3.47.29 \(\int \frac {81 x^2+18 x^4+x^6+(162 x+18 x^3) \log (2)+81 \log ^2(2)+(-81 x^2-18 x^3-18 x^4-2 x^5-x^6+(-162 x-18 x^2-18 x^3) \log (2)-81 \log ^2(2)) \log (x)+(18 x^3+x^4+2 x^5+18 x^2 \log (2)) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} (27 x+78 x^2+9 x^3+18 x^4+x^6+(162 x+18 x^3) \log (2)+81 \log ^2(2)+(-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)) \log (x)+x^4 \log ^2(x))}{81 x^4+18 x^6+x^8+(162 x^3+18 x^5) \log (2)+81 x^2 \log ^2(2)+(-18 x^5-2 x^7-18 x^4 \log (2)) \log (x)+x^6 \log ^2(x)} \, dx\)

Optimal. Leaf size=34 \[ \frac {-e^{\frac {1}{3 \left (x+\log (2)+\frac {1}{9} x^2 (x-\log (x))\right )}}+\log (x)}{x} \]

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Rubi [F]  time = 32.57, 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 {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(81*x^2 + 18*x^4 + x^6 + (162*x + 18*x^3)*Log[2] + 81*Log[2]^2 + (-81*x^2 - 18*x^3 - 18*x^4 - 2*x^5 - x^6
+ (-162*x - 18*x^2 - 18*x^3)*Log[2] - 81*Log[2]^2)*Log[x] + (18*x^3 + x^4 + 2*x^5 + 18*x^2*Log[2])*Log[x]^2 -
x^4*Log[x]^3 + (27*x + 78*x^2 + 9*x^3 + 18*x^4 + x^6 + (162*x + 18*x^3)*Log[2] + 81*Log[2]^2 + (-6*x^2 - 18*x^
3 - 2*x^5 - 18*x^2*Log[2])*Log[x] + x^4*Log[x]^2)/E^(3/(-9*x - x^3 - 9*Log[2] + x^2*Log[x])))/(81*x^4 + 18*x^6
+ x^8 + (162*x^3 + 18*x^5)*Log[2] + 81*x^2*Log[2]^2 + (-18*x^5 - 2*x^7 - 18*x^4*Log[2])*Log[x] + x^6*Log[x]^2
),x]

[Out]

