Integrand size = 129, antiderivative size = 25 \[ \int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8+\left (-4660 x^2+240 x^3-2164 x^6+112 x^7\right ) \log (79-4 x)+\left (-1580 x+80 x^2-2796 x^5+144 x^6\right ) \log ^2(79-4 x)+\left (-1564 x^4+80 x^5\right ) \log ^3(79-4 x)+\left (-316 x^3+16 x^4\right ) \log ^4(79-4 x)}{-79+4 x} \, dx=-3-x+\left (5+x^2 (x+\log (67-4 (-3+x)))^2\right )^2 \]
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Leaf count is larger than twice the leaf count of optimal. \(637\) vs. \(2(25)=50\).
Time = 1.60 (sec) , antiderivative size = 637, normalized size of antiderivative = 25.48, number of steps used = 167, number of rules used = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.155, Rules used = {6874, 1864, 2465, 2436, 2332, 2442, 45, 2437, 2338, 2333, 2448, 2342, 2341, 2445, 2458, 2372, 12, 14, 2339, 30} \[ \int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8+\left (-4660 x^2+240 x^3-2164 x^6+112 x^7\right ) \log (79-4 x)+\left (-1580 x+80 x^2-2796 x^5+144 x^6\right ) \log ^2(79-4 x)+\left (-1564 x^4+80 x^5\right ) \log ^3(79-4 x)+\left (-316 x^3+16 x^4\right ) \log ^4(79-4 x)}{-79+4 x} \, dx=x^8+4 x^7 \log (79-4 x)-\frac {x^6}{3}+6 x^6 \log ^2(79-4 x)+2 x^6 \log (79-4 x)-\frac {869 x^5}{50}+\frac {12}{5} x^5 \log ^2(79-4 x)+\frac {237}{5} x^5 \log (79-4 x)-\frac {227717 x^4}{320}+\frac {237}{4} x^4 \log ^2(79-4 x)+\frac {18723}{16} x^4 \log (79-4 x)-\frac {9367741 x^3}{320}+\frac {6241}{4} x^3 \log ^2(79-4 x)+\frac {493359}{16} x^3 \log (79-4 x)-\frac {3388669847 x^2}{2560}+\frac {116851523}{128} x^2 \log (79-4 x)+\frac {655414019067 x}{5120}+\frac {(79-4 x)^6}{12288}-\frac {711 (79-4 x)^5}{12800}+\frac {280845 (79-4 x)^4}{16384}-\frac {2465195}{768} (79-4 x)^3+\frac {1752754925 (79-4 x)^2}{4096}+\frac {1}{256} (79-4 x)^4 \log ^4(79-4 x)-\frac {79}{64} (79-4 x)^3 \log ^4(79-4 x)+\frac {18723}{128} (79-4 x)^2 \log ^4(79-4 x)-\frac {493039}{64} (79-4 x) \log ^4(79-4 x)+\frac {38950081}{256} \log ^4(79-4 x)-\frac {1}{256} (79-4 x)^5 \log ^3(79-4 x)+\frac {395}{256} (79-4 x)^4 \log ^3(79-4 x)-\frac {31205}{128} (79-4 x)^3 \log ^3(79-4 x)+\frac {2465195}{128} (79-4 x)^2 \log ^3(79-4 x)-\frac {194750405}{256} (79-4 x) \log ^3(79-4 x)+\frac {3077056399}{256} \log ^3(79-4 x)+\frac {3 (79-4 x)^5 \log ^2(79-4 x)}{1280}-\frac {1185 (79-4 x)^4 \log ^2(79-4 x)}{1024}+\frac {31205}{128} (79-4 x)^3 \log ^2(79-4 x)-\frac {13311733}{512} (79-4 x)^2 \log ^2(79-4 x)+\frac {350525449}{256} (79-4 x) \log ^2(79-4 x)-\frac {144601679553 \log ^2(79-4 x)}{5120}-\frac {(79-4 x)^6 \log (79-4 x)}{2048}+\frac {711 (79-4 x)^5 \log (79-4 x)}{2560}-\frac {280845 (79-4 x)^4 \log (79-4 x)}{4096}+\frac {2465195}{256} (79-4 x)^3 \log (79-4 x)-\frac {1752754925 (79-4 x)^2 \log (79-4 x)}{2048}+\frac {46155947105 (79-4 x) \log (79-4 x)}{1024}-\frac {21148688515127 \log (79-4 x)}{20480} \]
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Rule 12
Rule 14
Rule 30
Rule 45
Rule 1864
Rule 2332
Rule 2333
Rule 2338
Rule 2339
Rule 2341
Rule 2342
