Integrand size = 129, antiderivative size = 25 \[ \int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8+\left (-4660 x^2+240 x^3-2164 x^6+112 x^7\right ) \log (79-4 x)+\left (-1580 x+80 x^2-2796 x^5+144 x^6\right ) \log ^2(79-4 x)+\left (-1564 x^4+80 x^5\right ) \log ^3(79-4 x)+\left (-316 x^3+16 x^4\right ) \log ^4(79-4 x)}{-79+4 x} \, dx=-3-x+\left (5+x^2 (x+\log (67-4 (-3+x)))^2\right )^2 \] Output:
((ln(-4*x+79)+x)^2*x^2+5)^2-3-x
Leaf count is larger than twice the leaf count of optimal. \(73\) vs. \(2(25)=50\).
Time = 0.03 (sec) , antiderivative size = 73, normalized size of antiderivative = 2.92 \[ \int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8+\left (-4660 x^2+240 x^3-2164 x^6+112 x^7\right ) \log (79-4 x)+\left (-1580 x+80 x^2-2796 x^5+144 x^6\right ) \log ^2(79-4 x)+\left (-1564 x^4+80 x^5\right ) \log ^3(79-4 x)+\left (-316 x^3+16 x^4\right ) \log ^4(79-4 x)}{-79+4 x} \, dx=-x+10 x^4+x^8+4 x^3 \left (5+x^4\right ) \log (79-4 x)+2 x^2 \left (5+3 x^4\right ) \log ^2(79-4 x)+4 x^5 \log ^3(79-4 x)+x^4 \log ^4(79-4 x) \] Input:
Integrate[(79 - 4*x - 3080*x^3 + 160*x^4 - 616*x^7 + 32*x^8 + (-4660*x^2 + 240*x^3 - 2164*x^6 + 112*x^7)*Log[79 - 4*x] + (-1580*x + 80*x^2 - 2796*x^ 5 + 144*x^6)*Log[79 - 4*x]^2 + (-1564*x^4 + 80*x^5)*Log[79 - 4*x]^3 + (-31 6*x^3 + 16*x^4)*Log[79 - 4*x]^4)/(-79 + 4*x),x]
Output:
-x + 10*x^4 + x^8 + 4*x^3*(5 + x^4)*Log[79 - 4*x] + 2*x^2*(5 + 3*x^4)*Log[ 79 - 4*x]^2 + 4*x^5*Log[79 - 4*x]^3 + x^4*Log[79 - 4*x]^4
Leaf count is larger than twice the leaf count of optimal. \(637\) vs. \(2(25)=50\).
Time = 3.58 (sec) , antiderivative size = 637, normalized size of antiderivative = 25.48, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {7293, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {32 x^8-616 x^7+160 x^4-3080 x^3+\left (80 x^5-1564 x^4\right ) \log ^3(79-4 x)+\left (16 x^4-316 x^3\right ) \log ^4(79-4 x)+\left (144 x^6-2796 x^5+80 x^2-1580 x\right ) \log ^2(79-4 x)+\left (112 x^7-2164 x^6+240 x^3-4660 x^2\right ) \log (79-4 x)-4 x+79}{4 x-79} \, dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {4 (20 x-391) x^4 \log ^3(79-4 x)}{4 x-79}+4 x^3 \log ^4(79-4 x)+\frac {4 \left (36 x^5-699 x^4+20 x-395\right ) x \log ^2(79-4 x)}{4 x-79}+\frac {4 \left (28 x^5-541 x^4+60 x-1165\right ) x^2 \log (79-4 x)}{4 x-79}+\frac {32 x^8-616 x^7+160 x^4-3080 x^3-4 x+79}{4 x-79}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle x^8+4 x^7 \log (79-4 x)-\frac {x^6}{3}+6 x^6 \log ^2(79-4 x)+2 x^6 \log (79-4 x)-\frac {869 x^5}{50}+\frac {12}{5} x^5 \log ^2(79-4 x)+\frac {237}{5} x^5 \log (79-4 x)-\frac {227717 x^4}{320}+\frac {237}{4} x^4 \log ^2(79-4 x)+\frac {18723}{16} x^4 \log (79-4 x)-\frac {9367741 x^3}{320}+\frac {6241}{4} x^3 \log ^2(79-4 x)+\frac {493359}{16} x^3 \log (79-4 x)-\frac {3388669847 x^2}{2560}+\frac {116851523}{128} x^2 \log (79-4 x)+\frac {655414019067 