(-6*Log[2])/x^3 + (2*Log[512])/(3*x^3) + Log[x]/x + Defer[Int][E^(3/(9*x + x^3 + Log[512] - x^2*Log[x]))/x^2,
x] + 81*Defer[Int][(9*x + x^3 + Log[512] - x^2*Log[x])^(-2), x] - 54*Log[512]*Defer[Int][(9*x + x^3 + Log[512]
- x^2*Log[x])^(-2), x] - 54*(3 + Log[512])*Defer[Int][(9*x + x^3 + Log[512] - x^2*Log[x])^(-2), x] + 9*(9 + 3
6*Log[2] + 8*Log[512])*Defer[Int][(9*x + x^3 + Log[512] - x^2*Log[x])^(-2), x] - 3*Defer[Int][E^(3/(9*x + x^3
+ Log[512] - x^2*Log[x]))/(9*x + x^3 + Log[512] - x^2*Log[x])^2, x] + 18*Log[2]*Log[512]^2*Defer[Int][1/(x^4*(
9*x + x^3 + Log[512] - x^2*Log[x])^2), x] - 2*Log[512]^3*Defer[Int][1/(x^4*(9*x + x^3 + Log[512] - x^2*Log[x])
^2), x] - 54*Log[512]^2*Defer[Int][1/(x^3*(9*x + x^3 + Log[512] - x^2*Log[x])^2), x] + 18*Log[512]*Log[1342177
28]*Defer[Int][1/(x^3*(9*x + x^3 + Log[512] - x^2*Log[x])^2), x] + 81*Log[2]^2*Defer[Int][1/(x^2*(9*x + x^3 +
Log[512] - x^2*Log[x])^2), x] - 243*Log[512]*Defer[Int][1/(x^2*(9*x + x^3 + Log[512] - x^2*Log[x])^2), x] + 9*
Log[2]*(486 + Log[512])*Defer[Int][1/(x^2*(9*x + x^3 + Log[512] - x^2*Log[x])^2), x] - Log[512]*(243 + 2*Log[5
12])*Defer[Int][1/(x^2*(9*x + x^3 + Log[512] - x^2*Log[x])^2), x] + (81*Log[2]^2 + Log[512]^2 - Log[512]*Log[2
62144] - Log[18014398509481984])*Defer[Int][E^(3/(9*x + x^3 + Log[512] - x^2*Log[x]))/(x^2*(9*x + x^3 + Log[51
2] - x^2*Log[x])^2), x] + 162*Log[2]*Defer[Int][1/(x*(9*x + x^3 + Log[512] - x^2*Log[x])^2), x] - 3*(243 + Log
[512]^2)*Defer[Int][1/(x*(9*x + x^3 + Log[512] - x^2*Log[x])^2), x] - 3*(243 + 12*Log[512] + Log[512]^2)*Defer
[Int][1/(x*(9*x + x^3 + Log[512] - x^2*Log[x])^2), x] + 2*(729 + 9*(1 + Log[4])*Log[512] + Log[512]^2)*Defer[I
nt][1/(x*(9*x + x^3 + Log[512] - x^2*Log[x])^2), x] - 27*Defer[Int][E^(3/(9*x + x^3 + Log[512] - x^2*Log[x]))/
(x*(9*x + x^3 + Log[512] - x^2*Log[x])^2), x] - 243*Defer[Int][x/(9*x + x^3 + Log[512] - x^2*Log[x])^2, x] + 1
8*Log[2]*Defer[Int][x/(9*x + x^3 + Log[512] - x^2*Log[x])^2, x] + 2*(243 + Log[512])*Defer[Int][x/(9*x + x^3 +
Log[512] - x^2*Log[x])^2, x] - (243 + 4*Log[512])*Defer[Int][x/(9*x + x^3 + Log[512] - x^2*Log[x])^2, x] + 3*
Defer[Int][(E^(3/(9*x + x^3 + Log[512] - x^2*Log[x]))*x)/(9*x + x^3 + Log[512] - x^2*Log[x])^2, x] + 18*Defer[
Int][x^2/(9*x + x^3 + Log[512] - x^2*Log[x])^2, x] - 3*Log[512]*Defer[Int][x^2/(9*x + x^3 + Log[512] - x^2*Log
[x])^2, x] + 6*(3 + Log[512])*Defer[Int][x^2/(9*x + x^3 + Log[512] - x^2*Log[x])^2, x] - 3*(12 + Log[512])*Def
er[Int][x^2/(9*x + x^3 + Log[512] - x^2*Log[x])^2, x] - 36*Log[2]*Log[512]*Defer[Int][1/(x^4*(9*x + x^3 + Log[
512] - x^2*Log[x])), x] + 4*Log[512]^2*Defer[Int][1/(x^4*(9*x + x^3 + Log[512] - x^2*Log[x])), x] + 243*Defer[
Int][1/(x^2*(9*x + x^3 + Log[512] - x^2*Log[x])), x] - 2*(162 + Log[512])*Defer[Int][1/(x^2*(9*x + x^3 + Log[5
12] - x^2*Log[x])), x] + (81 + 2*Log[512])*Defer[Int][1/(x^2*(9*x + x^3 + Log[512] - x^2*Log[x])), x] + 6*Defe
r[Int][E^(3/(9*x + x^3 + Log[512] - x^2*Log[x]))/(x^2*(9*x + x^3 + Log[512] - x^2*Log[x])), x] + 6*Log[512]*De
fer[Int][1/(x*(9*x + x^3 + Log[512] - x^2*Log[x])), x] + 2*(9 + Log[512])*Defer[Int][1/(x*(9*x + x^3 + Log[512
] - x^2*Log[x])), x] - 2*(9 + 2*Log[262144])*Defer[Int][1/(x*(9*x + x^3 + Log[512] - x^2*Log[x])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx\\ &=\int \left (\frac {81}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}+\frac {18 x^2}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}+\frac {x^4}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}+\frac {18 \left (9+x^2\right ) \log (2)}{x \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}+\frac {81 \log ^2(2)}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}-\frac {\left (9 x+x^3+\log (512)\right ) \left (9 x+2 x^2+x^3+\log (512)\right ) \log (x)}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}+\frac {\left (18 x+x^2+2 x^3+18 \log (2)\right ) \log ^2(x)}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}-\frac {x^2 \log ^3(x)}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}+\frac {e^{\frac {3}{9 x+x^3+\log (512)-x^2 \log (x)}} \left (78 x^2+18 x^4+x^6+81 \log ^2(2)+9 x^3 (1+\log (4))+27 x (1+\log (64))-18 x^3 \log (x)-2 x^5 \log (x)-6 x^2 (1+\log (8)) \log (x)+x^4 \log ^2(x)\right )}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}\right ) \, dx\\ &=18 \int \frac {x^2}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+81 \int \frac {1}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+(18 \log (2)) \int \frac {9+x^2}{x \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\left (81 \log ^2(2)\right ) \int \frac {1}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\int \frac {x^4}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx-\int \frac {\left (9 x+x^3+\log (512)\right ) \left (9 x+2 x^2+x^3+\log (512)\right ) \log (x)}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\int \frac {\left (18 x+x^2+2 x^3+18 \log (2)\right ) \log ^2(x)}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx-\int \frac {x^2 \log ^3(x)}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\int \frac {e^{\frac {3}{9 x+x^3+\log (512)-x^2 \log (x)}} \left (78 x^2+18 x^4+x^6+81 \log ^2(2)+9 x^3 (1+\log (4))+27 x (1+\log (64))-18 x^3 \log (x)-2 x^5 \log (x)-6 x^2 (1+\log (8)) \log (x)+x^4 \log ^2(x)\right )}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx\\ &=18 \int \frac {x^2}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+81 \int \frac {1}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+(18 \log (2)) \int \left (\frac {9}{x \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}+\frac {x}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}\right ) \, dx+\left (81 \log ^2(2)\right ) \int \frac {1}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\int \frac {x^4}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\int \left (\frac {e^{\frac {3}{9 x+x^3+\log (512)-x^2 \log (x)}}}{x^2}+\frac {e^{\frac {3}{9 x+x^3+\log (512)-x^2 \log (x)}} \left (-27 x-3 x^2+3 x^3+81 \log ^2(2)+\log ^2(512)-\log (512) \log (262144)-\log (18014398509481984)\right )}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}+\frac {6 e^{\frac {3}{9 x+x^3+\log (512)-x^2 \log (x)}}}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )}\right ) \, dx+\int \left (\frac {18 x+x^2+2 x^3+18 \log (2)}{x^4}+\frac {\left (18 x+x^2+2 x^3+18 \log (2)\right ) \left (9 x+x^3+\log (512)\right )^2}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}-\frac {2 \left (18 x+x^2+2 x^3+18 \log (2)\right ) \left (9 x+x^3+\log (512)\right )}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )}\right ) \, dx-\int \left (\frac {2 \left (9 x+x^3+\log (512)\right )}{x^4}+\frac {\log (x)}{x^2}+\frac {\left (9 x+x^3+\log (512)\right )^3}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}-\frac {3 \left (9 x+x^3+\log (512)\right )^2}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )}\right ) \, dx-\int \left (\frac {\left (9 x+x^3+\log (512)\right )^2 \left (9 x+2 x^2+x^3+\log (512)\right )}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}-\frac {\left (9 x+x^3+\log (512)\right ) \left (9 x+2 x^2+x^3+\log (512)\right )}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )}\right ) \, dx\\ &=-\left (2 \int \frac {9 x+x^3+\log (512)}{x^4} \, dx\right )-2 \int \frac {\left (18 x+x^2+2 x^3+18 \log (2)\right ) \left (9 x+x^3+\log (512)\right )}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )} \, dx+3 \int \frac {\left (9 x+x^3+\log (512)\right )^2}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )} \, dx+6 \int \frac {e^{\frac {3}{9 x+x^3+\log (512)-x^2 \log (x)}}}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )} \, dx+18 \int \frac {x^2}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+81 \int \frac {1}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+(18 \log (2)) \int \frac {x}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+(162 \log (2)) \int \frac {1}{x \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\left (81 \log ^2(2)\right ) \int \frac {1}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\int \frac {e^{\frac {3}{9 x+x^3+\log (512)-x^2 \log (x)}}}{x^2} \, dx+\int \frac {18 x+x^2+2 x^3+18 \log (2)}{x^4} \, dx-\int \frac {\log (x)}{x^2} \, dx+\int \frac {x^4}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\int \frac {\left (18 x+x^2+2 x^3+18 \log (2)\right ) \left (9 x+x^3+\log (512)\right )^2}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx-\int \frac {\left (9 x+x^3+\log (512)\right )^3}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx-\int \frac {\left (9 x+x^3+\log (512)\right )^2 \left (9 x+2 x^2+x^3+\log (512)\right )}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\int \frac {e^{\frac {3}{9 x+x^3+\log (512)-x^2 \log (x)}} \left (-27 x-3 x^2+3 x^3+81 \log ^2(2)+\log ^2(512)-\log (512) \log (262144)-\log (18014398509481984)\right )}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\int \frac {\left (9 x+x^3+\log (512)\right ) \left (9 x+2 x^2+x^3+\log (512)\right )}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [F]  time = 0.55, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(81*x^2 + 18*x^4 + x^6 + (162*x + 18*x^3)*Log[2] + 81*Log[2]^2 + (-81*x^2 - 18*x^3 - 18*x^4 - 2*x^5
- x^6 + (-162*x - 18*x^2 - 18*x^3)*Log[2] - 81*Log[2]^2)*Log[x] + (18*x^3 + x^4 + 2*x^5 + 18*x^2*Log[2])*Log[x
]^2 - x^4*Log[x]^3 + (27*x + 78*x^2 + 9*x^3 + 18*x^4 + x^6 + (162*x + 18*x^3)*Log[2] + 81*Log[2]^2 + (-6*x^2 -
18*x^3 - 2*x^5 - 18*x^2*Log[2])*Log[x] + x^4*Log[x]^2)/E^(3/(-9*x - x^3 - 9*Log[2] + x^2*Log[x])))/(81*x^4 +
18*x^6 + x^8 + (162*x^3 + 18*x^5)*Log[2] + 81*x^2*Log[2]^2 + (-18*x^5 - 2*x^7 - 18*x^4*Log[2])*Log[x] + x^6*Lo
g[x]^2),x]