Rule 2372
Rule 2436
Rule 2437
Rule 2442
Rule 2445
Rule 2448
Rule 2458
Rule 2465
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8}{-79+4 x}+\frac {4 x^2 \left (-1165+60 x-541 x^4+28 x^5\right ) \log (79-4 x)}{-79+4 x}+\frac {4 x \left (-395+20 x-699 x^4+36 x^5\right ) \log ^2(79-4 x)}{-79+4 x}+\frac {4 x^4 (-391+20 x) \log ^3(79-4 x)}{-79+4 x}+4 x^3 \log ^4(79-4 x)\right ) \, dx \\ & = 4 \int \frac {x^2 \left (-1165+60 x-541 x^4+28 x^5\right ) \log (79-4 x)}{-79+4 x} \, dx+4 \int \frac {x \left (-395+20 x-699 x^4+36 x^5\right ) \log ^2(79-4 x)}{-79+4 x} \, dx+4 \int \frac {x^4 (-391+20 x) \log ^3(79-4 x)}{-79+4 x} \, dx+4 \int x^3 \log ^4(79-4 x) \, dx+\int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8}{-79+4 x} \, dx \\ & = 4 \int \left (\frac {9231270317 \log (79-4 x)}{1024}+\frac {116851523}{256} x \log (79-4 x)+\frac {1480077}{64} x^2 \log (79-4 x)+\frac {18723}{16} x^3 \log (79-4 x)+\frac {237}{4} x^4 \log (79-4 x)+3 x^5 \log (79-4 x)+7 x^6 \log (79-4 x)+\frac {729270355043 \log (79-4 x)}{1024 (-79+4 x)}\right ) \, dx+4 \int \left (\frac {116850243}{256} \log ^2(79-4 x)+\frac {1479437}{64} x \log ^2(79-4 x)+\frac {18723}{16} x^2 \log ^2(79-4 x)+\frac {237}{4} x^3 \log ^2(79-4 x)+3 x^4 \log ^2(79-4 x)+9 x^5 \log ^2(79-4 x)+\frac {9231169197 \log ^2(79-4 x)}{256 (-79+4 x)}\right ) \, dx+4 \int \left (\frac {493039}{64} \log ^3(79-4 x)+\frac {6241}{16} x \log ^3(79-4 x)+\frac {79}{4} x^2 \log ^3(79-4 x)+x^3 \log ^3(79-4 x)+5 x^4 \log ^3(79-4 x)+\frac {38950081 \log ^3(79-4 x)}{64 (-79+4 x)}\right ) \, dx+4 \int \left (\frac {493039}{64} \log ^4(79-4 x)-\frac {18723}{64} (79-4 x) \log ^4(79-4 x)+\frac {237}{64} (79-4 x)^2 \log ^4(79-4 x)-\frac {1}{64} (79-4 x)^3 \log ^4(79-4 x)\right ) \, dx+\int \left (\frac {243095442977}{1024}+\frac {3077157519 x}{256}+\frac {38951361 x^2}{64}+\frac {493679 x^3}{16}+\frac {6241 x^4}{4}+79 x^5+4 x^6+8 x^7+\frac {19204540076079}{1024 (-79+4 x)}\right ) \, dx \\ & = \frac {243095442977 x}{1024}+\frac {3077157519 x^2}{512}+\frac {12983787 x^3}{64}+\frac {493679 x^4}{64}+\frac {6241 x^5}{20}+\frac {79 x^6}{6}+\frac {4 x^7}{7}+x^8+\frac {19204540076079 \log (79-4 x)}{4096}-\frac {1}{16} \int (79-4 x)^3 \log ^4(79-4 x) \, dx+4 \int x^3 \log ^3(79-4 x) \, dx+12 \int x^5 \log (79-4 x) \, dx+12 \int x^4 \log ^2(79-4 x) \, dx+\frac {237}{16} \int (79-4 x)^2 \log ^4(79-4 x) \, dx+20 \int x^4 \log ^3(79-4 x) \, dx+28 \int x^6 \log (79-4 x) \, dx+36 \int x^5 \log ^2(79-4 x) \, dx+79 \int x^2 \log ^3(79-4 x) \, dx+237 \int x^4 \log (79-4 x) \, dx+237 \int x^3 \log ^2(79-4 x) \, dx-\frac {18723}{16} \int (79-4 x) \log ^4(79-4 x) \, dx+\frac {6241}{4} \int x \log ^3(79-4 x) \, dx+\frac {18723}{4} \int x^3 \log (79-4 x) \, dx+\frac {18723}{4} \int x^2 \log ^2(79-4 x) \, dx+\frac {493039}{16} \int \log ^3(79-4 x) \, dx+\frac {493039}{16} \int \log ^4(79-4 x) \, dx+\frac {1479437}{16} \int x \log ^2(79-4 x) \, dx+\frac {1480077}{16} \int x^2 \log (79-4 x) \, dx+\frac {116850243}{64} \int \log ^2(79-4 x) \, dx+\frac {116851523}{64} \int