3.43.94 \(\int \frac {e^6 (8-6 x)+e^3 (-8 x^2+8 x^3-2 x^4)+2 x^{19} \log (2 x)+(-16 x^4+24 x^5-12 x^6+2 x^7+e^3 (16 x^2-20 x^3+6 x^4)) \log (2 x)+x^{10} (-2 e^3 x^2+(14 e^3 x^2-12 x^4+6 x^5) \log (2 x))+x^5 (-14 e^6+e^3 (8 x^2-4 x^3)+(24 x^4-24 x^5+6 x^6+e^3 (-36 x^2+20 x^3)) \log (2 x))}{-8 x^5+12 x^6-6 x^7+x^8+x^{20}+x^{10} (-6 x^5+3 x^6)+x^5 (12 x^5-12 x^6+3 x^7)} \, dx\)

Optimal. Leaf size=24 \[ \left (\frac {e^3}{x^2 \left (-2+x+x^5\right )}-\log (2 x)\right )^2 \]

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Rubi [F]  time = 2.19, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {e^6 (8-6 x)+e^3 \left (-8 x^2+8 x^3-2 x^4\right )+2 x^{19} \log (2 x)+\left (-16 x^4+24 x^5-12 x^6+2 x^7+e^3 \left (16 x^2-20 x^3+6 x^4\right )\right ) \log (2 x)+x^{10} \left (-2 e^3 x^2+\left (14 e^3 x^2-12 x^4+6 x^5\right ) \log (2 x)\right )+x^5 \left (-14 e^6+e^3 \left (8 x^2-4 x^3\right )+\left (24 x^4-24 x^5+6 x^6+e^3 \left (-36 x^2+20 x^3\right )\right ) \log (2 x)\right )}{-8 x^5+12 x^6-6 x^7+x^8+x^{20}+x^{10} \left (-6 x^5+3 x^6\right )+x^5 \left (12 x^5-12 x^6+3 x^7\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^6*(8 - 6*x) + E^3*(-8*x^2 + 8*x^3 - 2*x^4) + 2*x^19*Log[2*x] + (-16*x^4 + 24*x^5 - 12*x^6 + 2*x^7 + E^3
*(16*x^2 - 20*x^3 + 6*x^4))*Log[2*x] + x^10*(-2*E^3*x^2 + (14*E^3*x^2 - 12*x^4 + 6*x^5)*Log[2*x]) + x^5*(-14*E
^6 + E^3*(8*x^2 - 4*x^3) + (24*x^4 - 24*x^5 + 6*x^6 + E^3*(-36*x^2 + 20*x^3))*Log[2*x]))/(-8*x^5 + 12*x^6 - 6*
x^7 + x^8 + x^20 + x^10*(-6*x^5 + 3*x^6) + x^5*(12*x^5 - 12*x^6 + 3*x^7)),x]

[Out]

E^6/(36*(1 - x)^2) + (11*E^6)/(54*(1 - x)) + E^6/(4*x^4) + E^6/(4*x^3) + E^3/(2*x^2) - (E^3*(8 - 3*E^3))/(16*x
^2) + E^3/(2*x) - (E^3*(4 - E^3))/(8*x) - (119*E^6)/(576*(2 + x + x^2 + x^3 + x^4)^2) - (83*E^6)/(432*(2 + x +
x^2 + x^3 + x^4)) + (E^3*Log[x])/4 + (E^3*Log[2*x])/x^2 + (E^3*Log[2*x])/(2*x) + (E^3*x*Log[2*x])/(3*(1 - x))
+ Log[2*x]^2 + (E^3*Log[2 + x + x^2 + x^3 + x^4])/48 - (305*E^6*Defer[Int][(2 + x + x^2 + x^3 + x^4)^(-3), x]
)/96 - (341*E^6*Defer[Int][x/(2 + x + x^2 + x^3 + x^4)^3, x])/144 - (209*E^6*Defer[Int][x^2/(2 + x + x^2 + x^3
+ x^4)^3, x])/288 + (121*E^6*Defer[Int][(2 + x + x^2 + x^3 + x^4)^(-2), x])/144 + (17*E^6*Defer[Int][x/(2 + x
+ x^2 + x^3 + x^4)^2, x])/27 + (181*E^6*Defer[Int][x^2/(2 + x + x^2 + x^3 + x^4)^2, x])/432 - (E^3*(7 - 4*E^3
)*Defer[Int][(2 + x + x^2 + x^3 + x^4)^(-1), x])/16 - (E^3*(57 + 4*E^3)*Defer[Int][x/(2 + x + x^2 + x^3 + x^4)
, x])/72 - (E^3*(63 + 34*E^3)*Defer[Int][x^2/(2 + x + x^2 + x^3 + x^4), x])/432 - (11*E^3*Defer[Int][Log[2*x]/
(2 + x + x^2 + x^3 + x^4)^2, x])/6 - (13*E^3*Defer[Int][(x*Log[2*x])/(2 + x + x^2 + x^3 + x^4)^2, x])/2 - (19*
E^3*Defer[Int][(x^2*Log[2*x])/(2 + x + x^2 + x^3 + x^4)^2, x])/6 - (5*E^3*Defer[Int][(x^3*Log[2*x])/(2 + x + x
^2 + x^3 + x^4)^2, x])/6 + (E^3*Defer[Int][Log[2*x]/(2 + x + x^2 + x^3 + x^4), x])/2 + (3*E^3*Defer[Int][(x*Lo
g[2*x])/(2 + x + x^2 + x^3 + x^4), x])/2 + (E^3*Defer[Int][(x^2*Log[2*x])/(2 + x + x^2 + x^3 + x^4), x])/6

