Integrand size = 93, antiderivative size = 26 \[ \int \frac {180 x-308 x^2-272 x^3-21 x^4+\left (-150+280 x+255 x^2+20 x^3\right ) \log (2)+\left (30 x-56 x^2-51 x^3-4 x^4+\left (-30+56 x+51 x^2+4 x^3\right ) \log (2)\right ) \log (x-\log (2))}{-3 x+3 \log (2)} \, dx=\left (5+\frac {x}{3}\right ) x \left (-2+2 x+x^2\right ) (5+\log (x-\log (2))) \] Output:
(1/3*x+5)*(ln(x-ln(2))+5)*x*(x^2+2*x-2)
Leaf count is larger than twice the leaf count of optimal. \(158\) vs. \(2(26)=52\).
Time = 0.26 (sec) , antiderivative size = 158, normalized size of antiderivative = 6.08 \[ \int \frac {180 x-308 x^2-272 x^3-21 x^4+\left (-150+280 x+255 x^2+20 x^3\right ) \log (2)+\left (30 x-56 x^2-51 x^3-4 x^4+\left (-30+56 x+51 x^2+4 x^3\right ) \log (2)\right ) \log (x-\log (2))}{-3 x+3 \log (2)} \, dx=\frac {1}{162} \left (3 x \left (-2700+1530 x^2+90 x^3-306 \log ^2(2)-18 \log ^3(2)+102 \log (2) \log (8)+\log (4) \log ^2(8)+x \left (2520-9 \log ^2(2)+\log ^2(8)\right )\right )+54 \left (-30 x+28 x^2+17 x^3+x^4-\log (2) \left (-30+28 \log (2)+17 \log ^2(2)+\log ^3(2)\right )\right ) \log (x-\log (2))-2 \left (45 \log (2) \left (-90+56 \log (8)+17 \log ^2(8)\right )+\log (8) \left (1620-924 \log (8)-7 \log ^3(8)+4 \log ^2(8) (-68+\log (32))\right )\right ) \log (3 x-\log (8))\right ) \] Input:
Integrate[(180*x - 308*x^2 - 272*x^3 - 21*x^4 + (-150 + 280*x + 255*x^2 + 20*x^3)*Log[2] + (30*x - 56*x^2 - 51*x^3 - 4*x^4 + (-30 + 56*x + 51*x^2 + 4*x^3)*Log[2])*Log[x - Log[2]])/(-3*x + 3*Log[2]),x]
Output:
(3*x*(-2700 + 1530*x^2 + 90*x^3 - 306*Log[2]^2 - 18*Log[2]^3 + 102*Log[2]* Log[8] + Log[4]*Log[8]^2 + x*(2520 - 9*Log[2]^2 + Log[8]^2)) + 54*(-30*x + 28*x^2 + 17*x^3 + x^4 - Log[2]*(-30 + 28*Log[2] + 17*Log[2]^2 + Log[2]^3) )*Log[x - Log[2]] - 2*(45*Log[2]*(-90 + 56*Log[8] + 17*Log[8]^2) + Log[8]* (1620 - 924*Log[8] - 7*Log[8]^3 + 4*Log[8]^2*(-68 + Log[32])))*Log[3*x - L og[8]])/162
Leaf count is larger than twice the leaf count of optimal. \(299\) vs. \(2(26)=52\).
Time = 0.83 (sec) , antiderivative size = 299, normalized size of antiderivative = 11.50, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.022, 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.