x \log (79-4 x) \, dx+\frac {38950081}{16} \int \frac {\log ^3(79-4 x)}{-79+4 x} \, dx+\frac {9231270317}{256} \int \log (79-4 x) \, dx+\frac {9231169197}{64} \int \frac {\log ^2(79-4 x)}{-79+4 x} \, dx+\frac {729270355043}{256} \int \frac {\log (79-4 x)}{-79+4 x} \, dx \\ & = \frac {243095442977 x}{1024}+\frac {3077157519 x^2}{512}+\frac {12983787 x^3}{64}+\frac {493679 x^4}{64}+\frac {6241 x^5}{20}+\frac {79 x^6}{6}+\frac {4 x^7}{7}+x^8+\frac {19204540076079 \log (79-4 x)}{4096}+\frac {116851523}{128} x^2 \log (79-4 x)+\frac {493359}{16} x^3 \log (79-4 x)+\frac {18723}{16} x^4 \log (79-4 x)+\frac {237}{5} x^5 \log (79-4 x)+2 x^6 \log (79-4 x)+4 x^7 \log (79-4 x)+\frac {6241}{4} x^3 \log ^2(79-4 x)+\frac {237}{4} x^4 \log ^2(79-4 x)+\frac {12}{5} x^5 \log ^2(79-4 x)+6 x^6 \log ^2(79-4 x)+\frac {1}{64} \text {Subst}\left (\int x^3 \log ^4(x) \, dx,x,79-4 x\right )-\frac {237}{64} \text {Subst}\left (\int x^2 \log ^4(x) \, dx,x,79-4 x\right )+4 \int \left (\frac {493039}{64} \log ^3(79-4 x)-\frac {18723}{64} (79-4 x) \log ^3(79-4 x)+\frac {237}{64} (79-4 x)^2 \log ^3(79-4 x)-\frac {1}{64} (79-4 x)^3 \log ^3(79-4 x)\right ) \, dx+8 \int \frac {x^6}{79-4 x} \, dx+16 \int \frac {x^7}{79-4 x} \, dx+\frac {96}{5} \int \frac {x^5 \log (79-4 x)}{79-4 x} \, dx+20 \int \left (\frac {38950081}{256} \log ^3(79-4 x)-\frac {493039}{64} (79-4 x) \log ^3(79-4 x)+\frac {18723}{128} (79-4 x)^2 \log ^3(79-4 x)-\frac {79}{64} (79-4 x)^3 \log ^3(79-4 x)+\frac {1}{256} (79-4 x)^4 \log ^3(79-4 x)\right ) \, dx+48 \int \frac {x^6 \log (79-4 x)}{79-4 x} \, dx+79 \int \left (\frac {6241}{16} \log ^3(79-4 x)-\frac {79}{8} (79-4 x) \log ^3(79-4 x)+\frac {1}{16} (79-4 x)^2 \log ^3(79-4 x)\right ) \, dx+\frac {948}{5} \int \frac {x^5}{79-4 x} \, dx+\frac {18723}{64} \text {Subst}\left (\int x \log ^4(x) \, dx,x,79-4 x\right )+474 \int \frac {x^4 \log (79-4 x)}{79-4 x} \, dx+\frac {6241}{4} \int \left (\frac {79}{4} \log ^3(79-4 x)-\frac {1}{4} (79-4 x) \log ^3(79-4 x)\right ) \, dx+\frac {18723}{4} \int \frac {x^4}{79-4 x} \, dx-\frac {493039}{64} \text {Subst}\left (\int \log ^3(x) \, dx,x,79-4 x\right )-\frac {493039}{64} \text {Subst}\left (\int \log ^4(x) \, dx,x,79-4 x\right )+12482 \int \frac {x^3 \log (79-4 x)}{79-4 x} \, dx+\frac {1479437}{16} \int \left (\frac {79}{4} \log ^2(79-4 x)-\frac {1}{4} (79-4 x) \log ^2(79-4 x)\right ) \, dx+\frac {493359}{4} \int \frac {x^3}{79-4 x} \, dx-\frac {116850243}{256} \text {Subst}\left (\int \log ^2(x) \, dx,x,79-4 x\right )+\frac {38950081}{64} \text {Subst}\left (\int \frac {\log ^3(x)}{x} \, dx,x,79-4 x\right )+\frac {116851523}{32} \int \frac {x^2}{79-4 x} \, dx-\frac {9231270317 \text {Subst}(\int \log (x) \, dx,x,79-4 x)}{1024}+\frac {9231169197}{256} \text {Subst}\left (\int \frac {\log ^2(x)}{x} \, dx,x,79-4 x\right )+\frac {729270355043 \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,79-4 x\right )}{1024} \\ & = \text {Too large to display} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(73\) vs. \(2(25)=50\).
