Integrand size = 98, antiderivative size = 25 \[ \int \frac {16 \left (4-12 e^{16} x\right )^4}{81 e^{64} x^4 \left (-25 x+75 e^{16} x^2+\frac {\left (4-12 e^{16} x\right )^4 \left (10 x-30 e^{16} x^2\right )}{81 e^{64} x^4}+\frac {\left (4-12 e^{16} x\right )^8 \left (-x+3 e^{16} x^2\right )}{6561 e^{128} x^8}\right )} \, dx=\frac {4}{5-\left (-4+\frac {4}{3 e^{16} x}\right )^4}+\log (15) \]
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Leaf count is larger than twice the leaf count of optimal. \(169\) vs. \(2(25)=50\).
Time = 0.61 (sec) , antiderivative size = 169, normalized size of antiderivative = 6.76, number of steps used = 7, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.041, Rules used = {12, 6820, 2127, 1602} \[ \int \frac {16 \left (4-12 e^{16} x\right )^4}{81 e^{64} x^4 \left (-25 x+75 e^{16} x^2+\frac {\left (4-12 e^{16} x\right )^4 \left (10 x-30 e^{16} x^2\right )}{81 e^{64} x^4}+\frac {\left (4-12 e^{16} x\right )^8 \left (-x+3 e^{16} x^2\right )}{6561 e^{128} x^8}\right )} \, dx=-\frac {110592 e^{48} x^3}{251 \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}+\frac {55296 e^{32} x^2}{251 \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {12288 e^{16} x}{251 \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}+\frac {1024}{251 \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )} \]
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Rule 12
Rule 1602
Rule 2127
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \frac {16 \int \frac {\left (4-12 e^{16} x\right )^4}{x^4 \left (-25 x+75 e^{16} x^2+\frac {\left (4-12 e^{16} x\right )^4 \left (10 x-30 e^{16} x^2\right )}{81 e^{64} x^4}+\frac {\left (4-12 e^{16} x\right )^8 \left (-x+3 e^{16} x^2\right )}{6561 e^{128} x^8}\right )} \, dx}{81 e^{64}} \\ & = \frac {16 \int \frac {1679616 e^{128} x^3 \left (-1+3 e^{16} x\right )^3}{\left (256-3072 e^{16} x+13824 e^{32} x^2-27648 e^{48} x^3+20331 e^{64} x^4\right )^2} \, dx}{81 e^{64}} \\ & = \left (331776 e^{64}\right ) \int \frac {x^3 \left (-1+3 e^{16} x\right )^3}{\left (256-3072 e^{16} x+13824 e^{32} x^2-27648 e^{48} x^3+20331 e^{64} x^4\right )^2} \, dx \\ & = -\frac {110592 e^{48} x^3}{251 \left (256-3072 e^{16} x+13824 e^{32} x^2-27648 e^{48} x^3+20331 e^{64} x^4\right )}-\frac {4096}{251} \int \frac {-20736 e^{48} x^2+186219 e^{64} x^3-556227 e^{80} x^4+548937 e^{96} x^5}{\left (256-3072 e^{16} x+13824 e^{32} x^2-27648 e^{48} x^3+20331 e^{64} x^4\right )^2} \, dx \\ & = \frac {55296 e^{32} x^2}{251 \left (256-3072 e^{16} x+13824 e^{32} x^2-27648 e^{48} x^3+20331 e^{64} x^4\right )}-\frac {110592 e^{48} x^3}{251 \left (256-3072 e^{16} x+13824 e^{32} x^2-27648 e^{48} x^3+20331 e^{64} x^4\right )}+\frac {2048 \int \frac {-281055744 e^{96} x+2529501696 e^{112} x^2-7572036978 e^{128} x^3+7440292098 e^{144} x^4}{\left (256-3072 e^{16} x+13824 e^{32} x^2-27648 e^{48} x^3+20331 e^{64} x^4\right )^2} \, dx}{5103081 e^{64}} \\ & = -\frac {12288 e^{16} x}{251 \left (256-3072 e^{16} x+13824 e^{32} x^2-27648 e^{48} x^3+20331 e^{64} x^4\right )}+\frac {55296 e^{32} x^2}{251 \left (256-3072 e^{16} x+13824 e^{32} x^2-27648 e^{48} x^3+20331 e^{64} x^4\right )}-\frac {110592 e^{48} x^3}{251 \left (256-3072 e^{16} x+13824 e^{32} x^2-27648 e^{48} x^3+20331 e^{64} x^4\right )}-\frac {2048 \int \frac {-1904714777088 e^{144}+17142432993792 e^{160} x-51427298981376 e^{176} x^2+50422859548146 e^{192} x^3}{\left (256-3072 e^{16} x+13824 e^{32} x^2-27648 e^{48} x^3+20331 e^{64} x^4\right )^2} \, dx}{311252219433 e^{128}} \\ & = \frac {1024}{251 \left (256-3072 e^{16} x+13824 e^{32} x^2-27648 e^{48} x^3+20331 e^{64} x^4\right )}-\frac {12288 e^{16} x}{251 \left (256-3072 e^{16} x+13824 e^{32} x^2-27648 e^{48} x^3+20331 e^{64} x^4\right )}+\frac {55296 e^{32} x^2}{251 \left (256-3072 e^{16} x+13824 e^{32} x^2-27648 e^{48} x^3+20331 e^{64} x^4\right )}-\frac {110592 e^{48} x^3}{251 \left (256-3072 e^{16} x+13824 e^{32} x^2-27648 e^{48} x^3+20331 e^{64} x^4\right )} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(62\) vs. \(2(25)=50\).