| \(\displaystyle \int \frac {-21 x^4-272 x^3-308 x^2+\left (20 x^3+255 x^2+280 x-150\right ) \log (2)+\left (-4 x^4-51 x^3-56 x^2+\left (4 x^3+51 x^2+56 x-30\right ) \log (2)+30 x\right ) \log (x-\log (2))+180 x}{3 \log (2)-3 x} \, dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {1}{3} \left (4 x^3+51 x^2+56 x-30\right ) \log (x-\log (2))+\frac {21 x^4+4 x^3 (68-\log (32))+x^2 (308-255 \log (2))-20 x (9+14 \log (2))+150 \log (2)}{3 x-\log (8)}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {5 x^4}{3}+\frac {1}{3} x^4 \log (x-\log (2))-\frac {17 x^3}{9}+\frac {17}{3} x^3 \log (x-\log (2))+\frac {1}{9} x^3 (272+\log (2))-\frac {1}{9} x^3 \log (2)-\frac {14 x^2}{3}+\frac {1}{18} x^2 \left (924+7 \log ^2(8)-765 \log (2)+4 \log (8) (68-\log (32))\right )-\frac {1}{6} x^2 \log ^2(2)+\frac {28}{3} x^2 \log (x-\log (2))-\frac {17}{6} x^2 \log (2)+10 x-\frac {1}{3} \log ^4(2) \log (x-\log (2))-\frac {1}{3} x \log ^3(2)-\frac {17}{3} \log ^3(2) \log (x-\log (2))-\frac {17}{3} x \log ^2(2)-\frac {28}{3} \log ^2(2) \log (x-\log (2))-\frac {1}{27} x \left (1620-7 \log ^3(8)-4 \log ^2(8) (68-\log (32))-924 \log (8)+45 \log (2) (56+17 \log (8))\right )-\frac {1}{27} \log (2) \left (270-7 \log ^3(8)-\log ^2(8) (17-4 \log (32))-84 \log (8)\right ) \log (3 x-\log (8))-\frac {28}{3} x \log (2)-10 (x-\log (2)) \log (x-\log (2))\) |
Input:
Int[(180*x - 308*x^2 - 272*x^3 - 21*x^4 + (-150 + 280*x + 255*x^2 + 20*x^3 )*Log[2] + (30*x - 56*x^2 - 51*x^3 - 4*x^4 + (-30 + 56*x + 51*x^2 + 4*x^3) *Log[2])*Log[x - Log[2]])/(-3*x + 3*Log[2]),x]
Output:
10*x - (14*x^2)/3 - (17*x^3)/9 + (5*x^4)/3 - (28*x*Log[2])/3 - (17*x^2*Log [2])/6 - (x^3*Log[2])/9 - (17*x*Log[2]^2)/3 - (x^2*Log[2]^2)/6 - (x*Log[2] ^3)/3 + (x^3*(272 + Log[2]))/9 + (x^2*(924 - 765*Log[2] + 7*Log[8]^2 + 4*L og[8]*(68 - Log[32])))/18 - (x*(1620 - 924*Log[8] - 7*Log[8]^3 + 45*Log[2] *(56 + 17*Log[8]) - 4*Log[8]^2*(68 - Log[32])))/27 + (28*x^2*Log[x - Log[2 ]])/3 + (17*x^3*Log[x - Log[2]])/3 + (x^4*Log[x - Log[2]])/3 - 10*(x - Log [2])*Log[x - Log[2]] - (28*Log[2]^2*Log[x - Log[2]])/3 - (17*Log[2]^3*Log[ x - Log[2]])/3 - (Log[2]^4*Log[x - Log[2]])/3 - (Log[2]*(270 - 84*Log[8] - 7*Log[8]^3 - Log[8]^2*(17 - 4*Log[32]))*Log[3*x - Log[8]])/27
Time = 1.77 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.81
| method | result | size |
| risch | \(\left (\frac {1}{3} x^{4}+\frac {17}{3} x^{3}+\frac {28}{3} x^{2}-10 x \right ) \ln \left (x -\ln \left (2\right )\right )+\frac {5 x^{4}}{3}+\frac {85 x^{3}}{3}+\frac {140 x^{2}}{3}-50 x\) | \(47\) |
| norman | \(-50 x +\frac {140 x^{2}}{3}+\frac {85 x^{3}}{3}+\frac {5 x^{4}}{3}-10 \ln \left (x -\ln \left (2\right )\right ) x +\frac {28 \ln \left (x -\ln \left (2\right )\right ) x^{2}}{3}+\frac {17 \ln \left (x -\ln \left (2\right )\right ) x^{3}}{3}+\frac {\ln \left (x -\ln \left (2\right )\right ) x^{4}}{3}\) | \(66\) |
| parallelrisch | \(\frac {\ln \left (x -\ln \left (2\right )\right ) x^{4}}{3}+\frac {5 x^{4}}{3}+\frac {17 \ln \left (x -\ln \left (2\right )\right ) x^{3}}{3}+\frac {85 x^{3}}{3}+\frac {28 \ln \left (x -\ln \left (2\right )\right ) x^{2}}{3}-\frac {140 \ln \left (2\right )^{2}}{3}+\frac {140 x^{2}}{3}-10 \ln \left (x -\ln \left (2\right )\right ) x -100 \ln \left (2\right )-50 x\) | \(76\) |
