Optimal. Leaf size=28 \[ \frac {\left (-1+e-\frac {x}{2}\right ) (x+\log (2 x))}{4 \left (-5+x+x^2+\log (4)\right )} \]
________________________________________________________________________________________
Rubi [C] time = 3.00, antiderivative size = 1473, normalized size of antiderivative = 52.61, number of steps used = 62, number of rules used = 20, integrand size = 131, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.153, Rules used = {6, 6741, 12, 6742, 1646, 800, 634, 618, 206, 628, 614, 740, 638, 2357, 2316, 2315, 2317, 2391, 2314, 31}
result too large to display
Antiderivative was successfully verified.
[In]
[Out]
Rule 6
Rule 12
Rule 31
Rule 206
Rule 614
Rule 618
Rule 628
Rule 634
Rule 638
Rule 740
Rule 800
Rule 1646
Rule 2314
Rule 2315
Rule 2316
Rule 2317
Rule 2357
Rule 2391
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {10+13 x+7 x^2+e \left (-10-8 x+2 x^2-2 x^3\right )+\left (-2-3 x-2 x^2+e (2+2 x)\right ) \log (4)+\left (7 x+4 x^2+x^3+e \left (-2 x-4 x^2\right )-x \log (4)\right ) \log (2 x)}{-80 x^2-72 x^3+16 x^4+8 x^5+\left (-80 x+16 x^2+16 x^3\right ) \log (4)+x \left (200+8 \log ^2(4)\right )} \, dx\\ &=\int \frac {10+13 x+7 x^2+e \left (-10-8 x+2 x^2-2 x^3\right )+\left (-2-3 x-2 x^2+e (2+2 x)\right ) \log (4)+\left (7 x+4 x^2+x^3+e \left (-2 x-4 x^2\right )-x \log (4)\right ) \log (2 x)}{8 x \left (5-x-x^2-\log (4)\right )^2} \, dx\\ &=\frac {1}{8} \int \frac {10+13 x+7 x^2+e \left (-10-8 x+2 x^2-2 x^3\right )+\left (-2-3 x-2 x^2+e (2+2 x)\right ) \log (4)+\left (7 x+4 x^2+x^3+e \left (-2 x-4 x^2\right )-x \log (4)\right ) \log (2 x)}{x \left (5-x-x^2-\log (4)\right )^2} \, dx\\ &=\frac {1}{8} \int \left (\frac {\left (-2 (1-e)-(3-2 e) x-2 x^2\right ) \log (4)}{x \left (5-x-x^2-\log (4)\right )^2}+\frac {13}{\left (-5+x+x^2+\log (4)\right )^2}+\frac {10}{x \left (-5+x+x^2+\log (4)\right )^2}+\frac {7 x}{\left (-5+x+x^2+\log (4)\right )^2}-\frac {2 e \left (5+4 x-x^2+x^3\right )}{x \left (-5+x+x^2+\log (4)\right )^2}+\frac {\left (7-2 e+4 (1-e) x+x^2-\log (4)\right ) \log (2 x)}{\left (5-x-x^2-\log (4)\right )^2}\right ) \, dx\\ &=\frac {1}{8} \int \frac {\left (7-2 e+4 (1-e) x+x^2-\log (4)\right ) \log (2 x)}{\left (5-x-x^2-\log (4)\right )^2} \, dx+\frac {7}{8} \int \frac {x}{\left (-5+x+x^2+\log (4)\right )^2} \, dx+\frac {5}{4} \int \frac {1}{x \left (-5+x+x^2+\log (4)\right )^2} \, dx+\frac {13}{8} \int \frac {1}{\left (-5+x+x^2+\log (4)\right )^2} \, dx-\frac {1}{4} e \int \frac {5+4 x-x^2+x^3}{x \left (-5+x+x^2+\log (4)\right )^2} \, dx+\frac {1}{8} \log (4) \int \frac {-2 (1-e)-(3-2 