x}{5120}+\frac {(79-4 x)^6}{12288}-\frac {711 (79-4 x)^5}{12800}+\frac {280845 (79-4 x)^4}{16384}-\frac {2465195}{768} (79-4 x)^3+\frac {1752754925 (79-4 x)^2}{4096}+\frac {1}{256} (79-4 x)^4 \log ^4(79-4 x)-\frac {79}{64} (79-4 x)^3 \log ^4(79-4 x)+\frac {18723}{128} (79-4 x)^2 \log ^4(79-4 x)-\frac {493039}{64} (79-4 x) \log ^4(79-4 x)+\frac {38950081}{256} \log ^4(79-4 x)-\frac {1}{256} (79-4 x)^5 \log ^3(79-4 x)+\frac {395}{256} (79-4 x)^4 \log ^3(79-4 x)-\frac {31205}{128} (79-4 x)^3 \log ^3(79-4 x)+\frac {2465195}{128} (79-4 x)^2 \log ^3(79-4 x)-\frac {194750405}{256} (79-4 x) \log ^3(79-4 x)+\frac {3077056399}{256} \log ^3(79-4 x)+\frac {3 (79-4 x)^5 \log ^2(79-4 x)}{1280}-\frac {1185 (79-4 x)^4 \log ^2(79-4 x)}{1024}+\frac {31205}{128} (79-4 x)^3 \log ^2(79-4 x)-\frac {13311733}{512} (79-4 x)^2 \log ^2(79-4 x)+\frac {350525449}{256} (79-4 x) \log ^2(79-4 x)-\frac {144601679553 \log ^2(79-4 x)}{5120}-\frac {(79-4 x)^6 \log (79-4 x)}{2048}+\frac {711 (79-4 x)^5 \log (79-4 x)}{2560}-\frac {280845 (79-4 x)^4 \log (79-4 x)}{4096}+\frac {2465195}{256} (79-4 x)^3 \log (79-4 x)-\frac {1752754925 (79-4 x)^2 \log (79-4 x)}{2048}+\frac {46155947105 (79-4 x) \log (79-4 x)}{1024}-\frac {21148688515127 \log (79-4 x)}{20480}\) |
Input:
Int[(79 - 4*x - 3080*x^3 + 160*x^4 - 616*x^7 + 32*x^8 + (-4660*x^2 + 240*x ^3 - 2164*x^6 + 112*x^7)*Log[79 - 4*x] + (-1580*x + 80*x^2 - 2796*x^5 + 14 4*x^6)*Log[79 - 4*x]^2 + (-1564*x^4 + 80*x^5)*Log[79 - 4*x]^3 + (-316*x^3 + 16*x^4)*Log[79 - 4*x]^4)/(-79 + 4*x),x]
Output:
(1752754925*(79 - 4*x)^2)/4096 - (2465195*(79 - 4*x)^3)/768 + (280845*(79 - 4*x)^4)/16384 - (711*(79 - 4*x)^5)/12800 + (79 - 4*x)^6/12288 + (6554140 19067*x)/5120 - (3388669847*x^2)/2560 - (9367741*x^3)/320 - (227717*x^4)/3 20 - (869*x^5)/50 - x^6/3 + x^8 - (21148688515127*Log[79 - 4*x])/20480 + ( 46155947105*(79 - 4*x)*Log[79 - 4*x])/1024 - (1752754925*(79 - 4*x)^2*Log[ 79 - 4*x])/2048 + (2465195*(79 - 4*x)^3*Log[79 - 4*x])/256 - (280845*(79 - 4*x)^4*Log[79 - 4*x])/4096 + (711*(79 - 4*x)^5*Log[79 - 4*x])/2560 - ((79 - 4*x)^6*Log[79 - 4*x])/2048 + (116851523*x^2*Log[79 - 4*x])/128 + (49335 9*x^3*Log[79 - 4*x])/16 + (18723*x^4*Log[79 - 4*x])/16 + (237*x^5*Log[79 - 4*x])/5 + 2*x^6*Log[79 - 4*x] + 4*x^7*Log[79 - 4*x] - (144601679553*Log[7 9 - 4*x]^2)/5120 + (350525449*(79 - 4*x)*Log[79 - 4*x]^2)/256 - (13311733* (79 - 4*x)^2*Log[79 - 4*x]^2)/512 + (31205*(79 - 4*x)^3*Log[79 - 4*x]^2)/1 28 - (1185*(79 - 4*x)^4*Log[79 - 4*x]^2)/1024 + (3*(79 - 4*x)^5*Log[79 - 4 *x]^2)/1280 + (6241*x^3*Log[79 - 4*x]^2)/4 + (237*x^4*Log[79 - 4*x]^2)/4 + (12*x^5*Log[79 - 4*x]^2)/5 + 6*x^6*Log[79 - 4*x]^2 + (3077056399*Log[79 - 4*x]^3)/256 - (194750405*(79 - 4*x)*Log[79 - 4*x]^3)/256 + (2465195*(79 - 4*x)^2*Log[79 - 4*x]^3)/128 - (31205*(79 - 4*x)^3*Log[79 - 4*x]^3)/128 + (395*(79 - 4*x)^4*Log[79 - 4*x]^3)/256 - ((79 - 4*x)^5*Log[79 - 4*x]^3)/25 6 + (38950081*Log[79 - 4*x]^4)/256 - (493039*(79 - 4*x)*Log[79 - 4*x]^4)/6 4 + (18723*(79 - 4*x)^2*Log[79 - 4*x]^4)/128 - (79*(79 - 4*x)^3*Log[79 ...