[Out]

Integrate[(81*x^2 + 18*x^4 + x^6 + (162*x + 18*x^3)*Log[2] + 81*Log[2]^2 + (-81*x^2 - 18*x^3 - 18*x^4 - 2*x^5
- x^6 + (-162*x - 18*x^2 - 18*x^3)*Log[2] - 81*Log[2]^2)*Log[x] + (18*x^3 + x^4 + 2*x^5 + 18*x^2*Log[2])*Log[x
]^2 - x^4*Log[x]^3 + (27*x + 78*x^2 + 9*x^3 + 18*x^4 + x^6 + (162*x + 18*x^3)*Log[2] + 81*Log[2]^2 + (-6*x^2 -
18*x^3 - 2*x^5 - 18*x^2*Log[2])*Log[x] + x^4*Log[x]^2)/E^(3/(-9*x - x^3 - 9*Log[2] + x^2*Log[x])))/(81*x^4 +
18*x^6 + x^8 + (162*x^3 + 18*x^5)*Log[2] + 81*x^2*Log[2]^2 + (-18*x^5 - 2*x^7 - 18*x^4*Log[2])*Log[x] + x^6*Lo
g[x]^2), x]

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fricas [A]  time = 1.53, size = 33, normalized size = 0.97 \begin {gather*} -\frac {e^{\left (\frac {3}{x^{3} - x^{2} \log \relax (x) + 9 \, x + 9 \, \log \relax (2)}\right )} - \log \relax (x)}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^4*log(x)^2+(-18*x^2*log(2)-2*x^5-18*x^3-6*x^2)*log(x)+81*log(2)^2+(18*x^3+162*x)*log(2)+x^6+18*x
^4+9*x^3+78*x^2+27*x)*exp(-3/(x^2*log(x)-9*log(2)-x^3-9*x))-x^4*log(x)^3+(18*x^2*log(2)+2*x^5+x^4+18*x^3)*log(
x)^2+(-81*log(2)^2+(-18*x^3-18*x^2-162*x)*log(2)-x^6-2*x^5-18*x^4-18*x^3-81*x^2)*log(x)+81*log(2)^2+(18*x^3+16
2*x)*log(2)+x^6+18*x^4+81*x^2)/(x^6*log(x)^2+(-18*x^4*log(2)-2*x^7-18*x^5)*log(x)+81*x^2*log(2)^2+(18*x^5+162*
x^3)*log(2)+x^8+18*x^6+81*x^4),x, algorithm="fricas")

[Out]