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (x^2 \left (-2+x+x^5\right )^2+e^3 \left (-4+3 x+7 x^5\right )\right ) \left (e^3-x^2 \left (-2+x+x^5\right ) \log (2 x)\right )}{x^5 \left (2-x-x^5\right )^3} \, dx\\ &=2 \int \frac {\left (x^2 \left (-2+x+x^5\right )^2+e^3 \left (-4+3 x+7 x^5\right )\right ) \left (e^3-x^2 \left (-2+x+x^5\right ) \log (2 x)\right )}{x^5 \left (2-x-x^5\right )^3} \, dx\\ &=2 \int \left (-\frac {e^3 \left (-4 e^3+3 e^3 x+4 x^2-4 x^3+x^4+7 e^3 x^5-4 x^7+2 x^8+x^{12}\right )}{x^5 \left (-2+x+x^5\right )^3}+\frac {\left (-4 e^3+3 e^3 x+4 x^2-4 x^3+x^4+7 e^3 x^5-4 x^7+2 x^8+x^{12}\right ) \log (2 x)}{x^3 \left (-2+x+x^5\right )^2}\right ) \, dx\\ &=2 \int \frac {\left (-4 e^3+3 e^3 x+4 x^2-4 x^3+x^4+7 e^3 x^5-4 x^7+2 x^8+x^{12}\right ) \log (2 x)}{x^3 \left (-2+x+x^5\right )^2} \, dx-\left (2 e^3\right ) \int \frac {-4 e^3+3 e^3 x+4 x^2-4 x^3+x^4+7 e^3 x^5-4 x^7+2 x^8+x^{12}}{x^5 \left (-2+x+x^5\right )^3} \, dx\\ &=2 \int \left (\frac {e^3 \log (2 x)}{6 (-1+x)^2}-\frac {e^3 \log (2 x)}{x^3}-\frac {e^3 \log (2 x)}{4 x^2}+\frac {\log (2 x)}{x}-\frac {e^3 \left (11+39 x+19 x^2+5 x^3\right ) \log (2 x)}{12 \left (2+x+x^2+x^3+x^4\right )^2}+\frac {e^3 \left (3+9 x+x^2\right ) \log (2 x)}{12 \left (2+x+x^2+x^3+x^4\right )}\right ) \, dx-\left (2 e^3\right ) \int \left (\frac {e^3}{36 (-1+x)^3}-\frac {11 e^3}{108 (-1+x)^2}+\frac {1}{6 (-1+x)}+\frac {e^3}{2 x^5}+\frac {3 e^3}{8 x^4}+\frac {-8+3 e^3}{16 x^3}+\frac {-4+e^3}{16 x^2}-\frac {1}{8 x}-\frac {e^3 \left (-199-111 x+37 x^2+119 x^3\right )}{144 \left (2+x+x^2+x^3+x^4\right )^3}-\frac {e^3 \left (223+219 x+215 x^2+166 x^3\right )}{432 \left (2+x+x^2+x^3+x^4\right )^2}+\frac {18 \left (5-3 e^3\right )+6 \left (27+2 e^3\right ) x+\left (18+17 e^3\right ) x^2-18 x^3}{432 \left (2+x+x^2+x^3+x^4\right )}\right ) \, dx\\ &=\frac {e^6}{36 (1-x)^2}+\frac {11 e^6}{54 (1-x)}+\frac {e^6}{4 x^4}+\frac {e^6}{4 x^3}-\frac {e^3 \left (8-3 e^3\right )}{16 x^2}-\frac {e^3 \left (4-e^3\right )}{8 x}-\frac {1}{3} e^3 \log (1-x)+\frac {1}{4} e^3 \log (x)+2 \int \frac {\log (2 x)}{x} \, dx-\frac {1}{216} e^3 \int \frac {18 \left (5-3 e^3\right )+6 \left (27+2 e^3\right ) x+\left (18+17 e^3\right ) x^2-18 x^3}{2+x+x^2+x^3+x^4} \, dx-\frac {1}{6} e^3 \int \frac {\left (11+39 x+19 x^2+5 x^3\right ) \log (2 x)}{\left (2+x+x^2+x^3+x^4\right )^2} \, dx+\frac {1}{6} e^3 \int \frac {\left (3+9 x+x^2\right ) \log (2 x)}{2+x+x^2+x^3+x^4} \, dx+\frac {1}{3} e^3 \int \frac {\log (2 x)}{(-1+x)^2} \, dx-\frac {1}{2} e^3 \int \frac {\log (2 x)}{x^2} \, dx-\left (2 e^3\right ) \int \frac {\log (2 x)}{x^3} \, dx+\frac {1}{216} e^6 \int \frac {223+219 x+215 x^2+166 x^3}{\left (2+x+x^2+x^3+x^4\right )^2} \, dx+\frac {1}{72} e^6 \int \frac {-199-111 x+37 x^2+119 x^3}{\left (2+x+x^2+x^3+x^4\right )^3} \, dx\\ &=\frac {e^6}{36 (1-x)^2}+\frac {11 e^6}{54 (1-x)}+\frac {e^6}{4 x^4}+\frac {e^6}{4 x^3}+\frac {e^3}{2 x^2}-\frac {e^3 \left (8-3 e^3\right )}{16 x^2}+\frac {e^3}{2 x}-\frac {e^3 \left (4-e^3\right )}{8 x}-\frac {119 e^6}{576 \left (2+x+x^2+x^3+x^4\right )^2}-\frac {83 e^6}{432 \left (2+x+x^2+x^3+x^4\right )}-\frac {1}{3} e^3 \log (1-x)+\frac {1}{4} e^3 \log (x)+\frac {e^3 \log (2 x)}{x^2}+\frac {e^3 \log (2 x)}{2 x}+\frac {e^3 x \log (2 x)}{3 (1-x)}+\log ^2(2 x)+\frac {1}{48} e^3 \log \left (2+x+x^2+x^3+x^4\right )-\frac {1}{864} e^3 \int \frac {54 \left (7-4 e^3\right )+12 \left (57+4 e^3\right ) x+2 \left (63+34 e^3\right ) x^2}{2+x+x^2+x^3+x^4} \, dx-\frac {1}{6} e^3 \int \left (\frac {11 \log (2 x)}{\left (2+x+x^2+x^3+x^4\right )^2}+\frac {39 x \log (2 x)}{\left (2+x+x^2+x^3+x^4\right )^2}+\frac {19 x^2 \log (2 x)}{\left (2+x+x^2+x^3+x^4\right )^2}+\frac {5 x^3 \log (2 x)}{\left (2+x+x^2+x^3+x^4\right )^2}\right ) \, dx+\frac {1}{6} e^3 \int \left (\frac {3 \log (2 x)}{2+x+x^2+x^3+x^4}+\frac {9 x \log (2 x)}{2+x+x^2+x^3+x^4}+\frac {x^2 \log (2 x)}{2+x+x^2+x^3+x^4}\right ) \, dx+\frac {1}{3} e^3 \int \frac {1}{-1+x} \, dx+\frac {1}{864} e^6 \int \frac {726+544 x+362 x^2}{\left (2+x+x^2+x^3+x^4\right )^2} \, dx+\frac {1}{288} e^6 \int \frac {-915-682 x-209 x^2}{\left (2+x+x^2+x^3+x^4\right )^3} \, dx\\ &=\frac {e^6}{36 (1-x)^2}+\frac {11 e^6}{54 (1-x)}+\frac {e^6}{4 x^4}+\frac {e^6}{4 x^3}+\frac {e^3}{2 x^2}-\frac {e^3 \left (8-3 e^3\right )}{16 x^2}+\frac {e^3}{2 x}-\frac {e^3 \left (4-e^3\right )}{8 x}-\frac {119 e^6}{576 \left (2+x+x^2+x^3+x^4\right )^2}-\frac {83 e^6}{432 \left (2+x+x^2+x^3+x^4\right )}+\frac {1}{4} e^3 \log (x)+\frac {e^3 \log (2 x)}{x^2}+\frac {e^3 \log (2 x)}{2 x}+\frac {e^3 x \log (2 x)}{3 (1-x)}+\log ^2(2 x)+\frac {1}{48} e^3 \log \left (2+x+x^2+x^3+x^4\right )-\frac {1}{864} e^3 \int \left (-\frac {54 \left (-7+4 e^3\right )}{2+x+x^2+x^3+x^4}+\frac {12 \left (57+4 e^3\right ) x}{2+x+x^2+x^3+x^4}+\frac {2 \left (63+34 e^3\right ) x^2}{2+x+x^2+x^3+x^4}\right ) \, dx+\frac {1}{6} e^3 \int \frac {x^2 \log (2 x)}{2+x+x^2+x^3+x^4} \, dx+\frac {1}{2} e^3 \int \frac {\log (2 x)}{2+x+x^2+x^3+x^4} \, dx-\frac {1}{6} \left (5 e^3\right ) \int \frac {x^3 \log (2 x)}{\left (2+x+x^2+x^3+x^4\right )^2} \, dx+\frac {1}{2} \left (3 e^3\right ) \int \frac {x \log (2 x)}{2+x+x^2+x^3+x^4} \, dx-\frac {1}{6} \left (11 e^3\right ) \int \frac {\log (2 x)}{\left (2+x+x^2+x^3+x^4\right )^2} \, dx-\frac {1}{6} \left (19 e^3\right ) \int \frac {x^2 \log (2 x)}{\left (2+x+x^2+x^3+x^4\right )^2} \, dx-\frac {1}{2} \left (13 e^3\right ) \int \frac {x \log (2 x)}{\left (2+x+x^2+x^3+x^4\right )^2} \, dx+\frac {1}{864} e^6 \int \left (\frac {726}{\left (2+x+x^2+x^3+x^4\right )^2}+\frac {544 x}{\left (2+x+x^2+x^3+x^4\right )^2}+\frac {362 x^2}{\left (2+x+x^2+x^3+x^4\right )^2}\right ) \, dx+\frac {1}{288} e^6 \int \left (-\frac {915}{\left (2+x+x^2+x^3+x^4\right )^3}-\frac {682 x}{\left (2+x+x^2+x^3+x^4\right )^3}-\frac {209 x^2}{\left (2+x+x^2+x^3+x^4\right )^3}\right ) \, dx\\ &=\frac {e^6}{36 (1-x)^2}+\frac {11 e^6}{54 (1-x)}+\frac {e^6}{4 x^4}+\frac {e^6}{4 x^3}+\frac {e^3}{2 x^2}-\frac {e^3 \left (8-3 e^3\right )}{16 x^2}+\frac {e^3}{2 x}-\frac {e^3 \left (4-e^3\right )}{8 x}-\frac {119 e^6}{576 \left (2+x+x^2+x^3+x^4\right )^2}-\frac {83 e^6}{432 \left (2+x+x^2+x^3+x^4\right )}+\frac {1}{4} e^3 \log (x)+\frac {e^3 \log (2 x)}{x^2}+\frac {e^3 \log (2 x)}{2 x}+\frac {e^3 x \log (2 x)}{3 (1-x)}+\log ^2(2 x)+\frac {1}{48} e^3 \log \left (2+x+x^2+x^3+x^4\right )+\frac {1}{6} e^3 \int \frac {x^2 \log (2 x)}{2+x+x^2+x^3+x^4} \, dx+\frac {1}{2} e^3 \int \frac {\log (2 x)}{2+x+x^2+x^3+x^4} \, dx-\frac {1}{6} \left (5 e^3\right ) \int \frac {x^3 \log (2 x)}{\left (2+x+x^2+x^3+x^4\right )^2} \, dx+\frac {1}{2} \left (3 e^3\right ) \int \frac {x \log (2 x)}{2+x+x^2+x^3+x^4} \, dx-\frac {1}{6} \left (11 e^3\right ) \int \frac {\log (2 x)}{\left (2+x+x^2+x^3+x^4\right )^2} \, dx-\frac {1}{6} \left (19 e^3\right ) \int \frac {x^2 \log (2 x)}{\left (2+x+x^2+x^3+x^4\right )^2} \, dx-\frac {1}{2} \left (13 e^3\right ) \int \frac {x \log (2 x)}{\left (2+x+x^2+x^3+x^4\right )^2} \, dx+\frac {1}{432} \left (181 e^6\right ) \int \frac {x^2}{\left (2+x+x^2+x^3+x^4\right )^2} \, dx+\frac {1}{27} \left (17 e^6\right ) \int \frac {x}{\left (2+x+x^2+x^3+x^4\right )^2} \, dx-\frac {1}{288} \left (209 e^6\right ) \int \frac {x^2}{\left (2+x+x^2+x^3+x^4\right )^3} \, dx+\frac {1}{144} \left (121 e^6\right ) \int \frac {1}{\left (2+x+x^2+x^3+x^4\right )^2} \, dx-\frac {1}{144} \left (341 e^6\right ) \int \frac {x}{\left (2+x+x^2+x^3+x^4\right )^3} \, dx-\frac {1}{96} \left (305 e^6\right ) \int \frac {1}{\left (2+x+x^2+x^3+x^4\right )^3} \, dx-\frac {1}{16} \left (e^3 \left (7-4 e^3\right )\right ) \int \frac {1}{2+x+x^2+x^3+x^4} \, dx-\frac {1}{72} \left (e^3 \left (57+4 e^3\right )\right ) \int \frac {x}{2+x+x^2+x^3+x^4} \, dx-\frac {1}{432} \left (e^3 \left (63+34 e^3\right )\right ) \int \frac {x^2}{2+x+x^2+x^3+x^4} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.91, size = 33, normalized size = 1.38 \begin {gather*} \frac {\left (e^3-x^2 \left (-2+x+x^5\right ) \log (2 x)\right )^2}{x^4 \left (-2+x+x^5\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^6*(8 - 6*x) + E^3*(-8*x^2 + 8*x^3 - 2*x^4) + 2*x^19*Log[2*x] + (-16*x^4 + 24*x^5 - 12*x^6 + 2*x^7
+ E^3*(16*x^2 - 20*x^3 + 6*x^4))*Log[2*x] + x^10*(-2*E^3*x^2 + (14*E^3*x^2 - 12*x^4 + 6*x^5)*Log[2*x]) + x^5*
(-14*E^6 + E^3*(8*x^2 - 4*x^3) + (24*x^4 - 24*x^5 + 6*x^6 + E^3*(-36*x^2 + 20*x^3))*Log[2*x]))/(-8*x^5 + 12*x^
6 - 6*x^7 + x^8 + x^20 + x^10*(-6*x^5 + 3*x^6) + x^5*(12*x^5 - 12*x^6 + 3*x^7)),x]