Time = 0.04 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.48 \[ \int \frac {16 \left (4-12 e^{16} x\right )^4}{81 e^{64} x^4 \left (-25 x+75 e^{16} x^2+\frac {\left (4-12 e^{16} x\right )^4 \left (10 x-30 e^{16} x^2\right )}{81 e^{64} x^4}+\frac {\left (4-12 e^{16} x\right )^8 \left (-x+3 e^{16} x^2\right )}{6561 e^{128} x^8}\right )} \, dx=\frac {1024 \left (1-12 e^{16} x+54 e^{32} x^2-108 e^{48} x^3\right )}{251 \left (256-3072 e^{16} x+13824 e^{32} x^2-27648 e^{48} x^3+20331 e^{64} x^4\right )} \]
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Time = 2.01 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.84
method | result | size |
norman | \(-\frac {324 \,{\mathrm e}^{64} x^{4}}{20331 x^{4} {\mathrm e}^{64}-27648 \,{\mathrm e}^{48} x^{3}+13824 x^{2} {\mathrm e}^{32}-3072 x \,{\mathrm e}^{16}+256}\) | \(46\) |
parallelrisch | \(-\frac {324 \,{\mathrm e}^{64} x^{4}}{20331 x^{4} {\mathrm e}^{64}-27648 \,{\mathrm e}^{48} x^{3}+13824 x^{2} {\mathrm e}^{32}-3072 x \,{\mathrm e}^{16}+256}\) | \(46\) |
risch | \(\frac {16 \,{\mathrm e}^{-64} \left (-\frac {6912 \,{\mathrm e}^{112} x^{3}}{63001}+\frac {3456 \,{\mathrm e}^{96} x^{2}}{63001}-\frac {768 \,{\mathrm e}^{80} x}{63001}+\frac {64 \,{\mathrm e}^{64}}{63001}\right )}{81 \left (x^{4} {\mathrm e}^{64}-\frac {1024 \,{\mathrm e}^{48} x^{3}}{753}+\frac {512 x^{2} {\mathrm e}^{32}}{753}-\frac {1024 x \,{\mathrm e}^{16}}{6777}+\frac {256}{20331}\right )}\) | \(58\) |
gosper | \(-\frac {1024 \left (108 \,{\mathrm e}^{48} x^{3}-54 x^{2} {\mathrm e}^{32}+12 x \,{\mathrm e}^{16}-1\right )}{251 \left (20331 x^{4} {\mathrm e}^{64}-27648 \,{\mathrm e}^{48} x^{3}+13824 x^{2} {\mathrm e}^{32}-3072 x \,{\mathrm e}^{16}+256\right )}\) | \(64\) |
default | \(13824 \,{\mathrm e}^{64} \left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (413349561 \textit {\_Z}^{8} {\mathrm e}^{128}-1124222976 \,{\mathrm e}^{112} \textit {\_Z}^{7}+1326523392 \,{\mathrm e}^{96} \textit {\_Z}^{6}-889325568 \,{\mathrm e}^{80} \textit {\_Z}^{5}+371381760 \textit {\_Z}^{4} {\mathrm e}^{64}-99090432 \,{\mathrm e}^{48} \textit {\_Z}^{3}+16515072 \textit {\_Z}^{2} {\mathrm e}^{32}-1572864 \,{\mathrm e}^{16} \textit {\_Z} +65536\right )}{\sum }\frac {\left (-27 \,{\mathrm e}^{48} \textit {\_R}^{6}+27 \,{\mathrm e}^{32} \textit {\_R}^{5}-9 \,{\mathrm e}^{16} \textit {\_R}^{4}+\textit {\_R}^{3}\right ) \ln \left (x -\textit {\_R} \right )}{-137783187 \textit {\_R}^{7} {\mathrm e}^{128}+327898368 \,{\mathrm e}^{112} \textit {\_R}^{6}-331630848 \,{\mathrm e}^{96} \textit {\_R}^{5}+185276160 \,{\mathrm e}^{80} \textit {\_R}^{4}-61896960 \textit {\_R}^{3} {\mathrm e}^{64}+12386304 \,{\mathrm e}^{48} \textit {\_R}^{2}-1376256 \textit {\_R} \,{\mathrm e}^{32}+65536 \,{\mathrm e}^{16}}\right )\) | \(157\) |
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Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (21) = 42\).