| parts | \(-50 x -10 \ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )-\frac {2 \ln \left (2\right )^{4} \ln \left (x -\ln \left (2\right )\right )}{3}+\frac {28 \ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )^{2}}{3}+\frac {17 \ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )^{3}}{3}+\frac {\ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )^{4}}{3}-\frac {56 \ln \left (2\right )^{2} \ln \left (x -\ln \left (2\right )\right )}{3}+\frac {25 \ln \left (2\right )^{4}}{36}+\frac {187 \ln \left (2\right )^{3}}{18}+14 \ln \left (2\right )^{2}+\frac {140 x^{2}}{3}-10 \ln \left (2\right )+\frac {85 x^{3}}{3}+\frac {5 x^{4}}{3}+\frac {4 \ln \left (2\right )^{3} \ln \left (x -\ln \left (2\right )\right ) x}{3}-2 \ln \left (2\right )^{2} \ln \left (x -\ln \left (2\right )\right ) x^{2}+\frac {4 \ln \left (2\right ) \ln \left (x -\ln \left (2\right )\right ) x^{3}}{3}-17 \ln \left (2\right )^{2} \ln \left (x -\ln \left (2\right )\right ) x +17 \ln \left (2\right ) \ln \left (x -\ln \left (2\right )\right ) x^{2}+\frac {56 \ln \left (2\right ) \ln \left (x -\ln \left (2\right )\right ) x}{3}+\frac {\ln \left (2\right ) \left (\ln \left (2\right )^{3}+17 \ln \left (2\right )^{2}+28 \ln \left (2\right )-30\right ) \ln \left (x -\ln \left (2\right )\right )}{3}\) | \(245\) |
| derivativedivides | \(-50 x +\frac {5 \left (x -\ln \left (2\right )\right )^{4}}{3}+\frac {85 \left (x -\ln \left (2\right )\right )^{3}}{3}+\frac {140 \left (x -\ln \left (2\right )\right )^{2}}{3}+11 \ln \left (2\right )^{2} \left (x -\ln \left (2\right )\right )^{2}+\frac {64 \ln \left (2\right ) \left (x -\ln \left (2\right )\right )^{3}}{9}+102 \ln \left (2\right )^{2} \left (x -\ln \left (2\right )\right )+\frac {187 \ln \left (2\right ) \left (x -\ln \left (2\right )\right )^{2}}{2}+112 \ln \left (2\right ) \left (x -\ln \left (2\right )\right )+\frac {17 \ln \left (x -\ln \left (2\right )\right ) \ln \left (2\right )^{3}}{3}-10 \ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )+\frac {56 \ln \left (2\right ) \left (\ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )-x +\ln \left (2\right )\right )}{3}+\frac {\ln \left (2\right )^{4} \ln \left (x -\ln \left (2\right )\right )}{3}+17 \ln \left (2\right )^{2} \left (\ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )-x +\ln \left (2\right )\right )+\frac {28 \ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )^{2}}{3}+34 \ln \left (2\right ) \left (\frac {\ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )^{2}}{2}-\frac {\left (x -\ln \left (2\right )\right )^{2}}{4}\right )+4 \ln \left (2\right )^{2} \left (\frac {\ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )^{2}}{2}-\frac {\left (x -\ln \left (2\right )\right )^{2}}{4}\right )+\frac {17 \ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )^{3}}{3}+4 \ln \left (2\right ) \left (\frac {\ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )^{3}}{3}-\frac {\left (x -\ln \left (2\right )\right )^{3}}{9}\right )+\frac {4 \ln \left (2\right )^{3} \left (\ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )-x +\ln \left (2\right )\right )}{3}+\frac {\ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )^{4}}{3}+8 \ln \left (2\right )^{3} \left (x -\ln \left (2\right )\right )-10 \ln \left (2\right ) \ln \left (x -\ln \left (2\right )\right )+\frac {28 \ln \left (2\right )^{2} \ln \left (x -\ln \left (2\right )\right )}{3}+50 \ln \left (2\right )\) | \(401\) |