e) x-2 x^2}{x \left (5-x-x^2-\log (4)\right )^2} \, dx\\ &=\frac {13 (1+2 x)}{8 \left (5-x-x^2-\log (4)\right ) (21-\log (256))}-\frac {\log (4) \left (137-e (32-6 \log (4))-47 \log (4)+4 \log ^2(4)+2 (1-e) x (11-\log (16))\right )}{8 (5-\log (4)) \left (5-x-x^2-\log (4)\right ) (21-\log (256))}+\frac {7 (10-x-\log (16))}{8 \left (5-x-x^2-\log (4)\right ) (21-\log (256))}+\frac {5 (11+x-\log (16))}{4 (5-\log (4)) \left (5-x-x^2-\log (4)\right ) (21-\log (256))}-\frac {e \left (x \left (105-30 \log (4)+2 \log ^2(4)\right )+\log (4) (16-\log (64))\right )}{4 (5-\log (4)) \left (5-x-x^2-\log (4)\right ) (21-\log (256))}+\frac {1}{8} \int \left (\frac {((3-4 e) x+2 (6-e-\log (4))) \log (2 x)}{\left (5-x-x^2-\log (4)\right )^2}+\frac {\log (2 x)}{-5+x+x^2+\log (4)}\right ) \, dx+\frac {7 \int \frac {1}{-5+x+x^2+\log (4)} \, dx}{8 (21-\log (256))}-\frac {13 \int \frac {1}{-5+x+x^2+\log (4)} \, dx}{4 (21-\log (256))}+\frac {e \int \frac {\frac {x \log (4) (11-\log (16))}{5-\log (4)}+\frac {5 (21-\log (256))}{5-\log (4)}}{x \left (-5+x+x^2+\log (4)\right )} \, dx}{4 (21-\log (256))}+\frac {5 \int \frac {-21-x+\log (256)}{x \left (-5+x+x^2+\log (4)\right )} \, dx}{4 (5-\log (4)) (21-\log (256))}-\frac {\log (4) \int \frac {\frac {2 (1-e) x (11-\log (16))}{5-\log (4)}+\frac {2 (1-e) (21-\log (256))}{5-\log (4)}}{x \left (5-x-x^2-\log (4)\right )} \, dx}{8 (21-\log (256))}\\ &=\frac {13 (1+2 x)}{8 \left (5-x-x^2-\log (4)\right ) (21-\log (256))}-\frac {\log (4) \left (137-e (32-6 \log (4))-47 \log (4)+4 \log ^2(4)+2 (1-e) x (11-\log (16))\right )}{8 (5-\log (4)) \left (5-x-x^2-\log (4)\right ) (21-\log (256))}+\frac {7 (10-x-\log (16))}{8 \left (5-x-x^2-\log (4)\right ) (21-\log (256))}+\frac {5 (11+x-\log (16))}{4 (5-\log (4)) \left (5-x-x^2-\log (4)\right ) (21-\log (256))}-\frac {e \left (x \left (105-30 \log (4)+2 \log ^2(4)\right )+\log (4) (16-\log (64))\right )}{4 (5-\log (4)) \left (5-x-x^2-\log (4)\right ) (21-\log (256))}+\frac {1}{8} \int \frac {((3-4 e) x+2 (6-e-\log (4))) \log (2 x)}{\left (5-x-x^2-\log (4)\right )^2} \, dx+\frac {1}{8} \int \frac {\log (2 x)}{-5+x+x^2+\log (4)} \, dx-\frac {7 \operatorname {Subst}\left (\int \frac {1}{21-x^2-4 \log (4)} \, dx,x,1+2 x\right )}{4 (21-\log (256))}+\frac {13 \operatorname {Subst}\left (\int \frac {1}{21-x^2-4 \log (4)} \, dx,x,1+2 x\right )}{2 (21-\log (256))}+\frac {e \int \left (\frac {-5 \log (4) (11-\log (16))+\log ^2(4) (11-\log (16))-5 (21-\log (256))-5 x (21-\log (256))}{(5-\log (4))^2 \left (5-x-x^2-\log (4)\right )}+\frac {5 (-21+\log (256))}{x (-5+\log (4))^2}\right ) \, dx}{4 (21-\log (256))}+\frac {5 \int \left (\frac {-21+\log (256)}{x (-5+\log (4))}+\frac {26+x (21-\log (256))-\log (1024)}{(5-\log (4)) \left (5-x-x^2-\log (4)\right )}\right ) \, dx}{4 (5-\log (4)) (21-\log (256))}-\frac {\log (4) \int \left (\frac {2 (1-e) (76-\log (4) (11-\log (16))-5 \log (16)+x (21-\log (256))-\log (256))}{(5-\log (4))^2 \left (5-x-x^2-\log (4)\right )}+\frac {2 (-1+e) (-21+\log (256))}{x (-5+\log (4))^2}\right ) \, dx}{8 (21-\log (256))}\\ &=\frac {19 \tanh ^{-1}\left (\frac {1+2 x}{\sqrt {21-4 \log (4)}}\right )}{4 (21-\log (256))^{3/2}}+\frac {13 (1+2 x)}{8 \left (5-x-x^2-\log (4)\right ) (21-\log (256))}-\frac {\log (4) \left (137-e (32-6 \log (4))-47 \log (4)+4 \log ^2(4)+2 (1-e) x (11-\log (16))\right )}{8 (5-\log (4)) \left (5-x-x^2-\log (4)\right ) (21-\log (256))}+\frac {7 (10-x-\log (16))}{8 \left (5-x-x^2-\log (4)\right ) (21-\log (256))}+\frac {5 (11+x-\log (16))}{4 (5-\log (4)) \left (5-x-x^2-\log (4)\right ) (21-\log (256))}-\frac {e \left (x \left (105-30 \log (4)+2 \log ^2(4)\right )+\log (4) (16-\log (64))\right )}{4 (5-\log (4)) \left (5-x-x^2-\log (4)\right ) (21-\log (256))}+\frac {5 \log (x)}{4 (5-\log (4))^2}-\frac {5 e \log (x)}{4 (5-\log (4))^2}-\frac {(1-e) \log (4) \log (x)}{4 (5-\log (4))^2}+\frac {1}{8} \int \left (-\frac {2 \log (2 x)}{\left (-1-2 x+\sqrt {21-4 \log (4)}\right ) \sqrt {21-4 \log (4)}}-\frac {2 \log (2 x)}{\left (1+2 x+\sqrt {21-4 \log (4)}\right ) \sqrt {21-4 \log (4)}}\right ) \, dx+\frac {1}{8} \int \left (-\frac {(-3+4 e) x \log (2 x)}{\left (-5+x+x^2+\log (4)\right )^2}-\frac {2 (-6+e+\log (4)) \log (2 x)}{\left (-5+x+x^2+\log (4)\right )^2}\right ) \, dx+\frac {5 \int \frac {26+x (21-\log (256))-\log (1024)}{5-x-x^2-\log (4)} \, dx}{4 (5-\log (4))^2 (21-\log (256))}+\frac {e \int \frac {-5 \log (4) (11-\log (16))+\log ^2(4) (11-\log (16))-5 (21-\log (256))-5 x (21-\log (256))}{5-x-x^2-\log (4)} \, dx}{4 (5-\log (4))^2 (21-\log (256))}-\frac {((1-e) \log (4)) \int \frac {76-\log (4) (11-\log (16))-5 \log (16)+x (21-\log (256))-\log (256)}{5-x-x^2-\log (4)} \, dx}{4 (5-\log (4))^2 (21-\log (256))}\\ &=\frac {19 \tanh ^{-1}\left (\frac {1+2 x}{\sqrt {21-4 \log (4)}}\right )}{4 (21-\log (256))^{3/2}}+\frac {13 (1+2 x)}{8 \left (5-x-x^2-\log (4)\right ) (21-\log (256))}-\frac {\log (4) \left (137-e (32-6 \log (4))-47 \log (4)+4 \log ^2(4)+2 (1-e) x (11-\log (16))\right )}{8 (5-\log (4)) \left (5-x-x^2-\log (4)\right ) (21-\log (256))}+\frac {7 (10-x-\log (16))}{8 \left (5-x-x^2-\log (4)\right ) (21-\log (256))}+\frac {5 (11+x-\log (16))}{4 (5-\log (4)) \left (5-x-x^2-\log (4)\right ) (21-\log (256))}-\frac {e \left (x \left (105-30 \log (4)+2 \log ^2(4)\right )+\log (4) (16-\log (64))\right )}{4 (5-\log (4)) \left (5-x-x^2-\log (4)\right ) (21-\log (256))}+\frac {5 \log (x)}{4 (5-\log (4))^2}-\frac {5 e \log (x)}{4 (5-\log (4))^2}-\frac {(1-e) \log (4) \log (x)}{4 (5-\log (4))^2}+\frac {1}{8} (3-4 e) \int \frac {x \log (2 x)}{\left (-5+x+x^2+\log (4)\right )^2} \, dx-\frac {\int \frac {\log (2 x)}{-1-2 x+\sqrt {21-4 \log (4)}} \, dx}{4 \sqrt {21-4 \log (4)}}-\frac {\int \frac {\log (2 x)}{1+2 x+\sqrt {21-4 \log (4)}} \, dx}{4 \sqrt {21-4 \log (4)}}-\frac {5 \int \frac {-1-2 x}{5-x-x^2-\log (4)} \, dx}{8 (5-\log (4))^2}+\frac {(5 e) \int \frac {-1-2 x}{5-x-x^2-\log (4)} \, dx}{8 (5-\log (4))^2}+\frac {1}{4} (6-e-\log (4)) \int \frac {\log (2 x)}{\left (-5+x+x^2+\log (4)\right )^2} \, dx+\frac {((1-e) \log (4)) \int \frac {-1-2 x}{5-x-x^2-\log (4)} \, dx}{8 (5-\log (4))^2}-\frac {\left (e \left (10 \log (4) (11-\log (16))-2 \log ^2(4) (11-\log (16))+5 (21-\log (256))\right )\right ) \int \frac {1}{5-x-x^2-\log (4)} \, dx}{8 (5-\log (4))^2 (21-\log (256))}-\frac {\left ((1-e) \log (4) \left (131-22 \log (4)-10 \log (16)+\log ^2(16)-\log (256)\right )\right ) \int \frac {1}{5-x-x^2-\log (4)} \, dx}{8 (5-\log (4))^2 (21-\log (256))}+\frac {(5 (31-\log (4096))) \int \frac {1}{5-x-x^2-\log (4)} \, dx}{8 (5-\log (4))^2 (21-\log (256))}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.07, size = 38, normalized size = 1.36 \begin {gather*} \frac {-5+(-1+2 e) x+\log (4)+(-2+2 e-x) \log (2 x)}{8 \left (-5+x+x^2+\log (4)\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.68, size = 41, normalized size = 1.46 \begin {gather*} \frac {2 \, x e - {\left (x - 2 \, e + 2\right )} \log \left (2 \, x\right ) - x + 2 \, \log \relax (2) - 5}{8 \, {\left (x^{2} + x + 2 \, \log \relax (2) - 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.16, size = 50, normalized size = 1.79 \begin {gather*} \frac {2 \, x e - x \log \relax (2) + 2 \, e \log \relax (2) - x \log \relax (x) + 2 \, e \log \relax (x) - x - 2 \, \log \relax (x) - 5}{8 \, {\left (x^{2} + x + 2 \, \log \relax (2) - 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.20, size = 46, normalized size = 1.64
method | result | size |
norman | \(\frac {\left (\frac {{\mathrm e}}{4}-\frac {1}{8}\right ) x +\left (\frac {{\mathrm e}}{4}-\frac {1}{4}\right ) \ln \left (2 x \right )-\frac {x \ln \left (2 x \right )}{8}-\frac {5}{8}+\frac {\ln \relax (2)}{4}}{x^{2}+2 \ln \relax (2)+x -5}\) | \(46\) |
