Integrand size = 80, antiderivative size = 21 \[ \int \left (18+e^{e^x} \left (12 e^{5+3 x} x^5+e^{5+2 x} \left (60 x^4+24 x^5\right )\right )+e^{2 e^x} \left (4 e^{10+5 x} x^9+e^{10+4 x} \left (18 x^8+8 x^9\right )\right )\right ) \, dx=2 x \left (3+e^{5+e^x+2 x} x^4\right )^2 \]
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Time = 0.03 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.71, number of steps used = 3, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {2326} \[ \int \left (18+e^{e^x} \left (12 e^{5+3 x} x^5+e^{5+2 x} \left (60 x^4+24 x^5\right )\right )+e^{2 e^x} \left (4 e^{10+5 x} x^9+e^{10+4 x} \left (18 x^8+8 x^9\right )\right )\right ) \, dx=2 e^{4 x+2 e^x+10} x^9+12 e^{2 x+e^x+5} x^5+18 x \]
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Rule 2326
Rubi steps \begin{align*} \text {integral}& = 18 x+\int e^{e^x} \left (12 e^{5+3 x} x^5+e^{5+2 x} \left (60 x^4+24 x^5\right )\right ) \, dx+\int e^{2 e^x} \left (4 e^{10+5 x} x^9+e^{10+4 x} \left (18 x^8+8 x^9\right )\right ) \, dx \\ & = 18 x+12 e^{5+e^x+2 x} x^5+2 e^{10+2 e^x+4 x} x^9 \\ \end{align*}
Time = 0.05 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00 \[ \int \left (18+e^{e^x} \left (12 e^{5+3 x} x^5+e^{5+2 x} \left (60 x^4+24 x^5\right )\right )+e^{2 e^x} \left (4 e^{10+5 x} x^9+e^{10+4 x} \left (18 x^8+8 x^9\right )\right )\right ) \, dx=2 x \left (3+e^{5+e^x+2 x} x^4\right )^2 \]
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Time = 8.93 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.57
method | result | size |
risch | \(2 x^{9} {\mathrm e}^{4 x +10+2 \,{\mathrm e}^{x}}+12 x^{5} {\mathrm e}^{{\mathrm e}^{x}+5+2 x}+18 x\) | \(33\) |
parallelrisch | \(2 \,{\mathrm e}^{10} {\mathrm e}^{4 x} {\mathrm e}^{2 \,{\mathrm e}^{x}} x^{9}+12 \,{\mathrm e}^{5} {\mathrm e}^{2 x} {\mathrm e}^{{\mathrm e}^{x}} x^{5}+18 x\) | \(37\) |
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Time = 0.25 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.52 \[ \int \left (18+e^{e^x} \left (12 e^{5+3 x} x^5+e^{5+2 x} \left (60 x^4+24 x^5\right )\right )+e^{2 e^x} \left (4 e^{10+5 x} x^9+e^{10+4 x} \left (18 x^8+8 x^9\right )\right )\right ) \, dx=2 \, x^{9} e^{\left (4 \, x + 2 \, e^{x} + 10\right )} + 12 \, x^{5} e^{\left (2 \, x + e^{x} + 5\right )} + 18 \, x \]
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Time = 0.18 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.95 \[ \int \left (18+e^{e^x} \left (12 e^{5+3 x} x^5+e^{5+2 x} \left (60 x^4+24 x^5\right )\right )+e^{2 e^x} \left (4 e^{10+5 x} x^9+e^{10+4 x} \left (18 x^8+8 x^9\right )\right )\right ) \, dx=2 x^{9} e^{10} e^{4 x} e^{2 e^{x}} + 12 x^{5} e^{5} e^{2 x} e^{e^{x}} + 18 x \]
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Time = 0.24 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.52 \[ \int \left (18+e^{e^x} \left (12 e^{5+3 x} x^5+e^{5+2 x} \left (60 x^4+24 x^5\right )\right )+e^{2 e^x} \left (4 e^{10+5 x} x^9+e^{10+4 x} \left (18 x^8+8 x^9\right )\right )\right ) \, dx=2 \, x^{9} e^{\left (4 \, x + 2 \, e^{x} + 10\right )} + 12 \, x^{5} e^{\left (2 \, x + e^{x} + 5\right )} + 18 \, x \]
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Time = 0.28 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.52 \[ \int \left (18+e^{e^x} \left (12 e^{5+3 x} x^5+e^{5+2 x} \left (60 x^4+24 x^5\right )\right )+e^{2 e^x} \left (4 e^{10+5 x} x^9+e^{10+4 x} \left (18 x^8+8 x^9\right )\right )\right ) \, dx=2 \, x^{9} e^{\left (4 \, x + 2 \, e^{x} + 10\right )} + 12 \, x^{5} e^{\left (2 \, x + e^{x} + 5\right )} + 18 \, x \]
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Time = 8.05 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.62 \[ \int \left (18+e^{e^x} \left (12 e^{5+3 x} x^5+e^{5+2 x} \left (60 x^4+24 x^5\right )\right )+e^{2 e^x} \left (4 e^{10+5 x} x^9+e^{10+4 x} \left (18 x^8+8 x^9\right )\right )\right ) \, dx=18\,x+12\,x^5\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^5+2\,x^9\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{10}\,{\mathrm {e}}^{2\,{\mathrm {e}}^x} \]
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