| default | \(-50 x +\frac {5 \left (x -\ln \left (2\right )\right )^{4}}{3}+\frac {85 \left (x -\ln \left (2\right )\right )^{3}}{3}+\frac {140 \left (x -\ln \left (2\right )\right )^{2}}{3}+11 \ln \left (2\right )^{2} \left (x -\ln \left (2\right )\right )^{2}+\frac {64 \ln \left (2\right ) \left (x -\ln \left (2\right )\right )^{3}}{9}+102 \ln \left (2\right )^{2} \left (x -\ln \left (2\right )\right )+\frac {187 \ln \left (2\right ) \left (x -\ln \left (2\right )\right )^{2}}{2}+112 \ln \left (2\right ) \left (x -\ln \left (2\right )\right )+\frac {17 \ln \left (x -\ln \left (2\right )\right ) \ln \left (2\right )^{3}}{3}-10 \ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )+\frac {56 \ln \left (2\right ) \left (\ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )-x +\ln \left (2\right )\right )}{3}+\frac {\ln \left (2\right )^{4} \ln \left (x -\ln \left (2\right )\right )}{3}+17 \ln \left (2\right )^{2} \left (\ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )-x +\ln \left (2\right )\right )+\frac {28 \ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )^{2}}{3}+34 \ln \left (2\right ) \left (\frac {\ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )^{2}}{2}-\frac {\left (x -\ln \left (2\right )\right )^{2}}{4}\right )+4 \ln \left (2\right )^{2} \left (\frac {\ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )^{2}}{2}-\frac {\left (x -\ln \left (2\right )\right )^{2}}{4}\right )+\frac {17 \ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )^{3}}{3}+4 \ln \left (2\right ) \left (\frac {\ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )^{3}}{3}-\frac {\left (x -\ln \left (2\right )\right )^{3}}{9}\right )+\frac {4 \ln \left (2\right )^{3} \left (\ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )-x +\ln \left (2\right )\right )}{3}+\frac {\ln \left (x -\ln \left (2\right )\right ) \left (x -\ln \left (2\right )\right )^{4}}{3}+8 \ln \left (2\right )^{3} \left (x -\ln \left (2\right )\right )-10 \ln \left (2\right ) \ln \left (x -\ln \left (2\right )\right )+\frac {28 \ln \left (2\right )^{2} \ln \left (x -\ln \left (2\right )\right )}{3}+50 \ln \left (2\right )\) | \(401\) |
Input:
int((((4*x^3+51*x^2+56*x-30)*ln(2)-4*x^4-51*x^3-56*x^2+30*x)*ln(x-ln(2))+( 20*x^3+255*x^2+280*x-150)*ln(2)-21*x^4-272*x^3-308*x^2+180*x)/(3*ln(2)-3*x ),x,method=_RETURNVERBOSE)
Output:
(1/3*x^4+17/3*x^3+28/3*x^2-10*x)*ln(x-ln(2))+5/3*x^4+85/3*x^3+140/3*x^2-50 *x
Time = 0.09 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.73 \[ \int \frac {180 x-308 x^2-272 x^3-21 x^4+\left (-150+280 x+255 x^2+20 x^3\right ) \log (2)+\left (30 x-56 x^2-51 x^3-4 x^4+\left (-30+56 x+51 x^2+4 x^3\right ) \log (2)\right ) \log (x-\log (2))}{-3 x+3 \log (2)} \, dx=\frac {5}{3} \, x^{4} + \frac {85}{3} \, x^{3} + \frac {140}{3} \, x^{2} + \frac {1}{3} \, {\left (x^{4} + 17 \, x^{3} + 28 \, x^{2} - 30 \, x\right )} \log \left (x - \log \left (2\right )\right ) - 50 \, x \] Input:
integrate((((4*x^3+51*x^2+56*x-30)*log(2)-4*x^4-51*x^3-56*x^2+30*x)*log(x- log(2))+(20*x^3+255*x^2+280*x-150)*log(2)-21*x^4-272*x^3-308*x^2+180*x)/(3 *log(2)-3*x),x, algorithm="fricas")
Output:
5/3*x^4 + 85/3*x^3 + 140/3*x^2 + 1/3*(x^4 + 17*x^3 + 28*x^2 - 30*x)*log(x - log(2)) - 50*x
Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (22) = 44\).