[Out]

(E^3 - x^2*(-2 + x + x^5)*Log[2*x])^2/(x^4*(-2 + x + x^5)^2)

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fricas [B]  time = 0.65, size = 91, normalized size = 3.79 \begin {gather*} -\frac {2 \, {\left (x^{7} + x^{3} - 2 \, x^{2}\right )} e^{3} \log \left (2 \, x\right ) - {\left (x^{14} + 2 \, x^{10} - 4 \, x^{9} + x^{6} - 4 \, x^{5} + 4 \, x^{4}\right )} \log \left (2 \, x\right )^{2} - e^{6}}{x^{14} + 2 \, x^{10} - 4 \, x^{9} + x^{6} - 4 \, x^{5} + 4 \, x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x^19*log(2*x)+((14*x^2*exp(3)+6*x^5-12*x^4)*log(2*x)-2*x^2*exp(3))*x^10+(((20*x^3-36*x^2)*exp(3)+
6*x^6-24*x^5+24*x^4)*log(2*x)-14*exp(3)^2+(-4*x^3+8*x^2)*exp(3))*x^5+((6*x^4-20*x^3+16*x^2)*exp(3)+2*x^7-12*x^
6+24*x^5-16*x^4)*log(2*x)+(-6*x+8)*exp(3)^2+(-2*x^4+8*x^3-8*x^2)*exp(3))/(x^20+(3*x^6-6*x^5)*x^10+(3*x^7-12*x^
6+12*x^5)*x^5+x^8-6*x^7+12*x^6-8*x^5),x, algorithm="fricas")

[Out]

-(2*(x^7 + x^3 - 2*x^2)*e^3*log(2*x) - (x^14 + 2*x^10 - 4*x^9 + x^6 - 4*x^5 + 4*x^4)*log(2*x)^2 - e^6)/(x^14 +
2*x^10 - 4*x^9 + x^6 - 4*x^5 + 4*x^4)