-(e^(3/(x^3 - x^2*log(x) + 9*x + 9*log(2))) - log(x))/x

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giac [A]  time = 1.85, size = 63, normalized size = 1.85 \begin {gather*} -\frac {e^{\left (-\frac {x^{3} - x^{2} \log \relax (x) + 9 \, x}{3 \, {\left (x^{3} \log \relax (2) - x^{2} \log \relax (2) \log \relax (x) + 9 \, x \log \relax (2) + 9 \, \log \relax (2)^{2}\right )}} + \frac {1}{3 \, \log \relax (2)}\right )} - \log \relax (x)}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^4*log(x)^2+(-18*x^2*log(2)-2*x^5-18*x^3-6*x^2)*log(x)+81*log(2)^2+(18*x^3+162*x)*log(2)+x^6+18*x
^4+9*x^3+78*x^2+27*x)*exp(-3/(x^2*log(x)-9*log(2)-x^3-9*x))-x^4*log(x)^3+(18*x^2*log(2)+2*x^5+x^4+18*x^3)*log(
x)^2+(-81*log(2)^2+(-18*x^3-18*x^2-162*x)*log(2)-x^6-2*x^5-18*x^4-18*x^3-81*x^2)*log(x)+81*log(2)^2+(18*x^3+16
2*x)*log(2)+x^6+18*x^4+81*x^2)/(x^6*log(x)^2+(-18*x^4*log(2)-2*x^7-18*x^5)*log(x)+81*x^2*log(2)^2+(18*x^5+162*
x^3)*log(2)+x^8+18*x^6+81*x^4),x, algorithm="giac")

[Out]

-(e^(-1/3*(x^3 - x^2*log(x) + 9*x)/(x^3*log(2) - x^2*log(2)*log(x) + 9*x*log(2) + 9*log(2)^2) + 1/3/log(2)) -
log(x))/x

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maple [A]  time = 0.08, size = 36, normalized size = 1.06

method	result	size
risch	\(\frac {\ln \relax (x )}{x}-\frac {{\mathrm e}^{\frac {3}{-x^{2} \ln \relax (x )+9 \ln \relax (2)+x^{3}+9 x}}}{x}\)	\(36\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((x^4*ln(x)^2+(-18*x^2*ln(2)-2*x^5-18*x^3-6*x^2)*ln(x)+81*ln(2)^2+(18*x^3+162*x)*ln(2)+x^6+18*x^4+9*x^3+78
*x^2+27*x)*exp(-3/(x^2*ln(x)-9*ln(2)-x^3-9*x))-x^4*ln(x)^3+(18*x^2*ln(2)+2*x^5+x^4+18*x^3)*ln(x)^2+(-81*ln(2)^
2+(-18*x^3-18*x^2-162*x)*ln(2)-x^6-2*x^5-18*x^4-18*x^3-81*x^2)*ln(x)+81*ln(2)^2+(18*x^3+162*x)*ln(2)+x^6+18*x^
4+81*x^2)/(x^6*ln(x)^2+(-18*x^4*ln(2)-2*x^7-18*x^5)*ln(x)+81*x^2*ln(2)^2+(18*x^5+162*x^3)*ln(2)+x^8+18*x^6+81*
x^4),x,method=_RETURNVERBOSE)

[Out]

ln(x)/x-1/x*exp(3/(-x^2*ln(x)+9*ln(2)+x^3+9*x))

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maxima [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^4*log(x)^2+(-18*x^2*log(2)-2*x^5-18*x^3-6*x^2)*log(x)+81*log(2)^2+(18*x^3+162*x)*log(2)+x^6+18*x
^4+9*x^3+78*x^2+27*x)*exp(-3/(x^2*log(x)-9*log(2)-x^3-9*x))-x^4*log(x)^3+(18*x^2*log(2)+2*x^5+x^4+18*x^3)*log(
x)^2+(-81*log(2)^2+(-18*x^3-18*x^2-162*x)*log(2)-x^6-2*x^5-18*x^4-18*x^3-81*x^2)*log(x)+81*log(2)^2+(18*x^3+16
2*x)*log(2)+x^6+18*x^4+81*x^2)/(x^6*log(x)^2+(-18*x^4*log(2)-2*x^7-18*x^5)*log(x)+81*x^2*log(2)^2+(18*x^5+162*
x^3)*log(2)+x^8+18*x^6+81*x^4),x, algorithm="maxima")

[Out]

Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  0which is not
of the expected type LIST