Time = 0.10 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.96 \[ \int \frac {180 x-308 x^2-272 x^3-21 x^4+\left (-150+280 x+255 x^2+20 x^3\right ) \log (2)+\left (30 x-56 x^2-51 x^3-4 x^4+\left (-30+56 x+51 x^2+4 x^3\right ) \log (2)\right ) \log (x-\log (2))}{-3 x+3 \log (2)} \, dx=\frac {5 x^{4}}{3} + \frac {85 x^{3}}{3} + \frac {140 x^{2}}{3} - 50 x + \left (\frac {x^{4}}{3} + \frac {17 x^{3}}{3} + \frac {28 x^{2}}{3} - 10 x\right ) \log {\left (x - \log {\left (2 \right )} \right )} \] Input:
integrate((((4*x**3+51*x**2+56*x-30)*ln(2)-4*x**4-51*x**3-56*x**2+30*x)*ln (x-ln(2))+(20*x**3+255*x**2+280*x-150)*ln(2)-21*x**4-272*x**3-308*x**2+180 *x)/(3*ln(2)-3*x),x)
Output:
5*x**4/3 + 85*x**3/3 + 140*x**2/3 - 50*x + (x**4/3 + 17*x**3/3 + 28*x**2/3 - 10*x)*log(x - log(2))
Leaf count of result is larger than twice the leaf count of optimal. 606 vs. \(2 (23) = 46\).
Time = 0.12 (sec) , antiderivative size = 606, normalized size of antiderivative = 23.31 \[ \int \frac {180 x-308 x^2-272 x^3-21 x^4+\left (-150+280 x+255 x^2+20 x^3\right ) \log (2)+\left (30 x-56 x^2-51 x^3-4 x^4+\left (-30+56 x+51 x^2+4 x^3\right ) \log (2)\right ) \log (x-\log (2))}{-3 x+3 \log (2)} \, dx=\text {Too large to display} \] Input:
integrate((((4*x^3+51*x^2+56*x-30)*log(2)-4*x^4-51*x^3-56*x^2+30*x)*log(x- log(2))+(20*x^3+255*x^2+280*x-150)*log(2)-21*x^4-272*x^3-308*x^2+180*x)/(3 *log(2)-3*x),x, algorithm="maxima")
Output:
-2/3*log(2)^4*log(x - log(2))^2 + 38/9*log(2)^4*log(x - log(2)) - 17/2*log (2)^3*log(x - log(2))^2 + 5/3*x^4 + 56/27*x^3*log(2) + 25/9*x^2*log(2)^2 + 38/9*x*log(2)^3 + 119/2*log(2)^3*log(x - log(2)) - 28/3*log(2)^2*log(x - log(2))^2 + 85/3*x^3 + 153/4*x^2*log(2) + 119/2*x*log(2)^2 - 2/9*(6*log(2) ^3*log(x - log(2)) + 2*x^3 + 3*x^2*log(2) + 6*x*log(2)^2)*log(2)*log(x - l og(2)) - 17/2*(2*log(2)^2*log(x - log(2)) + x^2 + 2*x*log(2))*log(2)*log(x - log(2)) - 56/3*(log(2)*log(x - log(2)) + x)*log(2)*log(x - log(2)) + 22 4/3*log(2)^2*log(x - log(2)) + 10*log(2)*log(x - log(2))^2 + 140/3*x^2 + 1 /27*(18*log(2)^3*log(x - log(2))^2 + 66*log(2)^3*log(x - log(2)) + 4*x^3 + 15*x^2*log(2) + 66*x*log(2)^2)*log(2) - 10/9*(6*log(2)^3*log(x - log(2)) + 2*x^3 + 3*x^2*log(2) + 6*x*log(2)^2)*log(2) + 17/4*(2*log(2)^2*log(x - l og(2))^2 + 6*log(2)^2*log(x - log(2)) + x^2 + 6*x*log(2))*log(2) - 85/2*(2 *log(2)^2*log(x - log(2)) + x^2 + 