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giac [B]  time = 0.18, size = 130, normalized size = 5.42 \begin {gather*} \frac {x^{14} \log \left (2 \, x\right )^{2} + 2 \, x^{10} \log \left (2 \, x\right )^{2} - 4 \, x^{9} \log \left (2 \, x\right )^{2} - 2 \, x^{7} e^{3} \log \left (2 \, x\right ) + x^{6} \log \left (2 \, x\right )^{2} - 4 \, x^{5} \log \left (2 \, x\right )^{2} + 4 \, x^{4} \log \left (2 \, x\right )^{2} - 2 \, x^{3} e^{3} \log \left (2 \, x\right ) + 4 \, x^{2} e^{3} \log \left (2 \, x\right ) + e^{6}}{x^{14} + 2 \, x^{10} - 4 \, x^{9} + x^{6} - 4 \, x^{5} + 4 \, x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x^19*log(2*x)+((14*x^2*exp(3)+6*x^5-12*x^4)*log(2*x)-2*x^2*exp(3))*x^10+(((20*x^3-36*x^2)*exp(3)+
6*x^6-24*x^5+24*x^4)*log(2*x)-14*exp(3)^2+(-4*x^3+8*x^2)*exp(3))*x^5+((6*x^4-20*x^3+16*x^2)*exp(3)+2*x^7-12*x^
6+24*x^5-16*x^4)*log(2*x)+(-6*x+8)*exp(3)^2+(-2*x^4+8*x^3-8*x^2)*exp(3))/(x^20+(3*x^6-6*x^5)*x^10+(3*x^7-12*x^
6+12*x^5)*x^5+x^8-6*x^7+12*x^6-8*x^5),x, algorithm="giac")

[Out]

(x^14*log(2*x)^2 + 2*x^10*log(2*x)^2 - 4*x^9*log(2*x)^2 - 2*x^7*e^3*log(2*x) + x^6*log(2*x)^2 - 4*x^5*log(2*x)
^2 + 4*x^4*log(2*x)^2 - 2*x^3*e^3*log(2*x) + 4*x^2*e^3*log(2*x) + e^6)/(x^14 + 2*x^10 - 4*x^9 + x^6 - 4*x^5 +
4*x^4)

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maple [A]  time = 0.15, size = 41, normalized size = 1.71