Leaf count of result is larger than twice the leaf count of optimal. \(75\) vs. \(2(23)=46\).
Time = 98.62 (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 | \(-x +x^{8}+10 x^{4}+\frac {20913542825165551}{1720320}+\frac {38950081 \ln \left (-4 x +79\right )^{4}}{256}+\frac {3077056399 \ln \left (-4 x +79\right )^{3}}{256}+\frac {729270355043 \ln \left (-4 x +79\right )^{2}}{2048}-\frac {\ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{5}}{256}+\frac {18723 \ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )^{2}}{128}-\frac {31205 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{3}}{128}+\frac {280845 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{4}}{2048}-\frac {131061 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{5}}{4096}-\frac {493039 \ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )}{64}+\frac {2465195 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{2}}{128}-\frac {7395585 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{3}}{512}+\frac {17256365 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{4}}{4096}-\frac {194750405 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )}{256}+\frac {1752754925 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{2}}{2048}-\frac {1363254115 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{3}}{4096}-\frac {27693608711 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )}{1024}+\frac {64618487739 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{2}}{4096}-\frac {1701636154087 \ln \left (-4 x +79\right ) \left (-4 x +79\right )}{4096}+\frac {\ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )^{4}}{256}+\frac {3 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{6}}{2048}-\frac {\ln \left (-4 x +79\right ) \left (-4 x +79\right )^{7}}{4096}-\frac {79 \ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )^{3}}{64}+\frac {395 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{4}}{256}-\frac {711 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{5}}{1024}+\frac {553 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{6}}{4096}+\frac {19204540076079 \ln \left (4 x -79\right )}{4096}\) | \(404\) |
| derivativedivides | \(\frac {19204540074031 x}{2048}+\frac {19204540076079 \ln \left (-4 x +79\right )}{4096}-\frac {1517158665848449}{8192}+\frac {1701636154087 \left (-4 x +79\right )^{2}}{16384}+\frac {\left (-4 x +79\right )^{8}}{65536}-\frac {79 \left (-4 x +79\right )^{7}}{8192}+\frac {43687 \left (-4 x +79\right )^{6}}{16384}-\frac {3451273 \left (-4 x +79\right )^{5}}{8192}-\frac {21539495913 \left (-4 x +79\right )^{3}}{8192}+\frac {1363254115 \left (-4 x +79\right )^{4}}{32768}+\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 {\ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{5}}{256}+\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}-\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 {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 {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 {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}\) | \(459\) |
