Integrand size = 67, antiderivative size = 19 \[ \int \left (-13824+4608 x+e^{4 x} \left (4320-3168 x+576 x^2\right )+e^{3 x} \left (24192-18432 x+3456 x^2\right )+e^x \left (13824-18432 x+4608 x^2\right )+e^{2 x} \left (41472-34560 x+6912 x^2\right )\right ) \, dx=9 (-3+x)^2 \left (4+\log \left (e^{2 e^x}\right )\right )^4 \]
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Leaf count is larger than twice the leaf count of optimal. \(103\) vs. \(2(19)=38\).
Time = 0.11 (sec) , antiderivative size = 103, normalized size of antiderivative = 5.42, number of steps used = 33, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {2227, 2225, 2207} \[ \int \left (-13824+4608 x+e^{4 x} \left (4320-3168 x+576 x^2\right )+e^{3 x} \left (24192-18432 x+3456 x^2\right )+e^x \left (13824-18432 x+4608 x^2\right )+e^{2 x} \left (41472-34560 x+6912 x^2\right )\right ) \, dx=4608 e^x x^2+3456 e^{2 x} x^2+1152 e^{3 x} x^2+144 e^{4 x} x^2+2304 x^2-27648 e^x x-20736 e^{2 x} x-6912 e^{3 x} x-864 e^{4 x} x-13824 x+41472 e^x+31104 e^{2 x}+10368 e^{3 x}+1296 e^{4 x} \]
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Rule 2207
Rule 2225
Rule 2227
Rubi steps \begin{align*} \text {integral}& = -13824 x+2304 x^2+\int e^{4 x} \left (4320-3168 x+576 x^2\right ) \, dx+\int e^{3 x} \left (24192-18432 x+3456 x^2\right ) \, dx+\int e^x \left (13824-18432 x+4608 x^2\right ) \, dx+\int e^{2 x} \left (41472-34560 x+6912 x^2\right ) \, dx \\ & = -13824 x+2304 x^2+\int \left (13824 e^x-18432 e^x x+4608 e^x x^2\right ) \, dx+\int \left (41472 e^{2 x}-34560 e^{2 x} x+6912 e^{2 x} x^2\right ) \, dx+\int \left (24192 e^{3 x}-18432 e^{3 x} x+3456 e^{3 x} x^2\right ) \, dx+\int \left (4320 e^{4 x}-3168 e^{4 x} x+576 e^{4 x} x^2\right ) \, dx \\ & = -13824 x+2304 x^2+576 \int e^{4 x} x^2 \, dx-3168 \int e^{4 x} x \, dx+3456 \int e^{3 x} x^2 \, dx+4320 \int e^{4 x} \, dx+4608 \int e^x x^2 \, dx+6912 \int e^{2 x} x^2 \, dx+13824 \int e^x \, dx-18432 \int e^x x \, dx-18432 \int e^{3 x} x \, dx+24192 \int e^{3 x} \, dx-34560 \int e^{2 x} x \, dx+41472 \int e^{2 x} \, dx \\ & = 13824 e^x+20736 e^{2 x}+8064 e^{3 x}+1080 e^{4 x}-13824 x-18432 e^x x-17280 e^{2 x} x-6144 e^{3 x} x-792 e^{4 x} x+2304 x^2+4608 e^x x^2+3456 e^{2 x} x^2+1152 e^{3 x} x^2+144 e^{4 x} x^2-288 \int e^{4 x} x \, dx+792 \int e^{4 x} \, dx-2304 \int e^{3 x} x \, dx+6144 \int e^{3 x} \, dx-6912 \int e^{2 x} x \, dx-9216 \int e^x x \, dx+17280 \int e^{2 x} \, dx+18432 \int e^x \, dx \\ & = 32256 e^x+29376 e^{2 x}+10112 e^{3 x}+1278 e^{4 x}-13824 x-27648 e^x x-20736 e^{2 x} x-6912 e^{3 x} x-864 e^{4 x} x+2304 x^2+4608 e^x x^2+3456 e^{2 x} x^2+1152 e^{3 x} x^2+144 e^{4 x} x^2+72 \int e^{4 x} \, dx+768 \int e^{3 x} \, dx+3456 \int e^{2 x} \, dx+9216 \int e^x \, dx \\ & = 41472 e^x+31104 e^{2 x}+10368 e^{3 x}+1296 e^{4 x}-13824 x-27648 e^x x-20736 e^{2 x} x-6912 e^{3 x} x-864 e^{4 x} x+2304 x^2+4608 e^x x^2+3456 e^{2 x} x^2+1152 e^{3 x} x^2+144 e^{4 x} x^2 \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(57\) vs. \(2(19)=38\).
