3.34.51 \(\int \frac {6 x+2 x^2-25 x^3-81 x^4-63 x^5-19 x^6-2 x^7+(6 x+81 x^2+243 x^3+189 x^4+57 x^5+6 x^6) \log (\frac {e^2}{3 x})+(-81 x-243 x^2-189 x^3-57 x^4-6 x^5) \log ^2(\frac {e^2}{3 x})+(27+81 x+63 x^2+19 x^3+2 x^4) \log ^3(\frac {e^2}{3 x})}{-27 x^3-27 x^4-9 x^5-x^6+(81 x^2+81 x^3+27 x^4+3 x^5) \log (\frac {e^2}{3 x})+(-81 x-81 x^2-27 x^3-3 x^4) \log ^2(\frac {e^2}{3 x})+(27+27 x+9 x^2+x^3) \log ^3(\frac {e^2}{3 x})} \, dx\)
Optimal. Leaf size=32 \[ 10+x+x^2+\frac {x^2}{(3+x)^2 \left (-x+\log \left (\frac {e^2}{3 x}\right )\right )^2} \]
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Rubi [F] time = 25.44, 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 {6 x+2 x^2-25 x^3-81 x^4-63 x^5-19 x^6-2 x^7+\left (6 x+81 x^2+243 x^3+189 x^4+57 x^5+6 x^6\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-243 x^2-189 x^3-57 x^4-6 x^5\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+81 x+63 x^2+19 x^3+2 x^4\right ) \log ^3\left (\frac {e^2}{3 x}\right )}{-27 x^3-27 x^4-9 x^5-x^6+\left (81 x^2+81 x^3+27 x^4+3 x^5\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-81 x^2-27 x^3-3 x^4\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+27 x+9 x^2+x^3\right ) \log ^3\left (\frac {e^2}{3 x}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(6*x + 2*x^2 - 25*x^3 - 81*x^4 - 63*x^5 - 19*x^6 - 2*x^7 + (6*x + 81*x^2 + 243*x^3 + 189*x^4 + 57*x^5 + 6*
x^6)*Log[E^2/(3*x)] + (-81*x - 243*x^2 - 189*x^3 - 57*x^4 - 6*x^5)*Log[E^2/(3*x)]^2 + (27 + 81*x + 63*x^2 + 19
*x^3 + 2*x^4)*Log[E^2/(3*x)]^3)/(-27*x^3 - 27*x^4 - 9*x^5 - x^6 + (81*x^2 + 81*x^3 + 27*x^4 + 3*x^5)*Log[E^2/(
3*x)] + (-81*x - 81*x^2 - 27*x^3 - 3*x^4)*Log[E^2/(3*x)]^2 + (27 + 27*x + 9*x^2 + x^3)*Log[E^2/(3*x)]^3),x]
[Out]
3338*Defer[Int][(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^(-3), x] + 15336*Defer[Int][1/((-3 - x)^3*(x - 2*(1 - Log
[3]/2) - Log[x^(-1)])^3), x] + 16083*Defer[Int][1/((-3 - x)*(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3), x] + 621*
Defer[Int][x/(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3, x] + 108*Defer[Int][x^2/(x - 2*(1 - Log[3]/2) - Log[x^(-1
)])^3, x] + 7*Defer[Int][x^3/(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3, x] + 2*Defer[Int][x^4/(x - 2*(1 - Log[3]/
2) - Log[x^(-1)])^3, x] + 15426*Defer[Int][1/((3 + x)^3*(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3), x] + 23247*De
fer[Int][1/((3 + x)^2*(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3), x] + 16099*Defer[Int][1/((3 + x)*(x - 2*(1 - Lo
g[3]/2) - Log[x^(-1)])^3), x] + 1905*Defer[Int][Log[1/(3*x)]/(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3, x] + 1239
3*Defer[Int][Log[1/(3*x)]/((-3 - x)^3*(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3), x] + 9855*Defer[Int][Log[1/(3*x
)]/((-3 - x)*(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3), x] + 312*Defer[Int][(x*Log[1/(3*x)])/(x - 2*(1 - Log[3]/
2) - Log[x^(-1)])^3, x] + 54*Defer[Int][(x^2*Log[1/(3*x)])/(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3, x] + 12411*
Defer[Int][Log[1/(3*x)]/((3 + x)^3*(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3), x] + 16443*Defer[Int][Log[1/(3*x)]
/((3 + x)^2*(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3), x] + 9855*Defer[Int][Log[1/(3*x)]/((3 + x)*(x - 2*(1 - Lo