method	result	size
risch	\(\ln \left (2 x \right )^{2}-\frac {2 \,{\mathrm e}^{3} \ln \left (2 x \right )}{x^{2} \left (x^{5}+x -2\right )}+\frac {{\mathrm e}^{6}}{\left (x^{5}+x -2\right )^{2} x^{4}}\)	\(41\)
derivativedivides	\(\frac {4 \,{\mathrm e}^{3} \ln \left (2 x \right ) x^{4}}{3 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )}-\frac {4 \,{\mathrm e}^{3} \ln \left (2 x \right ) x^{3}}{3 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )}-\frac {12 \,{\mathrm e}^{3} \ln \left (2 x \right ) x^{2}}{16 x^{4}+16 x^{3}+16 x^{2}+16 x +32}-\frac {20 \,{\mathrm e}^{3} \ln \left (2 x \right ) x}{3 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )}-\frac {2 \,{\mathrm e}^{3} \ln \left (2 x \right ) x}{3 \left (2 x -2\right )}+\frac {544 x^{7} {\mathrm e}^{6}}{27 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )^{2}}+\frac {112 \,{\mathrm e}^{6} x^{6}}{3 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )^{2}}+\frac {256 x^{5} {\mathrm e}^{6}}{9 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )^{2}}-\frac {368 \,{\mathrm e}^{6} x^{4}}{27 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )^{2}}+\frac {224 \,{\mathrm e}^{6} x^{3}}{27 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )^{2}}-\frac {1072 x^{2} {\mathrm e}^{6}}{27 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )^{2}}-\frac {3200 \,{\mathrm e}^{6} x}{27 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )^{2}}+\ln \left (2 x \right )^{2}-\frac {4240 \,{\mathrm e}^{6}}{27 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )^{2}}+\frac {{\mathrm e}^{6}}{9 \left (2 x -2\right )^{2}}-\frac {11 \,{\mathrm e}^{6}}{27 \left (2 x -2\right )}+\frac {\ln \left (2 x \right ) {\mathrm e}^{3}}{4}+\frac {{\mathrm e}^{6}}{8 x}+\frac {3 \,{\mathrm e}^{6}}{16 x^{2}}+\frac {{\mathrm e}^{6}}{4 x^{4}}+\frac {{\mathrm e}^{6}}{4 x^{3}}+\frac {{\mathrm e}^{3} \ln \left (2 x \right )}{x^{2}}+\frac {{\mathrm e}^{3} \ln \left (2 x \right )}{2 x}\)	\(488\)
default	\(\frac {4 \,{\mathrm e}^{3} \ln \left (2 x \right ) x^{4}}{3 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )}-\frac {4 \,{\mathrm e}^{3} \ln \left (2 x \right ) x^{3}}{3 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )}-\frac {12 \,{\mathrm e}^{3} \ln \left (2 x \right ) x^{2}}{16 x^{4}+16 x^{3}+16 x^{2}+16 x +32}-\frac {20 \,{\mathrm e}^{3} \ln \left (2 x \right ) x}{3 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )}-\frac {2 \,{\mathrm e}^{3} \ln \left (2 x \right ) x}{3 \left (2 x -2\right )}+\frac {544 x^{7} {\mathrm e}^{6}}{27 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )^{2}}+\frac {112 \,{\mathrm e}^{6} x^{6}}{3 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )^{2}}+\frac {256 x^{5} {\mathrm e}^{6}}{9 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )^{2}}-\frac {368 \,{\mathrm e}^{6} x^{4}}{27 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )^{2}}+\frac {224 \,{\mathrm e}^{6} x^{3}}{27 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )^{2}}-\frac {1072 x^{2} {\mathrm e}^{6}}{27 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )^{2}}-\frac {3200 \,{\mathrm e}^{6} x}{27 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )^{2}}+\ln \left (2 x \right )^{2}-\frac {4240 \,{\mathrm e}^{6}}{27 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )^{2}}+\frac {{\mathrm e}^{6}}{9 \left (2 x -2\right )^{2}}-\frac {11 \,{\mathrm e}^{6}}{27 \left (2 x -2\right )}+\frac {\ln \left (2 x \right ) {\mathrm e}^{3}}{4}+\frac {{\mathrm e}^{6}}{8 x}+\frac {3 \,{\mathrm e}^{6}}{16 x^{2}}+\frac {{\mathrm e}^{6}}{4 x^{4}}+\frac {{\mathrm e}^{6}}{4 x^{3}}+\frac {{\mathrm e}^{3} \ln \left (2 x \right )}{x^{2}}+\frac {{\mathrm e}^{3} \ln \left (2 x \right )}{2 x}\)	\(488\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x^19*ln(2*x)+((14*x^2*exp(3)+6*x^5-12*x^4)*ln(2*x)-2*x^2*exp(3))*x^10+(((20*x^3-36*x^2)*exp(3)+6*x^6-24
*x^5+24*x^4)*ln(2*x)-14*exp(3)^2+(-4*x^3+8*x^2)*exp(3))*x^5+((6*x^4-20*x^3+16*x^2)*exp(3)+2*x^7-12*x^6+24*x^5-
16*x^4)*ln(2*x)+(-6*x+8)*exp(3)^2+(-2*x^4+8*x^3-8*x^2)*exp(3))/(x^20+(3*x^6-6*x^5)*x^10+(3*x^7-12*x^6+12*x^5)*
x^5+x^8-6*x^7+12*x^6-8*x^5),x,method=_RETURNVERBOSE)

[Out]

ln(2*x)^2-2*exp(3)/x^2/(x^5+x-2)*ln(2*x)+exp(6)/(x^5+x-2)^2/x^4

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maxima [B]  time = 0.48, size = 162, normalized size = 6.75 \begin {gather*} -\frac {2 \, x^{7} e^{3} \log \relax (2) + 2 \, x^{3} e^{3} \log \relax (2) - 4 \, x^{2} e^{3} \log \relax (2) - {\left (x^{14} + 2 \, x^{10} - 4 \, x^{9} + x^{6} - 4 \, x^{5} + 4 \, x^{4}\right )} \log \relax (x)^{2} - 2 \, {\left (x^{14} \log \relax (2) + 2 \, x^{10} \log \relax (2) - 4 \, x^{9} \log \relax (2) - x^{7} e^{3} + x^{6} \log \relax (2) - 4 \, x^{5} \log \relax (2) + 4 \, x^{4} \log \relax (2) - x^{3} e^{3} + 2 \, x^{2} e^{3}\right )} \log \relax (x) - e^{6}}{x^{14} + 2 \, x^{10} - 4 \, x^{9} + x^{6} - 4 \, x^{5} + 4 \, x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x^19*log(2*x)+((14*x^2*exp(3)+6*x^5-12*x^4)*log(2*x)-2*x^2*exp(3))*x^10+(((20*x^3-36*x^2)*exp(3)+
6*x^6-24*x^5+24*x^4)*log(2*x)-14*exp(3)^2+(-4*x^3+8*x^2)*exp(3))*x^5+((6*x^4-20*x^3+16*x^2)*exp(3)+2*x^7-12*x^
6+24*x^5-16*x^4)*log(2*x)+(-6*x+8)*exp(3)^2+(-2*x^4+8*x^3-8*x^2)*exp(3))/(x^20+(3*x^6-6*x^5)*x^10+(3*x^7-12*x^
6+12*x^5)*x^5+x^8-6*x^7+12*x^6-8*x^5),x, algorithm="maxima")

