Integrand size = 190, antiderivative size = 28 \[ \int \frac {262144+x^5-2 x^6+e^{12 x+10 x^4} \left (458752-1376256 x-4587520 x^4\right )+e^{18 x+15 x^4} \left (229376-1032192 x-3440640 x^4\right )+e^{6 x+5 x^4} \left (524288-786432 x-2621440 x^4\right )+e^{24 x+20 x^4} \left (71680-430080 x-1433600 x^4\right )+e^{30 x+25 x^4} \left (14336-107520 x-358400 x^4\right )+e^{36 x+30 x^4} \left (1792-16128 x-53760 x^4\right )+e^{42 x+35 x^4} \left (128-1344 x-4480 x^4\right )+e^{48 x+40 x^4} \left (4-48 x-160 x^4\right )}{x^5} \, dx=5-\frac {\left (4+e^{x+5 \left (x+x^4\right )}\right )^8}{x^4}+x-x^2 \]
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Leaf count is larger than twice the leaf count of optimal. \(291\) vs. \(2(28)=56\).
Time = 0.40 (sec) , antiderivative size = 291, normalized size of antiderivative = 10.39, number of steps used = 12, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {14, 2326} \[ \int \frac {262144+x^5-2 x^6+e^{12 x+10 x^4} \left (458752-1376256 x-4587520 x^4\right )+e^{18 x+15 x^4} \left (229376-1032192 x-3440640 x^4\right )+e^{6 x+5 x^4} \left (524288-786432 x-2621440 x^4\right )+e^{24 x+20 x^4} \left (71680-430080 x-1433600 x^4\right )+e^{30 x+25 x^4} \left (14336-107520 x-358400 x^4\right )+e^{36 x+30 x^4} \left (1792-16128 x-53760 x^4\right )+e^{42 x+35 x^4} \left (128-1344 x-4480 x^4\right )+e^{48 x+40 x^4} \left (4-48 x-160 x^4\right )}{x^5} \, dx=-\frac {65536}{x^4}-x^2-\frac {114688 e^{2 x \left (5 x^3+6\right )} \left (10 x^4+3 x\right )}{\left (10 x^3+3\right ) x^5}-\frac {57344 e^{3 x \left (5 x^3+6\right )} \left (10 x^4+3 x\right )}{\left (10 x^3+3\right ) x^5}-\frac {17920 e^{4 x \left (5 x^3+6\right )} \left (10 x^4+3 x\right )}{\left (10 x^3+3\right ) x^5}-\frac {3584 e^{5 x \left (5 x^3+6\right )} \left (10 x^4+3 x\right )}{\left (10 x^3+3\right ) x^5}-\frac {448 e^{6 x \left (5 x^3+6\right )} \left (10 x^4+3 x\right )}{\left (10 x^3+3\right ) x^5}-\frac {32 e^{7 x \left (5 x^3+6\right )} \left (10 x^4+3 x\right )}{\left (10 x^3+3\right ) x^5}-\frac {e^{8 x \left (5 x^3+6\right )} \left (10 x^4+3 x\right )}{\left (10 x^3+3\right ) x^5}-\frac {131072 e^{5 x^4+6 x} \left (10 x^4+3 x\right )}{\left (10 x^3+3\right ) x^5}+x \]
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Rule 14
Rule 2326
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {262144 e^{6 x+5 x^4} \left (-2+3 x+10 x^4\right )}{x^5}-\frac {458752 e^{2 x \left (6+5 x^3\right )} \left (-1+3 x+10 x^4\right )}{x^5}-\frac {71680 e^{4 x \left (6+5 x^3\right )} \left (-1+6 x+20 x^4\right )}{x^5}-\frac {114688 e^{3 x \left (6+5 x^3\right )} \left (-2+9 x+30 x^4\right )}{x^5}-\frac {1792 e^{6 x \left (6+5 x^3\right )} \left (-1+9 x+30 x^4\right )}{x^5}-\frac {4 e^{8 x \left (6+5 x^3\right )} \left (-1+12 x+40 x^4\right )}{x^5}-\frac {7168 e^{5 x \left (6+5 x^3\right )} \left (-2+15 x+50 x^4\right )}{x^5}-\frac {64 e^{7 x \left (6+5 x^3\right )} \left (-2+21 x+70 x^4\right )}{x^5}+\frac {262144+x^5-2 x^6}{x^5}\right ) \, dx \\ & = -\left (4 \int \frac {e^{8 x \left (6+5 x^3\right )} \left (-1+12 x+40 x^4\right )}{x^5} \, dx\right )-64 \int \frac {e^{7 x \left (6+5 x^3\right )} \left (-2+21 x+70 x^4\right )}{x^5} \, dx-1792 \int \frac {e^{6 x \left (6+5 x^3\right )} \left (-1+9 x+30 x^4\right )}{x^5} \, dx-7168 \int \frac {e^{5 x \left (6+5 x^3\right )} \left (-2+15 x+50 x^4\right )}{x^5} \, dx-71680 \int \frac {e^{4 x \left (6+5 x^3\right )} \left (-1+6 x+20 x^4\right )}{x^5} \, dx-114688 \int \frac {e^{3 x \left (6+5 x^3\right )} \left (-2+9 x+30 x^4\right )}{x^5} \, dx-262144 \int \frac {e^{6 x+5 x^4} \left (-2+3 x+10 x^4\right )}{x^5} \, dx-458752 \int \frac {e^{2 x \left (6+5 x^3\right )} \left (-1+3 x+10 x^4\right )}{x^5} \, dx+\int \frac {262144+x^5-2 x^6}{x^5} \, dx \\ & = -\frac {114688 e^{2 x \left (6+5 x^3\right )} \left (3 x+10 x^4\right )}{x^5 \left (3+10 x^3\right )}-\frac {57344 e^{3 x \left (6+5 x^3\right )} \left (3 x+10 x^4\right )}{x^5 \left (3+10 x^3\right )}-\frac {17920 e^{4 x \left (6+5 x^3\right )} \left (3 x+10 x^4\right )}{x^5 \left (3+10 x^3\right )}-\frac {3584 e^{5 x \left (6+5 x^3\right )} \left (3 x+10 x^4\right )}{x^5 \left (3+10 x^3\right )}-\frac {448 e^{6 x \left (6+5 x^3\right )} \left (3 x+10 x^4\right )}{x^5 \left (3+10 x^3\right )}-\frac {32 e^{7 x \left (6+5 x^3\right )} \left (3 x+10 x^4\right )}{x^5 \left (3+10 x^3\right )}-\frac {e^{8 x \left (6+5 x^3\right )} \left (3 x+10 x^4\right )}{x^5 \left (3+10 x^3\right )}-\frac {131072 e^{6 x+5 x^4} \left (3 x+10 x^4\right )}{x^5 \left (3+10 x^3\right )}+\int \left (1+\frac {262144}{x^5}-2 x\right ) \, dx \\ & = -\frac {65536}{x^4}+x-x^2-\frac {114688 e^{2 x \left (6+5 x^3\right )} \left (3 x+10 x^4\right )}{x^5 \left (3+10 x^3\right )}-\frac {57344 e^{3 x \left (6+5 x^3\right )} \left (3 x+10 x^4\right )}{x^5 \left (3+10 x^3\right )}-\frac {17920 e^{4 x \left (6+5 x^3\right )} \left (3 x+10 x^4\right )}{x^5 \left (3+10 x^3\right )}-\frac {3584 e^{5 x \left (6+5 x^3\right )} \left (3 x+10 x^4\right )}{x^5 \left (3+10 x^3\right )}-\frac {448 e^{6 x \left (6+5 x^3\right )} \left (3 x+10 x^4\right )}{x^5 \left (3+10 x^3\right )}-\frac {32 e^{7 x \left (6+5 x^3\right )} \left (3 x+10 x^4\right )}{x^5 \left (3+10 x^3\right )}-\frac {e^{8 x \left (6+5 x^3\right )} \left (3 x+10 x^4\right )}{x^5 \left (3+10 x^3\right )}-\frac {131072 e^{6 x+5 x^4} \left (3 x+10 x^4\right )}{x^5 \left (3+10 x^3\right )} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(124\) vs. \(2(28)=56\).
Time = 10.19 (sec) , antiderivative size = 124, normalized size of antiderivative = 4.43 \[ \int \frac {262144+x^5-2 x^6+e^{12 x+10 x^4} \left (458752-1376256 x-4587520 x^4\right )+e^{18 x+15 x^4} \left (229376-1032192 x-3440640 x^4\right )+e^{6 x+5 x^4} \left (524288-786432 x-2621440 x^4\right )+e^{24 x+20 x^4} \left (71680-430080 x-1433600 x^4\right )+e^{30 x+25 x^4} \left (14336-107520 x-358400 x^4\right )+e^{36 x+30 x^4} \left (1792-16128 x-53760 x^4\right )+e^{42 x+35 x^4} \left (128-1344 x-4480 x^4\right )+e^{48 x+40 x^4} \left (4-48 x-160 x^4\right )}{x^5} \, dx=-\frac {65536+114688 e^{2 x \left (6+5 x^3\right )}+57344 e^{3 x \left (6+5 x^3\right )}+17920 e^{4 x \left (6+5 x^3\right )}+3584 e^{5 x \left (6+5 x^3\right )}+448 e^{6 x \left (6+5 x^3\right )}+32 e^{7 x \left (6+5 x^3\right )}+e^{8 x \left (6+5 x^3\right )}+131072 e^{6 x+5 x^4}-x^5+x^6}{x^4} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(123\) vs. \(2(27)=54\).