g[3]/2) - Log[x^(-1)])^3), x] + 399*Defer[Int][Log[1/(3*x)]^2/(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3, x] + 486
0*Defer[Int][Log[1/(3*x)]^2/((-3 - x)^3*(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3), x] + 2430*Defer[Int][Log[1/(3
*x)]^2/((-3 - x)*(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3), x] + 45*Defer[Int][(x*Log[1/(3*x)]^2)/(x - 2*(1 - Lo
g[3]/2) - Log[x^(-1)])^3, x] + 6*Defer[Int][(x^2*Log[1/(3*x)]^2)/(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3, x] +
4860*Defer[Int][Log[1/(3*x)]^2/((3 + x)^3*(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3), x] + 5265*Defer[Int][Log[1/
(3*x)]^2/((3 + x)^2*(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3), x] + 2430*Defer[Int][Log[1/(3*x)]^2/((3 + x)*(x -
2*(1 - Log[3]/2) - Log[x^(-1)])^3), x] + 18*Defer[Int][Log[1/(3*x)]^3/(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3,
x] + 756*Defer[Int][Log[1/(3*x)]^3/((-3 - x)^3*(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3), x] + 171*Defer[Int][L
og[1/(3*x)]^3/((-3 - x)*(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3), x] + 756*Defer[Int][Log[1/(3*x)]^3/((3 + x)^3
*(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3), x] + 594*Defer[Int][Log[1/(3*x)]^3/((3 + x)^2*(x - 2*(1 - Log[3]/2)
- Log[x^(-1)])^3), x] + 171*Defer[Int][Log[1/(3*x)]^3/((3 + x)*(x - 2*(1 - Log[3]/2) - Log[x^(-1)])^3), x] + 3
348*Defer[Int][(-x + 2*(1 - Log[3]/2) + Log[x^(-1)])^(-3), x] + 625*Defer[Int][x/(-x + 2*(1 - Log[3]/2) + Log[
x^(-1)])^3, x] + 90*Defer[Int][x^2/(-x + 2*(1 - Log[3]/2) + Log[x^(-1)])^3, x] + 18*Defer[Int][x^3/(-x + 2*(1
- Log[3]/2) + Log[x^(-1)])^3, x] + 23307*Defer[Int][1/((3 + x)^2*(-x + 2*(1 - Log[3]/2) + Log[x^(-1)])^3), x]
+ 1917*Defer[Int][Log[1/(3*x)]/(-x + 2*(1 - Log[3]/2) + Log[x^(-1)])^3, x] + 324*Defer[Int][(x*Log[1/(3*x)])/(
-x + 2*(1 - Log[3]/2) + Log[x^(-1)])^3, x] + 33*Defer[Int][(x^2*Log[1/(3*x)])/(-x + 2*(1 - Log[3]/2) + Log[x^(
-1)])^3, x] + 6*Defer[Int][(x^3*Log[1/(3*x)])/(-x + 2*(1 - Log[3]/2) + Log[x^(-1)])^3, x] + 16449*Defer[Int][L
og[1/(3*x)]/((3 + x)^2*(-x + 2*(1 - Log[3]/2) + Log[x^(-1)])^3), x] + 405*Defer[Int][Log[1/(3*x)]^2/(-x + 2*(1
- Log[3]/2) + Log[x^(-1)])^3, x] + 54*Defer[Int][(x*Log[1/(3*x)]^2)/(-x + 2*(1 - Log[3]/2) + Log[x^(-1)])^3,
x] + 5265*Defer[Int][Log[1/(3*x)]^2/((3 + x)^2*(-x + 2*(1 - Log[3]/2) + Log[x^(-1)])^3), x] + 19*Defer[Int][Lo
g[1/(3*x)]^3/(-x + 2*(1 - Log[3]/2) + Log[x^(-1)])^3, x] + 2*Defer[Int][(x*Log[1/(3*x)]^3)/(-x + 2*(1 - Log[3]
/2) + Log[x^(-1)])^3, x] + 594*Defer[Int][Log[1/(3*x)]^3/((3 + x)^2*(-x + 2*(1 - Log[3]/2) + Log[x^(-1)])^3),
x]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-216-342 x+304 x^2+143 x^3-85 x^4-27 x^5+7 x^6+2 x^7-3 \left (108+218 x-45 x^2-95 x^3-5 x^4+11 x^5+2 x^6\right ) \log \left (\frac {1}{3 x}\right )+3 (3+x)^3 \left (-2-3 x+2 x^2\right ) \log ^2\left (\frac {1}{3 x}\right )-(3+x)^3 (1+2 x) \log ^3\left (\frac {1}{3 x}\right )}{(3+x)^3 \left (x-2 \left (1-\frac {\log (3)}{2}\right )-\log \left (\frac {1}{x}\right )\right )^3} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [B] time = 0.88, size = 1283, normalized size = 40.09
result too large to display
Warning: Unable to verify antiderivative.