Time = 0.05 (sec) , antiderivative size = 73, normalized size of antiderivative = 2.92 \[ \int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8+\left (-4660 x^2+240 x^3-2164 x^6+112 x^7\right ) \log (79-4 x)+\left (-1580 x+80 x^2-2796 x^5+144 x^6\right ) \log ^2(79-4 x)+\left (-1564 x^4+80 x^5\right ) \log ^3(79-4 x)+\left (-316 x^3+16 x^4\right ) \log ^4(79-4 x)}{-79+4 x} \, dx=-x+10 x^4+x^8+4 x^3 \left (5+x^4\right ) \log (79-4 x)+2 x^2 \left (5+3 x^4\right ) \log ^2(79-4 x)+4 x^5 \log ^3(79-4 x)+x^4 \log ^4(79-4 x) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(75\) vs. \(2(23)=46\).
Time = 0.25 (sec) , antiderivative size = 76, normalized size of antiderivative = 3.04
method | result | size |
risch | \(\ln \left (-4 x +79\right )^{4} x^{4}+4 \ln \left (-4 x +79\right )^{3} x^{5}+\left (6 x^{6}+10 x^{2}\right ) \ln \left (-4 x +79\right )^{2}+\left (4 x^{7}+20 x^{3}\right ) \ln \left (-4 x +79\right )+x^{8}+10 x^{4}-x\) | \(76\) |
parallelrisch | \(x^{8}+4 \ln \left (-4 x +79\right ) x^{7}+6 \ln \left (-4 x +79\right )^{2} x^{6}+4 \ln \left (-4 x +79\right )^{3} x^{5}+\ln \left (-4 x +79\right )^{4} x^{4}+10 x^{4}+20 \ln \left (-4 x +79\right ) x^{3}+10 \ln \left (-4 x +79\right )^{2} x^{2}-\frac {79}{8}-x\) | \(87\) |
parts | \(-x +x^{8}+10 x^{4}+\frac {64618487739 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{2}}{4096}-\frac {1701636154087 \ln \left (-4 x +79\right ) \left (-4 x +79\right )}{4096}+\frac {\ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )^{4}}{256}+\frac {38950081 \ln \left (-4 x +79\right )^{4}}{256}+\frac {3077056399 \ln \left (-4 x +79\right )^{3}}{256}+\frac {729270355043 \ln \left (-4 x +79\right )^{2}}{2048}-\frac {194750405 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )}{256}+\frac {1752754925 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{2}}{2048}-\frac {1363254115 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{3}}{4096}-\frac {27693608711 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )}{1024}+\frac {20913542825165551}{1720320}+\frac {19204540076079 \ln \left (4 x -79\right )}{4096}-\frac {131061 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{5}}{4096}-\frac {493039 \ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )}{64}+\frac {2465195 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{2}}{128}-\frac {7395585 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{3}}{512}+\frac {17256365 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{4}}{4096}-\frac {\ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{5}}{256}+\frac {3 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{6}}{2048}-\frac {\ln \left (-4 x +79\right ) \left (-4 x +79\right )^{7}}{4096}-\frac {79 \ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )^{3}}{64}+\frac {395 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{4}}{256}-\frac {711 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{5}}{1024}+\frac {553 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{6}}{4096}+\frac {18723 \ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )^{2}}{128}-\frac {31205 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{3}}{128}+\frac {280845 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{4}}{2048}\) | \(404\) |
derivativedivides | \(\frac {19204540074031 x}{2048}+\frac {19204540076079 \ln \left (-4 x +79\right )}{4096}+\frac {64618487739 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{2}}{4096}-\frac {1701636154087 \ln \left (-4 x +79\right ) \left (-4 x +79\right )}{4096}+\frac {\ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )^{4}}{256}+\frac {38950081 \ln \left (-4 x +79\right )^{4}}{256}+\frac {3077056399 \ln \left (-4 x +79\right )^{3}}{256}+\frac {729270355043 \ln \left (-4 x +79\right )^{2}}{2048}-\frac {194750405 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )}{256}+\frac {1752754925 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{2}}{2048}-\frac {1363254115 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{3}}{4096}-\frac {27693608711 