Time = 0.43 (sec) , antiderivative size = 124, normalized size of antiderivative = 4.43
method | result | size |
parallelrisch | \(-\frac {{\mathrm e}^{40 x^{4}+48 x}+32 \,{\mathrm e}^{35 x^{4}+42 x}+x^{6}+448 \,{\mathrm e}^{30 x^{4}+36 x}-x^{5}+65536+3584 \,{\mathrm e}^{25 x^{4}+30 x}+17920 \,{\mathrm e}^{20 x^{4}+24 x}+57344 \,{\mathrm e}^{15 x^{4}+18 x}+114688 \,{\mathrm e}^{10 x^{4}+12 x}+131072 \,{\mathrm e}^{5 x^{4}+6 x}}{x^{4}}\) | \(124\) |
risch | \(-x^{2}+x -\frac {65536}{x^{4}}-\frac {{\mathrm e}^{8 x \left (5 x^{3}+6\right )}}{x^{4}}-\frac {32 \,{\mathrm e}^{7 x \left (5 x^{3}+6\right )}}{x^{4}}-\frac {448 \,{\mathrm e}^{6 x \left (5 x^{3}+6\right )}}{x^{4}}-\frac {3584 \,{\mathrm e}^{5 x \left (5 x^{3}+6\right )}}{x^{4}}-\frac {17920 \,{\mathrm e}^{4 x \left (5 x^{3}+6\right )}}{x^{4}}-\frac {57344 \,{\mathrm e}^{3 x \left (5 x^{3}+6\right )}}{x^{4}}-\frac {114688 \,{\mathrm e}^{2 x \left (5 x^{3}+6\right )}}{x^{4}}-\frac {131072 \,{\mathrm e}^{x \left (5 x^{3}+6\right )}}{x^{4}}\) | \(140\) |
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Leaf count of result is larger than twice the leaf count of optimal. 109 vs. \(2 (27) = 54\).
Time = 0.24 (sec) , antiderivative size = 109, normalized size of antiderivative = 3.89 \[ \int \frac {262144+x^5-2 x^6+e^{12 x+10 x^4} \left (458752-1376256 x-4587520 x^4\right )+e^{18 x+15 x^4} \left (229376-1032192 x-3440640 x^4\right )+e^{6 x+5 x^4} \left (524288-786432 x-2621440 x^4\right )+e^{24 x+20 x^4} \left (71680-430080 x-1433600 x^4\right )+e^{30 x+25 x^4} \left (14336-107520 x-358400 x^4\right )+e^{36 x+30 x^4} \left (1792-16128 x-53760 x^4\right )+e^{42 x+35 x^4} \left (128-1344 x-4480 x^4\right )+e^{48 x+40 x^4} \left (4-48 x-160 x^4\right )}{x^5} \, dx=-\frac {x^{6} - x^{5} + e^{\left (40 \, x^{4} + 48 \, x\right )} + 32 \, e^{\left (35 \, x^{4} + 42 \, x\right )} + 448 \, e^{\left (30 \, x^{4} + 36 \, x\right )} + 3584 \, e^{\left (25 \, x^{4} + 30 \, x\right )} + 17920 \, e^{\left (20 \, x^{4} + 24 \, x\right )} + 57344 \, e^{\left (15 \, x^{4} + 18 \, x\right )} + 114688 \, e^{\left (10 \, x^{4} + 12 \, x\right )} + 131072 \, e^{\left (5 \, x^{4} + 6 \, x\right )} + 65536}{x^{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 134 vs. \(2 (22) = 44\).
Time = 0.16 (sec) , antiderivative size = 134, normalized size of antiderivative = 4.79 \[ \int \frac {262144+x^5-2 x^6+e^{12 x+10 x^4} \left (458752-1376256 x-4587520 x^4\right )+e^{18 x+15 x^4} \left (229376-1032192 x-3440640 x^4\right )+e^{6 x+5 x^4} \left (524288-786432 x-2621440 x^4\right )+e^{24 x+20 x^4} \left (71680-430080 x-1433600 x^4\right )+e^{30 x+25 x^4} \left (14336-107520 x-358400 x^4\right )+e^{36 x+30 x^4} \left (1792-16128 x-53760 x^4\right )+e^{42 x+35 x^4} \left (128-1344 x-4480 x^4\right )+e^{48 x+40 x^4} \left (4-48 x-160 x^4\right )}{x^5} \, dx=- x^{2} + x - \frac {65536}{x^{4}} + \frac {- 131072 x^{28} e^{5 x^{4} + 6 x} - 114688 x^{28} e^{10 x^{4} + 12 x} - 57344 x^{28} e^{15 x^{4} + 18 x} - 17920 x^{28} e^{20 x^{4} + 24 x} - 3584 x^{28} e^{25 x^{4} + 30 x} - 448 x^{28} e^{30 x^{4} + 36 x} - 32 x^{28} e^{35 x^{4} + 42 x} - x^{28} e^{40 x^{4} + 48 x}}{x^{32}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 112 vs. \(2 (27) = 54\).