[In]
Integrate[(6*x + 2*x^2 - 25*x^3 - 81*x^4 - 63*x^5 - 19*x^6 - 2*x^7 + (6*x + 81*x^2 + 243*x^3 + 189*x^4 + 57*x^
5 + 6*x^6)*Log[E^2/(3*x)] + (-81*x - 243*x^2 - 189*x^3 - 57*x^4 - 6*x^5)*Log[E^2/(3*x)]^2 + (27 + 81*x + 63*x^
2 + 19*x^3 + 2*x^4)*Log[E^2/(3*x)]^3)/(-27*x^3 - 27*x^4 - 9*x^5 - x^6 + (81*x^2 + 81*x^3 + 27*x^4 + 3*x^5)*Log
[E^2/(3*x)] + (-81*x - 81*x^2 - 27*x^3 - 3*x^4)*Log[E^2/(3*x)]^2 + (27 + 27*x + 9*x^2 + x^3)*Log[E^2/(3*x)]^3)
,x]
[Out]
(x*(648 + 2826*x + 4548*x^2 + 2780*x^3 - 508*x^4 - 1470*x^5 - 562*x^6 + 64*x^7 + 96*x^8 + 24*x^9 + 2*x^10 + 42
12*Log[3] + 14958*x*Log[3] + 6237*x^2*Log[3] - 10515*x^3*Log[3] - 8849*x^4*Log[3] - 646*x^5*Log[3] + 1429*x^6*
Log[3] + 571*x^7*Log[3] + 83*x^8*Log[3] - 4698*Log[3]^2 - 19188*x*Log[3]^2 - 15297*x^2*Log[3]^2 + 2964*x^3*Log
[3]^2 + 7472*x^4*Log[3]^2 + 2540*x^5*Log[3]^2 + 15*x^6*Log[3]^2 - 124*x^7*Log[3]^2 - 16*x^8*Log[3]^2 + 1620*Lo
g[3]^3 + 7506*x*Log[3]^3 + 8370*x^2*Log[3]^3 + 2400*x^3*Log[3]^3 - 1240*x^4*Log[3]^3 - 990*x^5*Log[3]^3 - 238*
x^6*Log[3]^3 - 20*x^7*Log[3]^3 - 162*Log[3]^4 - 864*x*Log[3]^4 - 1296*x^2*Log[3]^4 - 888*x^3*Log[3]^4 - 314*x^
4*Log[3]^4 - 56*x^5*Log[3]^4 - 4*x^6*Log[3]^4 + x^9*Log[81] + (-4*x^9 + x^8*(-83 + 32*Log[3]) + x^7*(-571 + 24
8*Log[3] + 60*Log[3]^2) + 324*(-13 + 29*Log[3] - 15*Log[3]^2 + 2*Log[3]^3) + x^6*(-1429 - 30*Log[3] + 714*Log[
3]^2 + 16*Log[3]^3) + 18*x*(-831 + 2132*Log[3] - 1251*Log[3]^2 + 192*Log[3]^3) + x^5*(646 - 5080*Log[3] + 2970
*Log[3]^2 + 224*Log[3]^3) + 3*x^3*(3505 - 1976*Log[3] - 2400*Log[3]^2 + 1184*Log[3]^3) + x^4*(8849 - 14944*Log
[3] + 3720*Log[3]^2 + 1256*Log[3]^3) + 3*x^2*(-2079 + 10198*Log[3] - 8370*Log[3]^2 + 1728*Log[3]^3))*Log[x^(-1
)] - (16*x^8 + 4*x^7*(31 + 15*Log[3]) + 162*(29 - 30*Log[3] + 6*Log[3]^2) + 3*x^6*(-5 + 238*Log[3] + 8*Log[3]^
2) + 18*x*(1066 - 1251*Log[3] + 288*Log[3]^2) + x^5*(-2540 + 2970*Log[3] + 336*Log[3]^2) + 12*x^3*(-247 - 600*
Log[3] + 444*Log[3]^2) + 4*x^4*(-1868 + 930*Log[3] + 471*Log[3]^2) + 3*x^2*(5099 - 8370*Log[3] + 2592*Log[3]^2
))*Log[x^(-1)]^2 + 2*(3 + x)^4*(-10 + 10*x^3 + x^2*(-1 + 8*Log[3]) + x*(-33 + 16*Log[3]) + Log[81])*Log[x^(-1)
]^3 - 2*(3 + x)^4*(1 + 4*x + 2*x^2)*Log[x^(-1)]^4 - 2*(3 + x)^4*Log[1/(3*x)]^3*(-1 + 4*x^3 + Log[3] + x^2*(5 +