Time = 0.28 (sec) , antiderivative size = 57, normalized size of antiderivative = 3.00 \[ \int \left (-13824+4608 x+e^{4 x} \left (4320-3168 x+576 x^2\right )+e^{3 x} \left (24192-18432 x+3456 x^2\right )+e^x \left (13824-18432 x+4608 x^2\right )+e^{2 x} \left (41472-34560 x+6912 x^2\right )\right ) \, dx=288 \left (16 e^x (-3+x)^2+12 e^{2 x} (-3+x)^2+4 e^{3 x} (-3+x)^2+\frac {1}{2} e^{4 x} (-3+x)^2+8 (-6+x) x\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(67\) vs. \(2(17)=34\).
Time = 0.14 (sec) , antiderivative size = 68, normalized size of antiderivative = 3.58
method | result | size |
risch | \(\left (144 x^{2}-864 x +1296\right ) {\mathrm e}^{4 x}+\left (1152 x^{2}-6912 x +10368\right ) {\mathrm e}^{3 x}+\left (3456 x^{2}-20736 x +31104\right ) {\mathrm e}^{2 x}+\left (4608 x^{2}-27648 x +41472\right ) {\mathrm e}^{x}+2304 x^{2}-13824 x\) | \(68\) |
default | \(4608 \,{\mathrm e}^{x} x^{2}+144 x^{2} {\mathrm e}^{4 x}+1152 x^{2} {\mathrm e}^{3 x}+3456 \,{\mathrm e}^{2 x} x^{2}-27648 \,{\mathrm e}^{x} x -864 x \,{\mathrm e}^{4 x}-6912 x \,{\mathrm e}^{3 x}-20736 x \,{\mathrm e}^{2 x}+2304 x^{2}+41472 \,{\mathrm e}^{x}+1296 \,{\mathrm e}^{4 x}+10368 \,{\mathrm e}^{3 x}+31104 \,{\mathrm e}^{2 x}-13824 x\) | \(92\) |
norman | \(4608 \,{\mathrm e}^{x} x^{2}+144 x^{2} {\mathrm e}^{4 x}+1152 x^{2} {\mathrm e}^{3 x}+3456 \,{\mathrm e}^{2 x} x^{2}-27648 \,{\mathrm e}^{x} x -864 x \,{\mathrm e}^{4 x}-6912 x \,{\mathrm e}^{3 x}-20736 x \,{\mathrm e}^{2 x}+2304 x^{2}+41472 \,{\mathrm e}^{x}+1296 \,{\mathrm e}^{4 x}+10368 \,{\mathrm e}^{3 x}+31104 \,{\mathrm e}^{2 x}-13824 x\) | \(92\) |
parallelrisch | \(4608 \,{\mathrm e}^{x} x^{2}+144 x^{2} {\mathrm e}^{4 x}+1152 x^{2} {\mathrm e}^{3 x}+3456 \,{\mathrm e}^{2 x} x^{2}-27648 \,{\mathrm e}^{x} x -864 x \,{\mathrm e}^{4 x}-6912 x \,{\mathrm e}^{3 x}-20736 x \,{\mathrm e}^{2 x}+2304 x^{2}+41472 \,{\mathrm e}^{x}+1296 \,{\mathrm e}^{4 x}+10368 \,{\mathrm e}^{3 x}+31104 \,{\mathrm e}^{2 x}-13824 x\) | \(92\) |
parts | \(4608 \,{\mathrm e}^{x} x^{2}+144 x^{2} {\mathrm e}^{4 x}+1152 x^{2} {\mathrm e}^{3 x}+3456 \,{\mathrm e}^{2 x} x^{2}-27648 \,{\mathrm e}^{x} x -864 x \,{\mathrm e}^{4 x}-6912 x \,{\mathrm e}^{3 x}-20736 x \,{\mathrm e}^{2 x}+2304 x^{2}+41472 \,{\mathrm e}^{x}+1296 \,{\mathrm e}^{4 x}+10368 \,{\mathrm e}^{3 x}+31104 \,{\mathrm e}^{2 x}-13824 x\) | \(92\) |
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Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (17) = 34\).