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )}{1024}+\frac {\left (-4 x +79\right )^{8}}{65536}+\frac {1701636154087 \left (-4 x +79\right )^{2}}{16384}-\frac {21539495913 \left (-4 x +79\right )^{3}}{8192}+\frac {1363254115 \left (-4 x +79\right )^{4}}{32768}-\frac {3451273 \left (-4 x +79\right )^{5}}{8192}+\frac {43687 \left (-4 x +79\right )^{6}}{16384}-\frac {79 \left (-4 x +79\right )^{7}}{8192}-\frac {1517158665848449}{8192}-\frac {131061 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{5}}{4096}-\frac {493039 \ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )}{64}+\frac {2465195 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{2}}{128}-\frac {7395585 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{3}}{512}+\frac {17256365 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{4}}{4096}-\frac {\ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{5}}{256}+\frac {3 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{6}}{2048}-\frac {\ln \left (-4 x +79\right ) \left (-4 x +79\right )^{7}}{4096}-\frac {79 \ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )^{3}}{64}+\frac {395 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{4}}{256}-\frac {711 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{5}}{1024}+\frac {553 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{6}}{4096}+\frac {18723 \ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )^{2}}{128}-\frac {31205 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{3}}{128}+\frac {280845 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{4}}{2048}\) | \(459\) |
default | \(\frac {19204540074031 x}{2048}+\frac {19204540076079 \ln \left (-4 x +79\right )}{4096}+\frac {64618487739 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{2}}{4096}-\frac {1701636154087 \ln \left (-4 x +79\right ) \left (-4 x +79\right )}{4096}+\frac {\ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )^{4}}{256}+\frac {38950081 \ln \left (-4 x +79\right )^{4}}{256}+\frac {3077056399 \ln \left (-4 x +79\right )^{3}}{256}+\frac {729270355043 \ln \left (-4 x +79\right )^{2}}{2048}-\frac {194750405 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )}{256}+\frac {1752754925 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{2}}{2048}-\frac {1363254115 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{3}}{4096}-\frac {27693608711 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )}{1024}+\frac {\left (-4 x +79\right )^{8}}{65536}+\frac {1701636154087 \left (-4 x +79\right )^{2}}{16384}-\frac {21539495913 \left (-4 x +79\right )^{3}}{8192}+\frac {1363254115 \left (-4 x +79\right )^{4}}{32768}-\frac {3451273 \left (-4 x +79\right )^{5}}{8192}+\frac {43687 \left (-4 x +79\right )^{6}}{16384}-\frac {79 \left (-4 x +79\right )^{7}}{8192}-\frac {1517158665848449}{8192}-\frac {131061 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{5}}{4096}-\frac {493039 \ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )}{64}+\frac {2465195 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{2}}{128}-\frac {7395585 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{3}}{512}+\frac {17256365 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{4}}{4096}-\frac {\ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{5}}{256}+\frac {3 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{6}}{2048}-\frac {\ln \left (-4 x +79\right ) \left (-4 x +79\right )^{7}}{4096}-\frac {79 \ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )^{3}}{64}+\frac {395 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{4}}{256}-\frac {711 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{5}}{1024}+\frac {553 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{6}}{4096}+\frac {18723 \ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )^{2}}{128}-\frac {31205 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{3}}{128}+\frac {280845 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{4}}{2048}\) | \(459\) |
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Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (23) = 46\).