| default | \(\frac {19204540074031 x}{2048}+\frac {19204540076079 \ln \left (-4 x +79\right )}{4096}-\frac {1517158665848449}{8192}+\frac {1701636154087 \left (-4 x +79\right )^{2}}{16384}+\frac {\left (-4 x +79\right )^{8}}{65536}-\frac {79 \left (-4 x +79\right )^{7}}{8192}+\frac {43687 \left (-4 x +79\right )^{6}}{16384}-\frac {3451273 \left (-4 x +79\right )^{5}}{8192}-\frac {21539495913 \left (-4 x +79\right )^{3}}{8192}+\frac {1363254115 \left (-4 x +79\right )^{4}}{32768}+\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 {\ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{5}}{256}+\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}-\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 {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 {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 {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}\) | \(459\) |
| orering | \(\text {Expression too large to display}\) | \(6505\) |
Input:
int(((16*x^4-316*x^3)*ln(-4*x+79)^4+(80*x^5-1564*x^4)*ln(-4*x+79)^3+(144*x ^6-2796*x^5+80*x^2-1580*x)*ln(-4*x+79)^2+(112*x^7-2164*x^6+240*x^3-4660*x^ 2)*ln(-4*x+79)+32*x^8-616*x^7+160*x^4-3080*x^3-4*x+79)/(4*x-79),x,method=_ RETURNVERBOSE)
Output:
ln(-4*x+79)^4*x^4+4*ln(-4*x+79)^3*x^5+(6*x^6+10*x^2)*ln(-4*x+79)^2+(4*x^7+ 20*x^3)*ln(-4*x+79)+x^8+10*x^4-x
Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (23) = 46\).
Time = 0.07 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.00 \[ \int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8+\left (-4660 x^2+240 x^3-2164 x^6+112 x^7\right ) \log (79-4 x)+\left (-1580 x+80 x^2-2796 x^5+144 x^6\right ) \log ^2(79-4 x)+\left (-1564 x^4+80 x^5\right ) \log ^3(79-4 x)+\left (-316 x^3+16 x^4\right ) \log ^4(79-4 x)}{-79+4 x} \, dx=x^{8} + 4 \, x^{5} \log \left (-4 \, x + 79\right )^{3} + x^{4} \log \left (-4 \, x + 79\right )^{4} + 10 \, x^{4} + 2 \, {\left (3 \, x^{6} + 5 \, x^{2}\right )} \log \left (-4 \, x + 79\right )^{2} + 4 \, {\left (x^{7} + 5 \, x^{3}\right )} \log \left (-4 \, x + 79\right ) - x \] Input:
integrate(((16*x^4-316*x^3)*log(-4*x+79)^4+(80*x^5-1564*x^4)*log(-4*x+79)^ 3+(144*x^6-2796*x^5+80*x^2-1580*x)*log(-4*x+79)^2+(112*x^7-2164*x^6+240*x^ 3-4660*x^2)*log(-4*x+79)+32*x^8-616*x^7+160*x^4-3080*x^3-4*x+79)/(4*x-79), x, algorithm="fricas")
Output:
x^8 + 4*x^5*log(-4*x + 79)^3 + x^4*log(-4*x + 79)^4 + 10*x^4 + 2*(3*x^6 + 5*x^2)*log(-4*x + 79)^2 + 4*(x^7 + 5*x^3)*log(-4*x + 79) - x
Leaf count of result is larger than twice the leaf count of optimal. 70 vs. \(2 (19) = 38\).