risch | \(\frac {\left (-x +2 \,{\mathrm e}-2\right ) \ln \left (2 x \right )}{8 x^{2}+16 \ln \relax (2)+8 x -40}+\frac {2 x \,{\mathrm e}+2 \ln \relax (2)-x -5}{8 x^{2}+16 \ln \relax (2)+8 x -40}\) | \(57\) |
derivativedivides | \(\frac {\ln \relax (2) {\mathrm e} x}{4 \left (2 \ln \relax (2)-5\right ) \left (\frac {x^{2}}{2}+\ln \relax (2)+\frac {x}{2}-\frac {5}{2}\right )}-\frac {x \ln \relax (2)}{8 \left (2 \ln \relax (2)-5\right ) \left (\frac {x^{2}}{2}+\ln \relax (2)+\frac {x}{2}-\frac {5}{2}\right )}-\frac {5 \,{\mathrm e} x}{8 \left (2 \ln \relax (2)-5\right ) \left (\frac {x^{2}}{2}+\ln \relax (2)+\frac {x}{2}-\frac {5}{2}\right )}+\frac {5 x}{16 \left (2 \ln \relax (2)-5\right ) \left (\frac {x^{2}}{2}+\ln \relax (2)+\frac {x}{2}-\frac {5}{2}\right )}+\frac {\ln \relax (2)^{2}}{4 \left (2 \ln \relax (2)-5\right ) \left (\frac {x^{2}}{2}+\ln \relax (2)+\frac {x}{2}-\frac {5}{2}\right )}-\frac {5 \ln \relax (2)}{4 \left (2 \ln \relax (2)-5\right ) \left (\frac {x^{2}}{2}+\ln \relax (2)+\frac {x}{2}-\frac {5}{2}\right )}+\frac {25}{16 \left (2 \ln \relax (2)-5\right ) \left (\frac {x^{2}}{2}+\ln \relax (2)+\frac {x}{2}-\frac {5}{2}\right )}+\frac {\ln \left (2 x \right ) {\mathrm e}}{8 \ln \relax (2)-20}-\frac {\ln \left (2 x \right )}{2 \left (4 \ln \relax (2)-10\right )}+\frac {\ln \left (2 x \right ) \left (\ln \left (\frac {-1+\sqrt {-8 \ln \relax (2)+21}-2 x}{-1+\sqrt {-8 \ln \relax (2)+21}}\right )-\ln \left (\frac {1+\sqrt {-8 \ln \relax (2)+21}+2 x}{1+\sqrt {-8 \ln \relax (2)+21}}\right )\right )}{8 \sqrt {-8 \ln \relax (2)+21}}-\frac {\ln \left (2 x \right ) \left (8 \ln \relax (2) \ln \left (\frac {-1+\sqrt {-8 \ln \relax (2)+21}-2 x}{-1+\sqrt {-8 \ln \relax (2)+21}}\right ) x^{2}-8 \ln \relax (2) \ln \left (\frac {1+\sqrt {-8 \ln \relax (2)+21}+2 x}{1+\sqrt {-8 \ln \relax (2)+21}}\right ) x^{2}+8 \,{\mathrm e} \sqrt {-8 \ln \relax (2)+21}\, x^{2}+16 \ln \relax (2)^{2} \ln \left (\frac {-1+\sqrt {-8 \ln \relax (2)+21}-2 x}{-1+\sqrt {-8 \ln \relax (2)+21}}\right )-16 \ln \relax (2)^{2} \ln \left (\frac {1+\sqrt {-8 \ln \relax (2)+21}+2 x}{1+\sqrt {-8 \ln \relax (2)+21}}\right )+8 \ln \relax (2) \ln \left (\frac {-1+\sqrt {-8 \ln \relax (2)+21}-2 x}{-1+\sqrt {-8 \ln \relax (2)+21}}\right ) x -8 \ln \relax (2) \ln \left (\frac {1+\sqrt {-8 \ln \relax (2)+21}+2 x}{1+\sqrt {-8 \ln \relax (2)+21}}\right ) x +8 \ln \relax (2) \sqrt {-8 \ln \relax (2)+21}\, x +8 \,{\mathrm e} \sqrt {-8 \ln \relax (2)+21}\, x -20 \ln \left (\frac {-1+\sqrt {-8 \ln \relax (2)+21}-2 x}{-1+\sqrt {-8 \ln \relax (2)+21}}\right ) x^{2}+20 \ln \left (\frac {1+\sqrt {-8 \ln \relax (2)+21}+2 x}{1+\sqrt {-8 \ln \relax (2)+21}}\right ) x^{2}-8 \sqrt {-8 \ln \relax (2)+21}\, x^{2}-80 \ln \relax (2) \ln \left (\frac {-1+\sqrt {-8 \ln \relax (2)+21}-2 x}{-1+\sqrt {-8 \ln \relax (2)+21}}\right )+80 \ln \relax (2) \ln \left (\frac {1+\sqrt {-8 \ln \relax (2)+21}+2 x}{1+\sqrt {-8 \ln \relax (2)+21}}\right )-20 \ln \left (\frac {-1+\sqrt {-8 \ln \relax (2)+21}-2 x}{-1+\sqrt {-8 \ln \relax (2)+21}}\right ) x +20 \ln \left (\frac {1+\sqrt {-8 \ln \relax (2)+21}+2 x}{1+\sqrt {-8 \ln \relax (2)+21}}\right ) x -28 x \sqrt {-8 \ln \relax (2)+21}+100 \ln \left (\frac {-1+\sqrt {-8 \ln \relax (2)+21}-2 x}{-1+\sqrt {-8 \ln \relax (2)+21}}\right )-100 \ln \left (\frac {1+\sqrt {-8 \ln \relax (2)+21}+2 x}{1+\sqrt {-8 \ln \relax (2)+21}}\right )\right )}{8 \left (4 x^{2}+8 \ln \relax (2)+4 x -20\right ) \left (2 \ln \relax (2)-5\right ) \sqrt {-8 \ln \relax (2)+21}}\) | \(835\) |
default | \(\frac {\ln \relax (2) {\mathrm e} x}{4 \left (2 \ln \relax (2)-5\right ) \left (\frac {x^{2}}{2}+\ln \relax (2)+\frac {x}{2}-\frac {5}{2}\right )}-\frac {x \ln \relax (2)}{8 \left (2 \ln \relax (2)-5\right ) \left (\frac {x^{2}}{2}+\ln \relax (2)+\frac {x}{2}-\frac {5}{2}\right )}-\frac {5 \,{\mathrm e} x}{8 \left (2 \ln \relax (2)-5\right ) \left (\frac {x^{2}}{2}+\ln \relax (2)+\frac {x}{2}-\frac {5}{2}\right )}+\frac {5 x}{16 \left (2 \ln \relax (2)-5\right ) \left (\frac {x^{2}}{2}+\ln \relax (2)+\frac {x}{2}-\frac {5}{2}\right )}+\frac {\ln \relax (2)^{2}}{4 \left (2 \ln \relax (2)-5\right ) \left (\frac {x^{2}}{2}+\ln \relax (2)+\frac {x}{2}-\frac {5}{2}\right )}-\frac {5 \ln \relax (2)}{4 \left (2 \ln \relax (2)-5\right ) \left (\frac {x^{2}}{2}+\ln \relax (2)+\frac {x}{2}-\frac {5}{2}\right )}+\frac {25}{16 \left (2 \ln \relax (2)-5\right ) \left (\frac {x^{2}}{2}+\ln \relax (2)+\frac {x}{2}-\frac {5}{2}\right )}+\frac {\ln \left (2 x \right ) {\mathrm e}}{8 \ln \relax (2)-20}-\frac {\ln \left (2 x \right )}{2 \left (4 \ln \relax (2)-10\right )}+\frac {\ln \left (2 x \right ) \left (\ln \left (\frac {-1+\sqrt {-8 \ln \relax (2)+21}-2 x}{-1+\sqrt {-8 \ln \relax (2)+21}}\right )-\ln \left (\frac {1+\sqrt {-8 \ln \relax (2)+21}+2 x}{1+\sqrt {-8 \ln \relax (2)+21}}\right )\right )}{8 \sqrt {-8 \ln \relax (2)+21}}-\frac {\ln \left (2 x \right ) \left (8 \ln \relax (2) \ln \left (\frac {-1+\sqrt {-8 \ln \relax (2)+21}-2 x}{-1+\sqrt {-8 \ln \relax (2)+21}}\right ) x^{2}-8 \ln \relax (2) \ln \left (\frac {1+\sqrt {-8 \ln \relax (2)+21}+2 x}{1+\sqrt {-8 \ln \relax (2)+21}}\right ) x^{2}+8 \,{\mathrm e} \sqrt {-8 \ln \relax (2)+21}\, x^{2}+16 \ln \relax (2)^{2} \ln \left (\frac {-1+\sqrt {-8 \ln \relax (2)+21}-2 x}{-1+\sqrt {-8 \ln \relax (2)+21}}\right )-16 \ln \relax (2)^{2} \ln \left (\frac {1+\sqrt {-8 \ln \relax (2)+21}+2 x}{1+\sqrt {-8 \ln \relax (2)+21}}\right )+8 \ln \relax (2) \ln \left (\frac {-1+\sqrt {-8 \ln \relax (2)+21}-2 x}{-1+\sqrt {-8 \ln \relax (2)+21}}\right ) x -8 \ln \relax (2) \ln \left (\frac {1+\sqrt {-8 \ln \relax (2)+21}+2 x}{1+\sqrt {-8 \ln \relax (2)+21}}\right ) x +8 \ln \relax (2) \sqrt {-8 \ln \relax (2)+21}\, x +8 \,{\mathrm e} \sqrt {-8 \ln \relax (2)+21}\, x -20 \ln \left (\frac {-1+\sqrt {-8 \ln \relax (2)+21}-2 x}{-1+\sqrt {-8 \ln \relax (2)+21}}\right ) x^{2}+20 \ln \left (\frac {1+\sqrt {-8 \ln \relax (2)+21}+2 x}{1+\sqrt {-8 \ln \relax (2)+21}}\right ) x^{2}-8 \sqrt {-8 \ln \relax (2)+21}\, x^{2}-80 \ln \relax (2) \ln \left (\frac {-1+\sqrt {-8 \ln \relax (2)+21}-2 x}{-1+\sqrt {-8 \ln \relax (2)+21}}\right )+80 \ln \relax (2) \ln \left (\frac {1+\sqrt {-8 \ln \relax (2)+21}+2 x}{1+\sqrt {-8 \ln \relax (2)+21}}\right )-20 \ln \left (\frac {-1+\sqrt {-8 \ln \relax (2)+21}-2 x}{-1+\sqrt {-8 \ln \relax (2)+21}}\right ) x +20 \ln \left (\frac {1+\sqrt {-8 \ln \relax (2)+21}+2 x}{1+\sqrt {-8 \ln \relax (2)+21}}\right ) x -28 x \sqrt {-8 \ln \relax (2)+21}+100 \ln \left (\frac {-1+\sqrt {-8 \ln \relax (2)+21}-2 x}{-1+\sqrt {-8 \ln \relax (2)+21}}\right )-100 \ln \left (\frac {1+\sqrt {-8 \ln \relax (2)+21}+2 x}{1+\sqrt {-8 \ln \relax (2)+21}}\right )\right )}{8 \left (4 x^{2}+8 \ln \relax (2)+4 x -20\right ) \left (2 \ln \relax (2)-5\right ) \sqrt {-8 \ln \relax (2)+21}}\) | \(835\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.54, size = 1589, normalized size = 56.75 result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {13\,x-2\,\ln \relax (2)\,\left (3\,x+2\,x^2-\mathrm {e}\,\left (2\,x+2\right )+2\right )+\ln \left (2\,x\right )\,\left (7\,x-\mathrm {e}\,\left (4\,x^2+2\,x\right )-2\,x\,\ln \relax (2)+4\,x^2+x^3\right )-\mathrm {e}\,\left (2\,x^3-2\,x^2+8\,x+10\right )+7\,x^2+10}{200\,x+2\,\ln \relax (2)\,\left (16\,x^3+16\,x^2-80\,x\right )+32\,x\,{\ln \relax (2)}^2-80\,x^2-72\,x^3+16\,x^4+8\,x^5} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 2.35, size = 58, normalized size = 2.07 \begin {gather*} \frac {\left (- x - 2 + 2 e\right ) \log {\left (2 x \right )}}{8 x^{2} + 8 x - 40 + 16 \log {\relax (2 )}} + \frac {x \left (-1 + 2 e\right ) - 5 + 2 \log {\relax (2 )}}{8 x^{2} + 8 x - 40 + 16 \log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________