2*x*log(2))*log(2) + 28/3*(log(2)*log(x - log(2))^2 + 2*log(2)*log(x - log(2)) + 2*x)*log(2) - 280/3*(log(2)*log(x - log(2)) + x)*log(2) + 224/3*x*log(2) + 1/9*(12*log(2)^4*log(x - log(2)) + 3*x^4 + 4*x^3*log(2) + 6*x^2*log(2)^2 + 12*x*log(2)^3)*log(x - log(2)) + 17/6*(6*log(2)^3*log(x - log(2)) + 2*x^3 + 3*x^2*log(2) + 6*x*log(2)^2)* log(x - log(2)) + 28/3*(2*log(2)^2*log(x - log(2)) + x^2 + 2*x*log(2))*log (x - log(2)) - 10*(log(2)*log(x - log(2)) + x)*log(x - log(2)) - 50*x
Time = 0.12 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.73 \[ \int \frac {180 x-308 x^2-272 x^3-21 x^4+\left (-150+280 x+255 x^2+20 x^3\right ) \log (2)+\left (30 x-56 x^2-51 x^3-4 x^4+\left (-30+56 x+51 x^2+4 x^3\right ) \log (2)\right ) \log (x-\log (2))}{-3 x+3 \log (2)} \, dx=\frac {5}{3} \, x^{4} + \frac {85}{3} \, x^{3} + \frac {140}{3} \, x^{2} + \frac {1}{3} \, {\left (x^{4} + 17 \, x^{3} + 28 \, x^{2} - 30 \, x\right )} \log \left (x - \log \left (2\right )\right ) - 50 \, x \] Input:
integrate((((4*x^3+51*x^2+56*x-30)*log(2)-4*x^4-51*x^3-56*x^2+30*x)*log(x- log(2))+(20*x^3+255*x^2+280*x-150)*log(2)-21*x^4-272*x^3-308*x^2+180*x)/(3 *log(2)-3*x),x, algorithm="giac")
Output:
5/3*x^4 + 85/3*x^3 + 140/3*x^2 + 1/3*(x^4 + 17*x^3 + 28*x^2 - 30*x)*log(x - log(2)) - 50*x
Time = 0.72 (sec) , antiderivative size = 400, normalized size of antiderivative = 15.38 \[ \int \frac {180 x-308 x^2-272 x^3-21 x^4+\left (-150+280 x+255 x^2+20 x^3\right ) \log (2)+\left (30 x-56 x^2-51 x^3-4 x^4+\left (-30+56 x+51 x^2+4 x^3\right ) \log (2)\right ) \log (x-\log (2))}{-3 x+3 \log (2)} \, dx=\frac {7\,x^2\,{\ln \left (2\right )}^2}{2}-60\,x-\ln \left (x-\ln \left (2\right )\right )\,\left (\frac {280\,{\ln \left (2\right )}^2}{3}-50\,\ln \left (2\right )+85\,{\ln \left (2\right )}^3+\frac {20\,{\ln \left (2\right )}^4}{3}\right )-x\,\left (\frac {280\,\ln \left (2\right )}{3}+\ln \left (2\right )\,\left (85\,\ln \left (2\right )+\frac {20\,{\ln \left (2\right )}^2}{3}\right )\right )+\frac {308\,\ln \left (x-\ln \left (2\right )\right )\,{\ln \left (2\right )}^2}{3}+\frac {272\,\ln \left (x-\ln \left (2\right )\right )\,{\ln \left (2\right )}^3}{3}+7\,\ln \left (x-\ln \left (2\right )\right )\,{\ln \left (2\right )}^4+\frac {308\,x\,\ln \left (2\right )}{3}-x^2\,\left (\frac {85\,\ln \left (2\right )}{2}+\frac {10\,{\ln \left (2\right )}^2}{3}\right )+\frac {272\,x\,{\ln \left (2\right )}^2}{3}+\frac {136\,x^2\,\ln \left (2\right )}{3}+7\,x\,{\ln \left (2\right )}^3+\frac {x^3\,\ln \left (2\right )}{9}+\frac {154\,x^2}{3}+\frac {272\,x^3}{9}+\frac {7\,x^4}{4}-60\,\ln \left (x-\ln \left (2\right )\right )\,\ln \left (2\right )-\frac {x^4\,\left (\frac {\ln \left (2\right )}{12}+\frac {17}{3}\right )-x^5\,\ln \left (x-\ln \left (2\right )\right )-\ln \left (x-\ln \left (2\right )\right )\,\left (28\,{\ln \left (2\right )}^3-30\,{\ln \left (2\right )}^2+17\,{\ln \left (2\right )}^4+{\ln \left (2\right )}^5\right )+x^3\,\left (\frac {17\,\ln \left (2\right )}{6}+\frac {{\ln \left (2\right )}^2}{6}+14\right )+x^2\,\left (14\,\ln \left (2\right )+\frac {17\,{\ln \left (2\right )}^2}{2}+\frac {{\ln \left (2\right )}^3}{2}-30\right )+\frac {x^5}{4}+x^4\,\ln \left (x-\ln \left (2\right )\right )\,\left (\ln \left (2\right )-17\right )+x\,\ln \left (x-\ln \left (2\right )\right )\,\left (28\,{\ln \left (2\right )}^2-60\,\ln \left (2\right )+17\,{\ln \left (2\right )}^3+{\ln \left (2\right )}^4\right )-\frac {x\,\left (28\,{\ln \left (2\right )}^3-30\,{\ln \left (2\right )}^2+17\,{\ln \left (2\right )}^4+{\ln \left (2\right )}^5\right )}{\ln \left (2\right )}+x^3\,\ln \left (x-\ln \left (2\right )\right )\,\left (17\,\ln \left (2\right )-28\right )+x^2\,\ln \left (x-\ln \left (2\right )\right )\,\left (28\,\ln \left (2\right )+30\right )}{3\,x-3\,\ln \left (2\right )} \] Input:
int((log(x - log(2))*(56*x^2 - log(2)*(56*x + 51*x^2 + 4*x^3 - 30) - 30*x + 51*x^3 + 4*x^4) - log(2)*(280*x + 255*x^2 + 20*x^3 - 150) - 180*x + 308* x^2 + 272*x^3 + 21*x^4)/(3*x - 3*log(2)),x)
Output:
(7*x^2*log(2)^2)/2 - 60*x - log(x - log(2))*((280*log(2)^2)/3 - 50*log(2) + 85*log(2)^3 + (20*log(2)^4)/3) - x*((280*log(2))/3 + log(2)*(85*log(2) + (20*log(2)^2)/3)) + (308*log(x - log(2))*log(2)^2)/3 + (272*log(x - log(2 ))*log(2)^3)/3 + 7*log(x - log(2))*log(2)^4 + (308*x*log(2))/3 - x^2*((85* log(2))/2 + (10*log(2)^2)/3) + (272*x*log(2)^2)/3 + (136*x^2*log(2))/3 + 7 *x*log(2)^3 + (x^3*log(2))/9 + (154*x^2)/3 + (272*x^3)/9 + (7*x^4)/4 - 60* log(x - log(2))*log(2) - (x^4*(log(2)/12 + 17/3) - x^5*log(x - log(2)) - l og(x - log(2))*(28*log(2)^3 - 30*log(2)^2 + 17*log(2)^4 + log(2)^5) + x^3* ((17*log(2))/6 + log(2)^2/6 + 14) + x^2*(14*log(2) + (17*log(2)^2)/2 + log (2)^3/2 - 30) + x^5/4 + x^4*log(x - log(2))*(log(2) - 17) + x*log(x - log( 2))*(28*log(2)^2 - 60*log(2) + 17*log(2)^3 + log(2)^4) - (x*(28*log(2)^3 - 30*log(2)^2 + 17*log(2)^4 + log(2)^5))/log(2) + x^3*log(x - log(2))*(17*l og(2) - 28) + x^2*log(x - log(2))*(28*log(2) + 30))/(3*x - 3*log(2))