Time = 0.13 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.80 \[ \int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8+\left (-4660 x^2+240 x^3-2164 x^6+112 x^7\right ) \log (79-4 x)+\left (-1580 x+80 x^2-2796 x^5+144 x^6\right ) \log ^2(79-4 x)+\left (-1564 x^4+80 x^5\right ) \log ^3(79-4 x)+\left (-316 x^3+16 x^4\right ) \log ^4(79-4 x)}{-79+4 x} \, dx=x^{8} + 4 x^{5} \log {\left (79 - 4 x \right )}^{3} + x^{4} \log {\left (79 - 4 x \right )}^{4} + 10 x^{4} - x + \left (6 x^{6} + 10 x^{2}\right ) \log {\left (79 - 4 x \right )}^{2} + \left (4 x^{7} + 20 x^{3}\right ) \log {\left (79 - 4 x \right )} \] Input:
integrate(((16*x**4-316*x**3)*ln(-4*x+79)**4+(80*x**5-1564*x**4)*ln(-4*x+7 9)**3+(144*x**6-2796*x**5+80*x**2-1580*x)*ln(-4*x+79)**2+(112*x**7-2164*x* *6+240*x**3-4660*x**2)*ln(-4*x+79)+32*x**8-616*x**7+160*x**4-3080*x**3-4*x +79)/(4*x-79),x)
Output:
x**8 + 4*x**5*log(79 - 4*x)**3 + x**4*log(79 - 4*x)**4 + 10*x**4 - x + (6* x**6 + 10*x**2)*log(79 - 4*x)**2 + (4*x**7 + 20*x**3)*log(79 - 4*x)
Leaf count of result is larger than twice the leaf count of optimal. 773 vs. \(2 (23) = 46\).
Time = 0.08 (sec) , antiderivative size = 773, normalized size of antiderivative = 30.92 \[ \int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8+\left (-4660 x^2+240 x^3-2164 x^6+112 x^7\right ) \log (79-4 x)+\left (-1580 x+80 x^2-2796 x^5+144 x^6\right ) \log ^2(79-4 x)+\left (-1564 x^4+80 x^5\right ) \log ^3(79-4 x)+\left (-316 x^3+16 x^4\right ) \log ^4(79-4 x)}{-79+4 x} \, dx=\text {Too large to display} \] Input:
integrate(((16*x^4-316*x^3)*log(-4*x+79)^4+(80*x^5-1564*x^4)*log(-4*x+79)^ 3+(144*x^6-2796*x^5+80*x^2-1580*x)*log(-4*x+79)^2+(112*x^7-2164*x^6+240*x^ 3-4660*x^2)*log(-4*x+79)+32*x^8-616*x^7+160*x^4-3080*x^3-4*x+79)/(4*x-79), x, algorithm="maxima")
Output:
x^8 + 1/12288*(18*log(-4*x + 79)^2 - 6*log(-4*x + 79) + 1)*(4*x - 79)^6 + 1/32000*(125*log(-4*x + 79)^3 - 75*log(-4*x + 79)^2 + 30*log(-4*x + 79) - 6)*(4*x - 79)^5 + 3567/128000*(25*log(-4*x + 79)^2 - 10*log(-4*x + 79) + 2 )*(4*x - 79)^5 - 1/3*x^6 + 1/8192*(32*log(-4*x + 79)^4 - 32*log(-4*x + 79) ^3 + 24*log(-4*x + 79)^2 - 12*log(-4*x + 79) + 3)*(4*x - 79)^4 + 99/2048*( 32*log(-4*x + 79)^3 - 24*log(-4*x + 79)^2 + 12*log(-4*x + 79) - 3)*(4*x - 79)^4 + 283215/16384*(8*log(-4*x + 79)^2 - 4*log(-4*x + 79) + 1)*(4*x - 79 )^4 - 869/50*x^5 + 79/1728*(27*log(-4*x + 79)^4 - 36*log(-4*x + 79)^3 + 36 *log(-4*x + 79)^2 - 24*log(-4*x + 79) + 8)*(4*x - 79)^3 + 94247/3456*(9*lo g(-4*x + 79)^3 - 9*log(-4*x + 79)^2 + 6*log(-4*x + 79) - 2)*(4*x - 79)^3 + 7520405/4608*(9*log(-4*x + 79)^2 - 6*log(-4*x + 79) + 2)*(4*x - 79)^3 - 2 27717/320*x^4 + 38950081/256*log(-4*x + 79)^4 + 18723/256*(2*log(-4*x + 79 )^4 - 4*log(-4*x + 79)^3 + 6*log(-4*x + 79)^2 - 6*log(-4*x + 79) + 3)*(4*x - 79)^2 + 2502641/512*(4*log(-4*x + 79)^3 - 6*log(-4*x + 79)^2 + 6*log(-4 *x + 79) - 3)*(4*x - 79)^2 + 1811919605/4096*(2*log(-4*x + 79)^2 - 2*log(- 4*x + 79) + 1)*(4*x - 79)^2 - 9367741/320*x^3 + 3077056399/256*log(-4*x + 79)^3 + 493039/64*(log(-4*x + 79)^4 - 4*log(-4*x + 79)^3 + 12*log(-4*x + 7 9)^2 - 24*log(-4*x + 79) + 24)*(4*x - 79) + 202639029/256*(log(-4*x + 79)^ 3 - 3*log(-4*x + 79)^2 + 6*log(-4*x + 79) - 6)*(4*x - 79) + 30030613571/10 24*(log(-4*x + 79)^2 - 2*log(-4*x + 79) + 2)*(4*x - 79) - 3388669847/25...
Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (23) = 46\).
Time = 0.15 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.00 \[ \int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8+\left (-4660 x^2+240 x^3-2164 x^6+112 x^7\right ) \log (79-4 x)+\left (-1580 x+80 x^2-2796 x^5+144 x^6\right ) \log ^2(79-4 x)+\left (-1564 x^4+80 x^5\right ) \log ^3(79-4 x)+\left (-316 x^3+16 x^4\right ) \log ^4(79-4 x)}{-79+4 x} \, dx=x^{8} + 4 \, x^{5} \log \left (-4 \, x + 79\right )^{3} + x^{4} \log \left (-4 \, x + 79\right )^{4} + 10 \, x^{4} + 2 \, {\left (3 \, x^{6} + 5 \, x^{2}\right )} \log \left (-4 \, x + 79\right )^{2} + 4 \, {\left (x^{7} + 5 \, x^{3}\right )} \log \left (-4 \, x + 79\right ) - x \] Input:
integrate(((16*x^4-316*x^3)*log(-4*x+79)^4+(80*x^5-1564*x^4)*log(-4*x+79)^ 3+(144*x^6-2796*x^5+80*x^2-1580*x)*log(-4*x+79)^2+(112*x^7-2164*x^6+240*x^ 3-4660*x^2)*log(-4*x+79)+32*x^8-616*x^7+160*x^4-3080*x^3-4*x+79)/(4*x-79), x, algorithm="giac")
Output:
x^8 + 4*x^5*log(-4*x + 79)^3 + x^4*log(-4*x + 79)^4 + 10*x^4 + 2*(3*x^6 + 5*x^2)*log(-4*x + 79)^2 + 4*(x^7 + 5*x^3)*log(-4*x + 79) - x