Log[9]) + x*(-3 + Log[81]) - (1 + 4*x + 2*x^2)*Log[x^(-1)]) - 6*(3 + x)^4*Log[1/(3*x)]^2*(4*x^4 + (-2 + Log[3
])^2 + x*(10 - 13*Log[3] + 4*Log[3]^2) + x^2*(-12 + 2*Log[3]^2 + Log[27]) + x^3*(-5 + Log[729]) - (-4 + 6*x^3
+ x*(-13 + 8*Log[3]) + Log[9] + x^2*(3 + Log[81]))*Log[x^(-1)] + (1 + 4*x + 2*x^2)*Log[x^(-1)]^2) - 3*Log[1/(3
*x)]*(x^8*(-9 + 14*Log[3]) + x^7*(-89 + 138*Log[3] + 16*Log[3]^2) + 162*(-10 + 14*Log[3] - 7*Log[3]^2 + Log[3]
^3) + x^6*(-231 + 355*Log[3] + 194*Log[3]^2 + 4*Log[3]^3) + x^5*(330 - 524*Log[3] + 842*Log[3]^2 + 56*Log[3]^3
) + 6*x*(-1005 + 1528*Log[3] - 873*Log[3]^2 + 144*Log[3]^3) + x^4*(2187 - 3380*Log[3] + 1270*Log[3]^2 + 314*Lo
g[3]^3) + x^3*(1601 - 2414*Log[3] - 1140*Log[3]^2 + 888*Log[3]^3) + x^2*(-4095 + 6395*Log[3] - 5562*Log[3]^2 +
1296*Log[3]^3) - (14*x^8 + 2*x^7*(69 + 16*Log[3]) + 162*(14 - 14*Log[3] + 3*Log[3]^2) + x^6*(355 + 388*Log[3]
+ 12*Log[3]^2) + 4*x^5*(-131 + 421*Log[3] + 42*Log[3]^2) + 12*x*(764 - 873*Log[3] + 216*Log[3]^2) + x^4*(-338
0 + 2540*Log[3] + 942*Log[3]^2) + x^3*(-2414 - 2280*Log[3] + 2664*Log[3]^2) + x^2*(6395 - 11124*Log[3] + 3888*
Log[3]^2))*Log[x^(-1)] + 2*(3 + x)^4*(-7 + 8*x^3 + x*(-23 + 12*Log[3]) + Log[27] + x^2*(1 + Log[729]))*Log[x^(
-1)]^2 - 2*(3 + x)^4*(1 + 4*x + 2*x^2)*Log[x^(-1)]^3)))/(2*(1 + x)^3*(3 + x)^4*(-2 + x + Log[3] - Log[x^(-1)])
^2)
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fricas [B] time = 0.49, size = 137, normalized size = 4.28 \begin {gather*} \frac {x^{6} + 7 \, x^{5} + 15 \, x^{4} + 9 \, x^{3} + {\left (x^{4} + 7 \, x^{3} + 15 \, x^{2} + 9 \, x\right )} \log \left (\frac {e^{2}}{3 \, x}\right )^{2} + x^{2} - 2 \, {\left (x^{5} + 7 \, x^{4} + 15 \, x^{3} + 9 \, x^{2}\right )} \log \left (\frac {e^{2}}{3 \, x}\right )}{x^{4} + 6 \, x^{3} + {\left (x^{2} + 6 \, x + 9\right )} \log \left (\frac {e^{2}}{3 \, x}\right )^{2} + 9 \, x^{2} - 2 \, {\left (x^{3} + 6 \, x^{2} + 9 \, x\right )} \log \left (\frac {e^{2}}{3 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((2*x^4+19*x^3+63*x^2+81*x+27)*log(1/3*exp(2)/x)^3+(-6*x^5-57*x^4-189*x^3-243*x^2-81*x)*log(1/3*exp(