[Out]

-(2*x^7*e^3*log(2) + 2*x^3*e^3*log(2) - 4*x^2*e^3*log(2) - (x^14 + 2*x^10 - 4*x^9 + x^6 - 4*x^5 + 4*x^4)*log(x
)^2 - 2*(x^14*log(2) + 2*x^10*log(2) - 4*x^9*log(2) - x^7*e^3 + x^6*log(2) - 4*x^5*log(2) + 4*x^4*log(2) - x^3
*e^3 + 2*x^2*e^3)*log(x) - e^6)/(x^14 + 2*x^10 - 4*x^9 + x^6 - 4*x^5 + 4*x^4)

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mupad [B]  time = 3.40, size = 44, normalized size = 1.83 \begin {gather*} \frac {{\left ({\mathrm {e}}^3+2\,x^2\,\ln \left (2\,x\right )-x^3\,\ln \left (2\,x\right )-x^7\,\ln \left (2\,x\right )\right )}^2}{x^4\,{\left (x^5+x-2\right )}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(x^5*(14*exp(6) + log(2*x)*(exp(3)*(36*x^2 - 20*x^3) - 24*x^4 + 24*x^5 - 6*x^6) - exp(3)*(8*x^2 - 4*x^3))
- x^10*(log(2*x)*(14*x^2*exp(3) - 12*x^4 + 6*x^5) - 2*x^2*exp(3)) - 2*x^19*log(2*x) - log(2*x)*(exp(3)*(16*x^
2 - 20*x^3 + 6*x^4) - 16*x^4 + 24*x^5 - 12*x^6 + 2*x^7) + exp(3)*(8*x^2 - 8*x^3 + 2*x^4) + exp(6)*(6*x - 8))/(
x^5*(12*x^5 - 12*x^6 + 3*x^7) - x^10*(6*x^5 - 3*x^6) - 8*x^5 + 12*x^6 - 6*x^7 + x^8 + x^20),x)

[Out]

(exp(3) + 2*x^2*log(2*x) - x^3*log(2*x) - x^7*log(2*x))^2/(x^4*(x + x^5 - 2)^2)

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sympy [B]  time = 0.90, size = 58, normalized size = 2.42 \begin {gather*} \log {\left (2 x \right )}^{2} + \frac {e^{6}}{x^{14} + 2 x^{10} - 4 x^{9} + x^{6} - 4 x^{5} + 4 x^{4}} - \frac {2 e^{3} \log {\left (2 x \right )}}{x^{7} + x^{3} - 2 x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x**19*ln(2*x)+((14*x**2*exp(3)+6*x**5-12*x**4)*ln(2*x)-2*x**2*exp(3))*x**10+(((20*x**3-36*x**2)*e
xp(3)+6*x**6-24*x**5+24*x**4)*ln(2*x)-14*exp(3)**2+(-4*x**3+8*x**2)*exp(3))*x**5+((6*x**4-20*x**3+16*x**2)*exp
(3)+2*x**7-12*x**6+24*x**5-16*x**4)*ln(2*x)+(-6*x+8)*exp(3)**2+(-2*x**4+8*x**3-8*x**2)*exp(3))/(x**20+(3*x**6-
6*x**5)*x**10+(3*x**7-12*x**6+12*x**5)*x**5+x**8-6*x**7+12*x**6-8*x**5),x)

[Out]

log(2*x)**2 + exp(6)/(x**14 + 2*x**10 - 4*x**9 + x**6 - 4*x**5 + 4*x**4) - 2*exp(3)*log(2*x)/(x**7 + x**3 - 2*
x**2)

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