x} x^4 \, dx-\frac {25272}{7} \int e^{14 x} x^3 \, dx+4374 \int e^{7 x} x^5 \, dx \\ & = -x-\frac {2187}{49} e^{14 x} x^2-\frac {2430}{49} e^{14 x} x^3+\frac {2430}{7} e^{7 x} x^4+\frac {70227}{98} e^{14 x} x^4+\frac {4374}{7} e^{7 x} x^5+486 e^{14 x} x^5+81 x^6+162 e^{7 x} x^6+81 e^{14 x} x^6+\frac {4374}{49} \int e^{14 x} x \, dx+\frac {1215}{7} \int e^{14 x} x^4 \, dx+\frac {36450}{49} \int e^{14 x} x^3 \, dx+\frac {37908}{49} \int e^{14 x} x^2 \, dx-972 \int e^{7 x} x^5 \, dx-\frac {9720}{7} \int e^{7 x} x^3 \, dx-\frac {21870}{7} \int e^{7 x} x^4 \, dx \\ & = -x+\frac {2187}{343} e^{14 x} x+\frac {3645}{343} e^{14 x} x^2-\frac {9720}{49} e^{7 x} x^3+\frac {1215}{343} e^{14 x} x^3-\frac {4860}{49} e^{7 x} x^4+729 e^{14 x} x^4+486 e^{7 x} x^5+486 e^{14 x} x^5+81 x^6+162 e^{7 x} x^6+81 e^{14 x} x^6-\frac {2187}{343} \int e^{14 x} \, dx-\frac {2430}{49} \int e^{14 x} x^3 \, dx-\frac {37908}{343} \int e^{14 x} x \, dx-\frac {54675}{343} \int e^{14 x} x^2 \, dx+\frac {29160}{49} \int e^{7 x} x^2 \, dx+\frac {4860}{7} \int e^{7 x} x^4 \, dx+\frac {87480}{49} \int e^{7 x} x^3 \, dx \\ & = -\frac {2187 e^{14 x}}{4802}-x-\frac {3645 e^{14 x} x}{2401}+\frac {29160}{343} e^{7 x} x^2-\frac {3645 e^{14 x} x^2}{4802}+\frac {19440}{343} e^{7 x} x^3+729 e^{14 x} x^4+486 e^{7 x} x^5+486 e^{14 x} x^5+81 x^6+162 e^{7 x} x^6+81 e^{14 x} x^6+\frac {18954 \int e^{14 x} \, dx}{2401}+\frac {3645}{343} \int e^{14 x} x^2 \, dx+\frac {54675 \int e^{14 x} x \, dx}{2401}-\frac {58320}{343} \int e^{7 x} x \, dx-\frac {19440}{49} \int e^{7 x} x^3 \, dx-\frac {262440}{343} \int e^{7 x} x^2 \, dx \\ & = \frac {3645 e^{14 x}}{33614}-x-\frac {58320 e^{7 x} x}{2401}+\frac {3645 e^{14 x} x}{33614}-\frac {58320 e^{7 x} x^2}{2401}+729 e^{14 x} x^4+486 e^{7 x} x^5+486 e^{14 x} x^5+81 x^6+162 e^{7 x} x^6+81 e^{14 x} x^6-\frac {3645 \int e^{14 x} x \, dx}{2401}-\frac {54675 \int e^{14 x} \, dx}{33614}+\frac {58320 \int e^{7 x} \, dx}{2401}+\frac {58320}{343} \int e^{7 x} x^2 \, dx+\frac {524880 \int e^{7 x} x \, dx}{2401} \\ & = \frac {58320 e^{7 x}}{16807}-\frac {3645 e^{14 x}}{470596}-x+\frac {116640 e^{7 x} x}{16807}+729 e^{14 x} x^4+486 e^{7 x} x^5+486 e^{14 x} x^5+81 x^6+162 e^{7 x} x^6+81 e^{14 x} x^6+\frac {3645 \int e^{14 x} \, dx}{33614}-\frac {524880 \int e^{7 x} \, dx}{16807}-\frac {116640 \int e^{7 x} x \, dx}{2401} \\ & = -\frac {116640 e^{7 x}}{117649}-x+729 e^{14 x} x^4+486 e^{7 x} x^5+486 e^{14 x} x^5+81 x^6+162 e^{7 x} x^6+81 e^{14 x} x^6+\frac {116640 \int e^{7 x} \, dx}{16807} \\ & = -x+729 e^{14 x} x^4+486 e^{7 x} x^5+486 e^{14 x} x^5+81 x^6+162 e^{7 x} x^6+81 e^{14 x} x^6 \\ \end{align*}
Time = 0.36 (sec) , antiderivative size = 52, normalized size of antiderivative = 2.00 \[ \int \left (-1+486 x^5+e^{7 x} \left (2430 x^4+4374 x^5+1134 x^6\right )+e^{14 x} \left (2916 x^3+12636 x^4+7290 x^5+1134 x^6\right )\right ) \, dx=-x+81 x^6+162 e^{14 x} \left (\frac {9 x^4}{2}+3 x^5+\frac {x^6}{2}\right )+162 e^{7 x} \left (3 x^5+x^6\right ) \]
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Time = 0.05 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.88
method | result | size |
risch | \(\left (81 x^{6}+486 x^{5}+729 x^{4}\right ) {\mathrm e}^{14 x}+\left (162 x^{6}+486 x^{5}\right ) {\mathrm e}^{7 x}+81 x^{6}-x\) | \(49\) |