2)/x)^2+(6*x^6+57*x^5+189*x^4+243*x^3+81*x^2+6*x)*log(1/3*exp(2)/x)-2*x^7-19*x^6-63*x^5-81*x^4-25*x^3+2*x^2+6*
x)/((x^3+9*x^2+27*x+27)*log(1/3*exp(2)/x)^3+(-3*x^4-27*x^3-81*x^2-81*x)*log(1/3*exp(2)/x)^2+(3*x^5+27*x^4+81*x
^3+81*x^2)*log(1/3*exp(2)/x)-x^6-9*x^5-27*x^4-27*x^3),x, algorithm="fricas")
[Out]
(x^6 + 7*x^5 + 15*x^4 + 9*x^3 + (x^4 + 7*x^3 + 15*x^2 + 9*x)*log(1/3*e^2/x)^2 + x^2 - 2*(x^5 + 7*x^4 + 15*x^3
+ 9*x^2)*log(1/3*e^2/x))/(x^4 + 6*x^3 + (x^2 + 6*x + 9)*log(1/3*e^2/x)^2 + 9*x^2 - 2*(x^3 + 6*x^2 + 9*x)*log(1
/3*e^2/x))
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giac [B] time = 0.48, size = 283, normalized size = 8.84 \begin {gather*} -\frac {{\left (\frac {2 \, e^{14} \log \left (\frac {e^{2}}{3 \, x}\right )}{x} - \frac {e^{14} \log \left (\frac {e^{2}}{3 \, x}\right )^{2}}{x^{2}} - \frac {7 \, e^{14}}{x} + \frac {14 \, e^{14} \log \left (\frac {e^{2}}{3 \, x}\right )}{x^{2}} - \frac {7 \, e^{14} \log \left (\frac {e^{2}}{3 \, x}\right )^{2}}{x^{3}} - \frac {15 \, e^{14}}{x^{2}} + \frac {30 \, e^{14} \log \left (\frac {e^{2}}{3 \, x}\right )}{x^{3}} - \frac {15 \, e^{14} \log \left (\frac {e^{2}}{3 \, x}\right )^{2}}{x^{4}} - \frac {9 \, e^{14}}{x^{3}} + \frac {18 \, e^{14} \log \left (\frac {e^{2}}{3 \, x}\right )}{x^{4}} - \frac {9 \, e^{14} \log \left (\frac {e^{2}}{3 \, x}\right )^{2}}{x^{5}} - \frac {e^{14}}{x^{4}} - e^{14}\right )} e^{\left (-2\right )}}{\frac {e^{12}}{x^{2}} - \frac {2 \, e^{12} \log \left (\frac {e^{2}}{3 \, x}\right )}{x^{3}} + \frac {e^{12} \log \left (\frac {e^{2}}{3 \, x}\right )^{2}}{x^{4}} + \frac {6 \, e^{12}}{x^{3}} - \frac {12 \, e^{12} \log \left (\frac {e^{2}}{3 \, x}\right )}{x^{4}} + \frac {6 \, e^{12} \log \left (\frac {e^{2}}{3 \, x}\right )^{2}}{x^{5}} + \frac {9 \, e^{12}}{x^{4}} - \frac {18 \, e^{12} \log \left (\frac {e^{2}}{3 \, x}\right )}{x^{5}} + \frac {9 \, e^{12} \log \left (\frac {e^{2}}{3 \, x}\right )^{2}}{x^{6}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((2*x^4+19*x^3+63*x^2+81*x+27)*log(1/3*exp(2)/x)^3+(-6*x^5-57*x^4-189*x^3-243*x^2-81*x)*log(1/3*exp(
2)/x)^2+(6*x^6+57*x^5+189*x^4+243*x^3+81*x^2+6*x)*log(1/3*exp(2)/x)-2*x^7-19*x^6-63*x^5-81*x^4-25*x^3+2*x^2+6*