Time = 1.74 (sec) , antiderivative size = 82, normalized size of antiderivative = 3.28 \[ \int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8+\left (-4660 x^2+240 x^3-2164 x^6+112 x^7\right ) \log (79-4 x)+\left (-1580 x+80 x^2-2796 x^5+144 x^6\right ) \log ^2(79-4 x)+\left (-1564 x^4+80 x^5\right ) \log ^3(79-4 x)+\left (-316 x^3+16 x^4\right ) \log ^4(79-4 x)}{-79+4 x} \, dx=10\,x^2\,{\ln \left (79-4\,x\right )}^2-x+4\,x^5\,{\ln \left (79-4\,x\right )}^3+6\,x^6\,{\ln \left (79-4\,x\right )}^2+x^4\,\left ({\ln \left (79-4\,x\right )}^4+10\right )+x^8+20\,x^3\,\ln \left (79-4\,x\right )+4\,x^7\,\ln \left (79-4\,x\right ) \] Input:
int(-(4*x + log(79 - 4*x)^4*(316*x^3 - 16*x^4) + log(79 - 4*x)^3*(1564*x^4 - 80*x^5) + log(79 - 4*x)^2*(1580*x - 80*x^2 + 2796*x^5 - 144*x^6) + log( 79 - 4*x)*(4660*x^2 - 240*x^3 + 2164*x^6 - 112*x^7) + 3080*x^3 - 160*x^4 + 616*x^7 - 32*x^8 - 79)/(4*x - 79),x)
Output:
10*x^2*log(79 - 4*x)^2 - x + 4*x^5*log(79 - 4*x)^3 + 6*x^6*log(79 - 4*x)^2 + x^4*(log(79 - 4*x)^4 + 10) + x^8 + 20*x^3*log(79 - 4*x) + 4*x^7*log(79 - 4*x)
Time = 0.28 (sec) , antiderivative size = 101, normalized size of antiderivative = 4.04 \[ \int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8+\left (-4660 x^2+240 x^3-2164 x^6+112 x^7\right ) \log (79-4 x)+\left (-1580 x+80 x^2-2796 x^5+144 x^6\right ) \log ^2(79-4 x)+\left (-1564 x^4+80 x^5\right ) \log ^3(79-4 x)+\left (-316 x^3+16 x^4\right ) \log ^4(79-4 x)}{-79+4 x} \, dx=\mathrm {log}\left (-4 x +79\right )^{4} x^{4}+4 \mathrm {log}\left (-4 x +79\right )^{3} x^{5}+6 \mathrm {log}\left (-4 x +79\right )^{2} x^{6}+10 \mathrm {log}\left (-4 x +79\right )^{2} x^{2}+4 \,\mathrm {log}\left (-4 x +79\right ) x^{7}+20 \,\mathrm {log}\left (-4 x +79\right ) x^{3}-\frac {19204540076079 \,\mathrm {log}\left (-4 x +79\right )}{4096}+\frac {19204540076079 \,\mathrm {log}\left (4 x -79\right )}{4096}+x^{8}+10 x^{4}-x \] Input:
int(((16*x^4-316*x^3)*log(-4*x+79)^4+(80*x^5-1564*x^4)*log(-4*x+79)^3+(144 *x^6-2796*x^5+80*x^2-1580*x)*log(-4*x+79)^2+(112*x^7-2164*x^6+240*x^3-4660 *x^2)*log(-4*x+79)+32*x^8-616*x^7+160*x^4-3080*x^3-4*x+79)/(4*x-79),x)
Output:
(4096*log( - 4*x + 79)**4*x**4 + 16384*log( - 4*x + 79)**3*x**5 + 24576*lo g( - 4*x + 79)**2*x**6 + 40960*log( - 4*x + 79)**2*x**2 + 16384*log( - 4*x + 79)*x**7 + 81920*log( - 4*x + 79)*x**3 - 19204540076079*log( - 4*x + 79 ) + 19204540076079*log(4*x - 79) + 4096*x**8 + 40960*x**4 - 4096*x)/4096