derivativedivides | \(162 \,{\mathrm e}^{7 x} x^{6}+81 \,{\mathrm e}^{14 x} x^{6}+486 \,{\mathrm e}^{7 x} x^{5}+486 \,{\mathrm e}^{14 x} x^{5}+81 x^{6}+729 \,{\mathrm e}^{14 x} x^{4}-x\) | \(61\) |
default | \(162 \,{\mathrm e}^{7 x} x^{6}+81 \,{\mathrm e}^{14 x} x^{6}+486 \,{\mathrm e}^{7 x} x^{5}+486 \,{\mathrm e}^{14 x} x^{5}+81 x^{6}+729 \,{\mathrm e}^{14 x} x^{4}-x\) | \(61\) |
norman | \(162 \,{\mathrm e}^{7 x} x^{6}+81 \,{\mathrm e}^{14 x} x^{6}+486 \,{\mathrm e}^{7 x} x^{5}+486 \,{\mathrm e}^{14 x} x^{5}+81 x^{6}+729 \,{\mathrm e}^{14 x} x^{4}-x\) | \(61\) |
parallelrisch | \(162 \,{\mathrm e}^{7 x} x^{6}+81 \,{\mathrm e}^{14 x} x^{6}+486 \,{\mathrm e}^{7 x} x^{5}+486 \,{\mathrm e}^{14 x} x^{5}+81 x^{6}+729 \,{\mathrm e}^{14 x} x^{4}-x\) | \(61\) |
parts | \(162 \,{\mathrm e}^{7 x} x^{6}+81 \,{\mathrm e}^{14 x} x^{6}+486 \,{\mathrm e}^{7 x} x^{5}+486 \,{\mathrm e}^{14 x} x^{5}+81 x^{6}+729 \,{\mathrm e}^{14 x} x^{4}-x\) | \(61\) |
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Time = 0.27 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.69 \[ \int \left (-1+486 x^5+e^{7 x} \left (2430 x^4+4374 x^5+1134 x^6\right )+e^{14 x} \left (2916 x^3+12636 x^4+7290 x^5+1134 x^6\right )\right ) \, dx=81 \, x^{6} + 81 \, {\left (x^{6} + 6 \, x^{5} + 9 \, x^{4}\right )} e^{\left (14 \, x\right )} + 162 \, {\left (x^{6} + 3 \, x^{5}\right )} e^{\left (7 \, x\right )} - x \]
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Leaf count of result is larger than twice the leaf count of optimal. 41 vs. \(2 (20) = 40\).
Time = 0.06 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.58 \[ \int \left (-1+486 x^5+e^{7 x} \left (2430 x^4+4374 x^5+1134 x^6\right )+e^{14 x} \left (2916 x^3+12636 x^4+7290 x^5+1134 x^6\right )\right ) \, dx=81 x^{6} - x + \left (162 x^{6} + 486 x^{5}\right ) e^{7 x} + \left (81 x^{6} + 486 x^{5} + 729 x^{4}\right ) e^{14 x} \]
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Time = 0.18 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.69 \[ \int \left (-1+486 x^5+e^{7 x} \left (2430 x^4+4374 x^5+1134 x^6\right )+e^{14 x} \left (2916 x^3+12636 x^4+7290 x^5+1134 x^6\right )\right ) \, dx=81 \, x^{6} + 81 \, {\left (x^{6} + 6 \, x^{5} + 9 \, x^{4}\right )} e^{\left (14 \, x\right )} + 162 \, {\left (x^{6} + 3 \, x^{5}\right )} e^{\left (7 \, x\right )} - x \]
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Time = 0.28 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.69 \[ \int \left (-1+486 x^5+e^{7 x} \left (2430 x^4+4374 x^5+1134 x^6\right )+e^{14 x} \left (2916 x^3+12636 x^4+7290 x^5+1134 x^6\right )\right ) \, dx=81 \, x^{6} + 81 \, {\left (x^{6} + 6 \, x^{5} + 9 \, x^{4}\right )} e^{\left (14 \, x\right )} + 162 \, {\left (x^{6} + 3 \, x^{5}\right )} e^{\left (7 \, x\right )} - x \]
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Time = 0.09 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.08 \[ \int \left (-1+486 x^5+e^{7 x} \left (2430 x^4+4374 x^5+1134 x^6\right )+e^{14 x} \left (2916 x^3+12636 x^4+7290 x^5+1134 x^6\right )\right ) \, dx=486\,x^5\,{\mathrm {e}}^{7\,x}-x+162\,x^6\,{\mathrm {e}}^{7\,x}+729\,x^4\,{\mathrm {e}}^{14\,x}+486\,x^5\,{\mathrm {e}}^{14\,x}+81\,x^6\,{\mathrm {e}}^{14\,x}+81\,x^6 \]
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