x)/((x^3+9*x^2+27*x+27)*log(1/3*exp(2)/x)^3+(-3*x^4-27*x^3-81*x^2-81*x)*log(1/3*exp(2)/x)^2+(3*x^5+27*x^4+81*x
^3+81*x^2)*log(1/3*exp(2)/x)-x^6-9*x^5-27*x^4-27*x^3),x, algorithm="giac")
[Out]
-(2*e^14*log(1/3*e^2/x)/x - e^14*log(1/3*e^2/x)^2/x^2 - 7*e^14/x + 14*e^14*log(1/3*e^2/x)/x^2 - 7*e^14*log(1/3
*e^2/x)^2/x^3 - 15*e^14/x^2 + 30*e^14*log(1/3*e^2/x)/x^3 - 15*e^14*log(1/3*e^2/x)^2/x^4 - 9*e^14/x^3 + 18*e^14
*log(1/3*e^2/x)/x^4 - 9*e^14*log(1/3*e^2/x)^2/x^5 - e^14/x^4 - e^14)*e^(-2)/(e^12/x^2 - 2*e^12*log(1/3*e^2/x)/
x^3 + e^12*log(1/3*e^2/x)^2/x^4 + 6*e^12/x^3 - 12*e^12*log(1/3*e^2/x)/x^4 + 6*e^12*log(1/3*e^2/x)^2/x^5 + 9*e^
12/x^4 - 18*e^12*log(1/3*e^2/x)/x^5 + 9*e^12*log(1/3*e^2/x)^2/x^6)
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maple [A] time = 0.10, size = 34, normalized size = 1.06
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result |
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\(x^{2}+x +\frac {x^{2}}{\left (x^{2}+6 x +9\right ) \left (x -\ln \left (\frac {{\mathrm e}^{2}}{3 x}\right )\right )^{2}}\) |
\(34\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((2*x^4+19*x^3+63*x^2+81*x+27)*ln(1/3*exp(2)/x)^3+(-6*x^5-57*x^4-189*x^3-243*x^2-81*x)*ln(1/3*exp(2)/x)^2+
(6*x^6+57*x^5+189*x^4+243*x^3+81*x^2+6*x)*ln(1/3*exp(2)/x)-2*x^7-19*x^6-63*x^5-81*x^4-25*x^3+2*x^2+6*x)/((x^3+
9*x^2+27*x+27)*ln(1/3*exp(2)/x)^3+(-3*x^4-27*x^3-81*x^2-81*x)*ln(1/3*exp(2)/x)^2+(3*x^5+27*x^4+81*x^3+81*x^2)*
ln(1/3*exp(2)/x)-x^6-9*x^5-27*x^4-27*x^3),x,method=_RETURNVERBOSE)
[Out]
x^2+x+x^2/(x^2+6*x+9)/(x-ln(1/3*exp(2)/x))^2
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maxima [B] time = 0.84, size = 236, normalized size = 7.38 \begin {gather*} \frac {x^{6} + x^{5} {\left (2 \, \log \relax (3) + 3\right )} + {\left (\log \relax (3)^{2} + 10 \, \log \relax (3) - 9\right )} x^{4} + {\left (7 \, \log \relax (3)^{2} + 2 \, \log \relax (3) - 23\right )} x^{3} + {\left (15 \, \log \relax (3)^{2} - 42 \, \log \relax (3) + 25\right )} x^{2} + {\left (x^{4} + 7 \, x^{3} + 15 \, x^{2} + 9 \, x\right )} \log \relax (x)^{2} + 9 \, {\left (\log \relax (3)^{2} - 4 \, \log \relax (3) + 4\right )} x + 2 \, {\left (x^{5} + x^{4} {\left (\log \relax (3) + 5\right )} + x^{3} {\left (7 \, \log \relax (3) + 1\right )} + 3 \, x^{2} {\left (5 \, \log \relax (3) - 7\right )} + 9 \, x {\left (\log \relax (3) - 2\right )}\right )} \log \relax (x)}{x^{4} + 2 \, x^{3} {\left (\log \relax (3) + 1\right )} + {\left (\log \relax (3)^{2} + 8 \, \log \relax (3) - 11\right )} x^{2} + {\left (x^{2} + 6 \, x + 9\right )} \log \relax (x)^{2} + 6 \, {\left (\log \relax (3)^{2} - \log \relax (3) - 2\right )} x + 9 \, \log \relax (3)^{2} + 2 \, {\left (x^{3} + x^{2} {\left (\log \relax (3) + 4\right )} + 3 \, x {\left (2 \, \log \relax (3) - 1\right )} + 9 \, \log \relax (3) - 18\right )} \log \relax (x) - 36 \, \log \relax (3) + 36} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((2*x^4+19*x^3+63*x^2+81*x+27)*log(1/3*exp(2)/x)^3+(-6*x^5-57*x^4-189*x^3-243*x^2-81*x)*log(1/3*exp(
2)/x)^2+(6*x^6+57*x^5+189*x^4+243*x^3+81*x^2+6*x)*log(1/3*exp(2)/x)-2*x^7-19*x^6-63*x^5-81*x^4-25*x^3+2*x^2+6*
x)/((x^3+9*x^2+27*x+27)*log(1/3*exp(2)/x)^3+(-3*x^4-27*x^3-81*x^2-81*x)*log(1/3*exp(2)/x)^2+(3*x^5+27*x^4+81*x
^3+81*x^2)*log(1/3*exp(2)/x)-x^6-9*x^5-27*x^4-27*x^3),x, algorithm="maxima")
[Out]
(x^6 + x^5*(2*log(3) + 3) + (log(3)^2 + 10*log(3) - 9)*x^4 + (7*log(3)^2 + 2*log(3) - 23)*x^3 + (15*log(3)^2 -
42*log(3) + 25)*x^2 + (x^4 + 7*x^3 + 15*x^2 + 9*x)*log(x)^2 + 9*(log(3)^2 - 4*log(3) + 4)*x + 2*(x^5 + x^4*(l
og(3) + 5) + x^3*(7*log(3) + 1) + 3*x^2*(5*log(3) - 7) + 9*x*(log(3) - 2))*log(x))/(x^4 + 2*x^3*(log(3) + 1) +
(log(3)^2 + 8*log(3) - 11)*x^2 + (x^2 + 6*x + 9)*log(x)^2 + 6*(log(3)^2 - log(3) - 2)*x + 9*log(3)^2 + 2*(x^3
+ x^2*(log(3) + 4) + 3*x*(2*log(3) - 1) + 9*log(3) - 18)*log(x) - 36*log(3) + 36)
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mupad [B] time = 2.57, size = 206, normalized size = 6.44 \begin {gather*} x+\frac {\frac {x^2\,\left (x^2+x+3\right )}{\left (x+1\right )\,{\left (x+3\right )}^3}+\frac {3\,x^2\,\ln \left (\frac {{\mathrm {e}}^2}{3\,x}\right )}{\left (x+1\right )\,{\left (x+3\right )}^3}}{x^2-2\,x\,\ln \left (\frac {{\mathrm {e}}^2}{3\,x}\right )+{\ln \left (\frac {{\mathrm {e}}^2}{3\,x}\right )}^2}+x^2+\frac {\frac {3\,x\,\left (3\,x^4+3\,x^3+x^2+3\,x\right )}{{\left (x+1\right )}^3\,{\left (x+3\right )}^4}+\frac {6\,x^2\,\ln \left (\frac {{\mathrm {e}}^2}{3\,x}\right )\,\left (-x^2+x+3\right )}{{\left (x+1\right )}^3\,{\left (x+3\right )}^4}}{x-\ln \left (\frac {{\mathrm {e}}^2}{3\,x}\right )}+\frac {-6\,x^4+6\,x^3+18\,x^2}{x^7+15\,x^6+93\,x^5+307\,x^4+579\,x^3+621\,x^2+351\,x+81} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((25*x^3 - log(exp(2)/(3*x))^3*(81*x + 63*x^2 + 19*x^3 + 2*x^4 + 27) - log(exp(2)/(3*x))*(6*x + 81*x^2 + 24
3*x^3 + 189*x^4 + 57*x^5 + 6*x^6) - 2*x^2 - 6*x + 81*x^4 + 63*x^5 + 19*x^6 + 2*x^7 + log(exp(2)/(3*x))^2*(81*x
+ 243*x^2 + 189*x^3 + 57*x^4 + 6*x^5))/(log(exp(2)/(3*x))^2*(81*x + 81*x^2 + 27*x^3 + 3*x^4) - log(exp(2)/(3*
x))^3*(27*x + 9*x^2 + x^3 + 27) - log(exp(2)/(3*x))*(81*x^2 + 81*x^3 + 27*x^4 + 3*x^5) + 27*x^3 + 27*x^4 + 9*x
^5 + x^6),x)
[Out]
x + ((x^2*(x + x^2 + 3))/((x + 1)*(x + 3)^3) + (3*x^2*log(exp(2)/(3*x)))/((x + 1)*(x + 3)^3))/(log(exp(2)/(3*x
))^2 + x^2 - 2*x*log(exp(2)/(3*x))) + x^2 + ((3*x*(3*x + x^2 + 3*x^3 + 3*x^4))/((x + 1)^3*(x + 3)^4) + (6*x^2*
log(exp(2)/(3*x))*(x - x^2 + 3))/((x + 1)^3*(x + 3)^4))/(x - log(exp(2)/(3*x))) + (18*x^2 + 6*x^3 - 6*x^4)/(35
1*x + 621*x^2 + 579*x^3 + 307*x^4 + 93*x^5 + 15*x^6 + x^7 + 81)
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sympy [B] time = 0.52, size = 63, normalized size = 1.97 \begin {gather*} x^{2} + \frac {x^{2}}{x^{4} + 6 x^{3} + 9 x^{2} + \left (x^{2} + 6 x + 9\right ) \log {\left (\frac {e^{2}}{3 x} \right )}^{2} + \left (- 2 x^{3} - 12 x^{2} - 18 x\right ) \log {\left (\frac {e^{2}}{3 x} \right )}} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((2*x**4+19*x**3+63*x**2+81*x+27)*ln(1/3*exp(2)/x)**3+(-6*x**5-57*x**4-189*x**3-243*x**2-81*x)*ln(1/
3*exp(2)/x)**2+(6*x**6+57*x**5+189*x**4+243*x**3+81*x**2+6*x)*ln(1/3*exp(2)/x)-2*x**7-19*x**6-63*x**5-81*x**4-
25*x**3+2*x**2+6*x)/((x**3+9*x**2+27*x+27)*ln(1/3*exp(2)/x)**3+(-3*x**4-27*x**3-81*x**2-81*x)*ln(1/3*exp(2)/x)
**2+(3*x**5+27*x**4+81*x**3+81*x**2)*ln(1/3*exp(2)/x)-x**6-9*x**5-27*x**4-27*x**3),x)
[Out]
x**2 + x**2/(x**4 + 6*x**3 + 9*x**2 + (x**2 + 6*x + 9)*log(exp(2)/(3*x))**2 + (-2*x**3 - 12*x**2 - 18*x)*log(e
xp(2)/(3*x))) + x
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