Time = 0.27 (sec) , antiderivative size = 112, normalized size of antiderivative = 4.00 \[ \int \frac {262144+x^5-2 x^6+e^{12 x+10 x^4} \left (458752-1376256 x-4587520 x^4\right )+e^{18 x+15 x^4} \left (229376-1032192 x-3440640 x^4\right )+e^{6 x+5 x^4} \left (524288-786432 x-2621440 x^4\right )+e^{24 x+20 x^4} \left (71680-430080 x-1433600 x^4\right )+e^{30 x+25 x^4} \left (14336-107520 x-358400 x^4\right )+e^{36 x+30 x^4} \left (1792-16128 x-53760 x^4\right )+e^{42 x+35 x^4} \left (128-1344 x-4480 x^4\right )+e^{48 x+40 x^4} \left (4-48 x-160 x^4\right )}{x^5} \, dx=-x^{2} + x - \frac {e^{\left (40 \, x^{4} + 48 \, x\right )} + 32 \, e^{\left (35 \, x^{4} + 42 \, x\right )} + 448 \, e^{\left (30 \, x^{4} + 36 \, x\right )} + 3584 \, e^{\left (25 \, x^{4} + 30 \, x\right )} + 17920 \, e^{\left (20 \, x^{4} + 24 \, x\right )} + 57344 \, e^{\left (15 \, x^{4} + 18 \, x\right )} + 114688 \, e^{\left (10 \, x^{4} + 12 \, x\right )} + 131072 \, e^{\left (5 \, x^{4} + 6 \, x\right )}}{x^{4}} - \frac {65536}{x^{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 109 vs. \(2 (27) = 54\).
Time = 0.36 (sec) , antiderivative size = 109, normalized size of antiderivative = 3.89 \[ \int \frac {262144+x^5-2 x^6+e^{12 x+10 x^4} \left (458752-1376256 x-4587520 x^4\right )+e^{18 x+15 x^4} \left (229376-1032192 x-3440640 x^4\right )+e^{6 x+5 x^4} \left (524288-786432 x-2621440 x^4\right )+e^{24 x+20 x^4} \left (71680-430080 x-1433600 x^4\right )+e^{30 x+25 x^4} \left (14336-107520 x-358400 x^4\right )+e^{36 x+30 x^4} \left (1792-16128 x-53760 x^4\right )+e^{42 x+35 x^4} \left (128-1344 x-4480 x^4\right )+e^{48 x+40 x^4} \left (4-48 x-160 x^4\right )}{x^5} \, dx=-\frac {x^{6} - x^{5} + e^{\left (40 \, x^{4} + 48 \, x\right )} + 32 \, e^{\left (35 \, x^{4} + 42 \, x\right )} + 448 \, e^{\left (30 \, x^{4} + 36 \, x\right )} + 3584 \, e^{\left (25 \, x^{4} + 30 \, x\right )} + 17920 \, e^{\left (20 \, x^{4} + 24 \, x\right )} + 57344 \, e^{\left (15 \, x^{4} + 18 \, x\right )} + 114688 \, e^{\left (10 \, x^{4} + 12 \, x\right )} + 131072 \, e^{\left (5 \, x^{4} + 6 \, x\right )} + 65536}{x^{4}} \]
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Time = 14.14 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93 \[ \int \frac {262144+x^5-2 x^6+e^{12 x+10 x^4} \left (458752-1376256 x-4587520 x^4\right )+e^{18 x+15 x^4} \left (229376-1032192 x-3440640 x^4\right )+e^{6 x+5 x^4} \left (524288-786432 x-2621440 x^4\right )+e^{24 x+20 x^4} \left (71680-430080 x-1433600 x^4\right )+e^{30 x+25 x^4} \left (14336-107520 x-358400 x^4\right )+e^{36 x+30 x^4} \left (1792-16128 x-53760 x^4\right )+e^{42 x+35 x^4} \left (128-1344 x-4480 x^4\right )+e^{48 x+40 x^4} \left (4-48 x-160 x^4\right )}{x^5} \, dx=-x\,\left (x-1\right )-\frac {{\left ({\mathrm {e}}^{5\,x^4+6\,x}+4\right )}^8}{x^4} \]
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