Time = 0.24 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.00 \[ \int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8+\left (-4660 x^2+240 x^3-2164 x^6+112 x^7\right ) \log (79-4 x)+\left (-1580 x+80 x^2-2796 x^5+144 x^6\right ) \log ^2(79-4 x)+\left (-1564 x^4+80 x^5\right ) \log ^3(79-4 x)+\left (-316 x^3+16 x^4\right ) \log ^4(79-4 x)}{-79+4 x} \, dx=x^{8} + 4 \, x^{5} \log \left (-4 \, x + 79\right )^{3} + x^{4} \log \left (-4 \, x + 79\right )^{4} + 10 \, x^{4} + 2 \, {\left (3 \, x^{6} + 5 \, x^{2}\right )} \log \left (-4 \, x + 79\right )^{2} + 4 \, {\left (x^{7} + 5 \, x^{3}\right )} \log \left (-4 \, x + 79\right ) - x \]
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Leaf count of result is larger than twice the leaf count of optimal. 70 vs. \(2 (19) = 38\).
Time = 0.12 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.80 \[ \int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8+\left (-4660 x^2+240 x^3-2164 x^6+112 x^7\right ) \log (79-4 x)+\left (-1580 x+80 x^2-2796 x^5+144 x^6\right ) \log ^2(79-4 x)+\left (-1564 x^4+80 x^5\right ) \log ^3(79-4 x)+\left (-316 x^3+16 x^4\right ) \log ^4(79-4 x)}{-79+4 x} \, dx=x^{8} + 4 x^{5} \log {\left (79 - 4 x \right )}^{3} + x^{4} \log {\left (79 - 4 x \right )}^{4} + 10 x^{4} - x + \left (6 x^{6} + 10 x^{2}\right ) \log {\left (79 - 4 x \right )}^{2} + \left (4 x^{7} + 20 x^{3}\right ) \log {\left (79 - 4 x \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 773 vs. \(2 (23) = 46\).
Time = 0.22 (sec) , antiderivative size = 773, normalized size of antiderivative = 30.92 \[ \int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8+\left (-4660 x^2+240 x^3-2164 x^6+112 x^7\right ) \log (79-4 x)+\left (-1580 x+80 x^2-2796 x^5+144 x^6\right ) \log ^2(79-4 x)+\left (-1564 x^4+80 x^5\right ) \log ^3(79-4 x)+\left (-316 x^3+16 x^4\right ) \log ^4(79-4 x)}{-79+4 x} \, dx=\text {Too large to display} \]
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Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (23) = 46\).
Time = 0.28 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.00 \[ \int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8+\left (-4660 x^2+240 x^3-2164 x^6+112 x^7\right ) \log (79-4 x)+\left (-1580 x+80 x^2-2796 x^5+144 x^6\right ) \log ^2(79-4 x)+\left (-1564 x^4+80 x^5\right ) \log ^3(79-4 x)+\left (-316 x^3+16 x^4\right ) \log ^4(79-4 x)}{-79+4 x} \, dx=x^{8} + 4 \, x^{5} \log \left (-4 \, x + 79\right )^{3} + x^{4} \log \left (-4 \, x + 79\right )^{4} + 10 \, x^{4} + 2 \, {\left (3 \, x^{6} + 5 \, x^{2}\right )} \log \left (-4 \, x + 79\right )^{2} + 4 \, {\left (x^{7} + 5 \, x^{3}\right )} \log \left (-4 \, x + 79\right ) - x \]
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Time = 8.88 (sec) , antiderivative size = 82, normalized size of antiderivative = 3.28 \[ \int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8+\left (-4660 x^2+240 x^3-2164 x^6+112 x^7\right ) \log (79-4 x)+\left (-1580 x+80 x^2-2796 x^5+144 x^6\right ) \log ^2(79-4 x)+\left (-1564 x^4+80 x^5\right ) \log ^3(79-4 x)+\left (-316 x^3+16 x^4\right ) \log ^4(79-4 x)}{-79+4 x} \, dx=10\,x^2\,{\ln \left (79-4\,x\right )}^2-x+4\,x^5\,{\ln \left (79-4\,x\right )}^3+6\,x^6\,{\ln \left (79-4\,x\right )}^2+x^4\,\left ({\ln \left (79-4\,x\right )}^4+10\right )+x^8+20\,x^3\,\ln \left (79-4\,x\right )+4\,x^7\,\ln \left (79-4\,x\right ) \]
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