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {\ln \relax (2)\,\left (18\,x^3+162\,x\right )-x^4\,{\ln \relax (x)}^3+81\,{\ln \relax (2)}^2+81\,x^2+18\,x^4+x^6+{\ln \relax (x)}^2\,\left (2\,x^5+x^4+18\,x^3+18\,\ln \relax (2)\,x^2\right )-\ln \relax (x)\,\left (\ln \relax (2)\,\left (18\,x^3+18\,x^2+162\,x\right )+81\,{\ln \relax (2)}^2+81\,x^2+18\,x^3+18\,x^4+2\,x^5+x^6\right )+{\mathrm {e}}^{\frac {3}{9\,x+9\,\ln \relax (2)-x^2\,\ln \relax (x)+x^3}}\,\left (27\,x+\ln \relax (2)\,\left (18\,x^3+162\,x\right )+x^4\,{\ln \relax (x)}^2+81\,{\ln \relax (2)}^2+78\,x^2+9\,x^3+18\,x^4+x^6-\ln \relax (x)\,\left (18\,x^2\,\ln \relax (2)+6\,x^2+18\,x^3+2\,x^5\right )\right )}{81\,x^2\,{\ln \relax (2)}^2+x^6\,{\ln \relax (x)}^2+\ln \relax (2)\,\left (18\,x^5+162\,x^3\right )-\ln \relax (x)\,\left (2\,x^7+18\,x^5+18\,\ln \relax (2)\,x^4\right )+81\,x^4+18\,x^6+x^8} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(2)*(162*x + 18*x^3) - x^4*log(x)^3 + 81*log(2)^2 + 81*x^2 + 18*x^4 + x^6 + log(x)^2*(18*x^2*log(2) +
18*x^3 + x^4 + 2*x^5) - log(x)*(log(2)*(162*x + 18*x^2 + 18*x^3) + 81*log(2)^2 + 81*x^2 + 18*x^3 + 18*x^4 + 2*
x^5 + x^6) + exp(3/(9*x + 9*log(2) - x^2*log(x) + x^3))*(27*x + log(2)*(162*x + 18*x^3) + x^4*log(x)^2 + 81*lo
g(2)^2 + 78*x^2 + 9*x^3 + 18*x^4 + x^6 - log(x)*(18*x^2*log(2) + 6*x^2 + 18*x^3 + 2*x^5)))/(81*x^2*log(2)^2 +
x^6*log(x)^2 + log(2)*(162*x^3 + 18*x^5) - log(x)*(18*x^4*log(2) + 18*x^5 + 2*x^7) + 81*x^4 + 18*x^6 + x^8),x)

[Out]

int((log(2)*(162*x + 18*x^3) - x^4*log(x)^3 + 81*log(2)^2 + 81*x^2 + 18*x^4 + x^6 + log(x)^2*(18*x^2*log(2) +
18*x^3 + x^4 + 2*x^5) - log(x)*(log(2)*(162*x + 18*x^2 + 18*x^3) + 81*log(2)^2 + 81*x^2 + 18*x^3 + 18*x^4 + 2*
x^5 + x^6) + exp(3/(9*x + 9*log(2) - x^2*log(x) + x^3))*(27*x + log(2)*(162*x + 18*x^3) + x^4*log(x)^2 + 81*lo
g(2)^2 + 78*x^2 + 9*x^3 + 18*x^4 + x^6 - log(x)*(18*x^2*log(2) + 6*x^2 + 18*x^3 + 2*x^5)))/(81*x^2*log(2)^2 +
x^6*log(x)^2 + log(2)*(162*x^3 + 18*x^5) - log(x)*(18*x^4*log(2) + 18*x^5 + 2*x^7) + 81*x^4 + 18*x^6 + x^8), x
)

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sympy [A]  time = 0.92, size = 29, normalized size = 0.85 \begin {gather*} \frac {\log {\relax (x )}}{x} - \frac {e^{- \frac {3}{- x^{3} + x^{2} \log {\relax (x )} - 9 x - 9 \log {\relax (2 )}}}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x**4*ln(x)**2+(-18*x**2*ln(2)-2*x**5-18*x**3-6*x**2)*ln(x)+81*ln(2)**2+(18*x**3+162*x)*ln(2)+x**6+
18*x**4+9*x**3+78*x**2+27*x)*exp(-3/(x**2*ln(x)-9*ln(2)-x**3-9*x))-x**4*ln(x)**3+(18*x**2*ln(2)+2*x**5+x**4+18
*x**3)*ln(x)**2+(-81*ln(2)**2+(-18*x**3-18*x**2-162*x)*ln(2)-x**6-2*x**5-18*x**4-18*x**3-81*x**2)*ln(x)+81*ln(
2)**2+(18*x**3+162*x)*ln(2)+x**6+18*x**4+81*x**2)/(x**6*ln(x)**2+(-18*x**4*ln(2)-2*x**7-18*x**5)*ln(x)+81*x**2
*ln(2)**2+(18*x**5+162*x**3)*ln(2)+x**8+18*x**6+81*x**4),x)

[Out]

log(x)/x - exp(-3/(-x**3 + x**2*log(x) - 9*x - 9*log(2)))/x

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