Time = 0.20 (sec) , antiderivative size = 165, normalized size of antiderivative = 6.35 \[ \int \frac {180 x-308 x^2-272 x^3-21 x^4+\left (-150+280 x+255 x^2+20 x^3\right ) \log (2)+\left (30 x-56 x^2-51 x^3-4 x^4+\left (-30+56 x+51 x^2+4 x^3\right ) \log (2)\right ) \log (x-\log (2))}{-3 x+3 \log (2)} \, dx=\frac {\mathrm {log}\left (\mathrm {log}\left (2\right )-x \right ) \mathrm {log}\left (2\right )^{4}}{3}+\frac {17 \,\mathrm {log}\left (\mathrm {log}\left (2\right )-x \right ) \mathrm {log}\left (2\right )^{3}}{3}+\frac {28 \,\mathrm {log}\left (\mathrm {log}\left (2\right )-x \right ) \mathrm {log}\left (2\right )^{2}}{3}-10 \,\mathrm {log}\left (\mathrm {log}\left (2\right )-x \right ) \mathrm {log}\left (2\right )-\frac {\mathrm {log}\left (-\mathrm {log}\left (2\right )+x \right ) \mathrm {log}\left (2\right )^{4}}{3}-\frac {17 \,\mathrm {log}\left (-\mathrm {log}\left (2\right )+x \right ) \mathrm {log}\left (2\right )^{3}}{3}-\frac {28 \,\mathrm {log}\left (-\mathrm {log}\left (2\right )+x \right ) \mathrm {log}\left (2\right )^{2}}{3}+10 \,\mathrm {log}\left (-\mathrm {log}\left (2\right )+x \right ) \mathrm {log}\left (2\right )+\frac {\mathrm {log}\left (-\mathrm {log}\left (2\right )+x \right ) x^{4}}{3}+\frac {17 \,\mathrm {log}\left (-\mathrm {log}\left (2\right )+x \right ) x^{3}}{3}+\frac {28 \,\mathrm {log}\left (-\mathrm {log}\left (2\right )+x \right ) x^{2}}{3}-10 \,\mathrm {log}\left (-\mathrm {log}\left (2\right )+x \right ) x +\frac {5 x^{4}}{3}+\frac {85 x^{3}}{3}+\frac {140 x^{2}}{3}-50 x \] Input:
int((((4*x^3+51*x^2+56*x-30)*log(2)-4*x^4-51*x^3-56*x^2+30*x)*log(x-log(2) )+(20*x^3+255*x^2+280*x-150)*log(2)-21*x^4-272*x^3-308*x^2+180*x)/(3*log(2 )-3*x),x)
Output:
(log(log(2) - x)*log(2)**4 + 17*log(log(2) - x)*log(2)**3 + 28*log(log(2) - x)*log(2)**2 - 30*log(log(2) - x)*log(2) - log( - log(2) + x)*log(2)**4 - 17*log( - log(2) + x)*log(2)**3 - 28*log( - log(2) + x)*log(2)**2 + 30*l og( - log(2) + x)*log(2) + log( - log(2) + x)*x**4 + 17*log( - log(2) + x) *x**3 + 28*log( - log(2) + x)*x**2 - 30*log( - log(2) + x)*x + 5*x**4 + 85 *x**3 + 140*x**2 - 150*x)/3