Time = 0.25 (sec) , antiderivative size = 63, normalized size of antiderivative = 3.32 \[ \int \left (-13824+4608 x+e^{4 x} \left (4320-3168 x+576 x^2\right )+e^{3 x} \left (24192-18432 x+3456 x^2\right )+e^x \left (13824-18432 x+4608 x^2\right )+e^{2 x} \left (41472-34560 x+6912 x^2\right )\right ) \, dx=2304 \, x^{2} + 144 \, {\left (x^{2} - 6 \, x + 9\right )} e^{\left (4 \, x\right )} + 1152 \, {\left (x^{2} - 6 \, x + 9\right )} e^{\left (3 \, x\right )} + 3456 \, {\left (x^{2} - 6 \, x + 9\right )} e^{\left (2 \, x\right )} + 4608 \, {\left (x^{2} - 6 \, x + 9\right )} e^{x} - 13824 \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (17) = 34\).
Time = 0.08 (sec) , antiderivative size = 66, normalized size of antiderivative = 3.47 \[ \int \left (-13824+4608 x+e^{4 x} \left (4320-3168 x+576 x^2\right )+e^{3 x} \left (24192-18432 x+3456 x^2\right )+e^x \left (13824-18432 x+4608 x^2\right )+e^{2 x} \left (41472-34560 x+6912 x^2\right )\right ) \, dx=2304 x^{2} - 13824 x + \left (144 x^{2} - 864 x + 1296\right ) e^{4 x} + \left (1152 x^{2} - 6912 x + 10368\right ) e^{3 x} + \left (3456 x^{2} - 20736 x + 31104\right ) e^{2 x} + \left (4608 x^{2} - 27648 x + 41472\right ) e^{x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (17) = 34\).
Time = 0.20 (sec) , antiderivative size = 63, normalized size of antiderivative = 3.32 \[ \int \left (-13824+4608 x+e^{4 x} \left (4320-3168 x+576 x^2\right )+e^{3 x} \left (24192-18432 x+3456 x^2\right )+e^x \left (13824-18432 x+4608 x^2\right )+e^{2 x} \left (41472-34560 x+6912 x^2\right )\right ) \, dx=2304 \, x^{2} + 144 \, {\left (x^{2} - 6 \, x + 9\right )} e^{\left (4 \, x\right )} + 1152 \, {\left (x^{2} - 6 \, x + 9\right )} e^{\left (3 \, x\right )} + 3456 \, {\left (x^{2} - 6 \, x + 9\right )} e^{\left (2 \, x\right )} + 4608 \, {\left (x^{2} - 6 \, x + 9\right )} e^{x} - 13824 \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (17) = 34\).
Time = 0.29 (sec) , antiderivative size = 63, normalized size of antiderivative = 3.32 \[ \int \left (-13824+4608 x+e^{4 x} \left (4320-3168 x+576 x^2\right )+e^{3 x} \left (24192-18432 x+3456 x^2\right )+e^x \left (13824-18432 x+4608 x^2\right )+e^{2 x} \left (41472-34560 x+6912 x^2\right )\right ) \, dx=2304 \, x^{2} + 144 \, {\left (x^{2} - 6 \, x + 9\right )} e^{\left (4 \, x\right )} + 1152 \, {\left (x^{2} - 6 \, x + 9\right )} e^{\left (3 \, x\right )} + 3456 \, {\left (x^{2} - 6 \, x + 9\right )} e^{\left (2 \, x\right )} + 4608 \, {\left (x^{2} - 6 \, x + 9\right )} e^{x} - 13824 \, x \]
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Time = 15.16 (sec) , antiderivative size = 91, normalized size of antiderivative = 4.79 \[ \int \left (-13824+4608 x+e^{4 x} \left (4320-3168 x+576 x^2\right )+e^{3 x} \left (24192-18432 x+3456 x^2\right )+e^x \left (13824-18432 x+4608 x^2\right )+e^{2 x} \left (41472-34560 x+6912 x^2\right )\right ) \, dx=31104\,{\mathrm {e}}^{2\,x}-13824\,x+10368\,{\mathrm {e}}^{3\,x}+1296\,{\mathrm {e}}^{4\,x}+41472\,{\mathrm {e}}^x-20736\,x\,{\mathrm {e}}^{2\,x}-6912\,x\,{\mathrm {e}}^{3\,x}-864\,x\,{\mathrm {e}}^{4\,x}+4608\,x^2\,{\mathrm {e}}^x+3456\,x^2\,{\mathrm {e}}^{2\,x}+1152\,x^2\,{\mathrm {e}}^{3\,x}+144\,x^2\,{\mathrm {e}}^{4\,x}-27648\,x\,{\mathrm {e}}^x+2304\,x^2 \]
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