Time = 0.25 (sec) , antiderivative size = 53, normalized size of antiderivative = 2.12 \[ \int \frac {16 \left (4-12 e^{16} x\right )^4}{81 e^{64} x^4 \left (-25 x+75 e^{16} x^2+\frac {\left (4-12 e^{16} x\right )^4 \left (10 x-30 e^{16} x^2\right )}{81 e^{64} x^4}+\frac {\left (4-12 e^{16} x\right )^8 \left (-x+3 e^{16} x^2\right )}{6561 e^{128} x^8}\right )} \, dx=-\frac {1024 \, {\left (108 \, x^{3} e^{48} - 54 \, x^{2} e^{32} + 12 \, x e^{16} - 1\right )}}{251 \, {\left (20331 \, x^{4} e^{64} - 27648 \, x^{3} e^{48} + 13824 \, x^{2} e^{32} - 3072 \, x e^{16} + 256\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (17) = 34\).
Time = 0.73 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.32 \[ \int \frac {16 \left (4-12 e^{16} x\right )^4}{81 e^{64} x^4 \left (-25 x+75 e^{16} x^2+\frac {\left (4-12 e^{16} x\right )^4 \left (10 x-30 e^{16} x^2\right )}{81 e^{64} x^4}+\frac {\left (4-12 e^{16} x\right )^8 \left (-x+3 e^{16} x^2\right )}{6561 e^{128} x^8}\right )} \, dx=\frac {- 110592 x^{3} e^{48} + 55296 x^{2} e^{32} - 12288 x e^{16} + 1024}{5103081 x^{4} e^{64} - 6939648 x^{3} e^{48} + 3469824 x^{2} e^{32} - 771072 x e^{16} + 64256} \]
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Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (21) = 42\).
Time = 0.29 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.32 \[ \int \frac {16 \left (4-12 e^{16} x\right )^4}{81 e^{64} x^4 \left (-25 x+75 e^{16} x^2+\frac {\left (4-12 e^{16} x\right )^4 \left (10 x-30 e^{16} x^2\right )}{81 e^{64} x^4}+\frac {\left (4-12 e^{16} x\right )^8 \left (-x+3 e^{16} x^2\right )}{6561 e^{128} x^8}\right )} \, dx=-\frac {1024 \, {\left (108 \, x^{3} e^{112} - 54 \, x^{2} e^{96} + 12 \, x e^{80} - e^{64}\right )} e^{\left (-64\right )}}{251 \, {\left (20331 \, x^{4} e^{64} - 27648 \, x^{3} e^{48} + 13824 \, x^{2} e^{32} - 3072 \, x e^{16} + 256\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (21) = 42\).
Time = 0.28 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.32 \[ \int \frac {16 \left (4-12 e^{16} x\right )^4}{81 e^{64} x^4 \left (-25 x+75 e^{16} x^2+\frac {\left (4-12 e^{16} x\right )^4 \left (10 x-30 e^{16} x^2\right )}{81 e^{64} x^4}+\frac {\left (4-12 e^{16} x\right )^8 \left (-x+3 e^{16} x^2\right )}{6561 e^{128} x^8}\right )} \, dx=-\frac {1024 \, {\left (108 \, x^{3} e^{112} - 54 \, x^{2} e^{96} + 12 \, x e^{80} - e^{64}\right )} e^{\left (-64\right )}}{251 \, {\left (20331 \, x^{4} e^{64} - 27648 \, x^{3} e^{48} + 13824 \, x^{2} e^{32} - 3072 \, x e^{16} + 256\right )}} \]
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Time = 17.39 (sec) , antiderivative size = 53, normalized size of antiderivative = 2.12 \[ \int \frac {16 \left (4-12 e^{16} x\right )^4}{81 e^{64} x^4 \left (-25 x+75 e^{16} x^2+\frac {\left (4-12 e^{16} x\right )^4 \left (10 x-30 e^{16} x^2\right )}{81 e^{64} x^4}+\frac {\left (4-12 e^{16} x\right )^8 \left (-x+3 e^{16} x^2\right )}{6561 e^{128} x^8}\right )} \, dx=-\frac {\frac {110592\,{\mathrm {e}}^{48}\,x^3}{251}-\frac {55296\,{\mathrm {e}}^{32}\,x^2}{251}+\frac {12288\,{\mathrm {e}}^{16}\,x}{251}-\frac {1024}{251}}{20331\,{\mathrm {e}}^{64}\,x^4-27648\,{\mathrm {e}}^{48}\,x^3+13824\,{\mathrm {e}}^{32}\,x^2-3072\,{\mathrm {e}}^{16}\,x+256} \]
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