3.101.79 \(\int \frac {-16+136 x-248 x^2-96 x^3-256 x^4+(24-120 x+160 x^2-256 x^3) \log (x)+(-8 x+32 x^2+(-8+32 x) \log (x)) \log (x+\log (x))}{-1594323 x^4+2657205 x^5-1771470 x^6+590490 x^7-98415 x^8+6561 x^9+(-1594323 x^3+2657205 x^4-1771470 x^5+590490 x^6-98415 x^7+6561 x^8) \log (x)+(2657205 x^4-3542940 x^5+1771470 x^6-393660 x^7+32805 x^8+(2657205 x^3-3542940 x^4+1771470 x^5-393660 x^6+32805 x^7) \log (x)) \log (x+\log (x))+(-1771470 x^4+1771470 x^5-590490 x^6+65610 x^7+(-1771470 x^3+1771470 x^4-590490 x^5+65610 x^6) \log (x)) \log ^2(x+\log (x))+(590490 x^4-393660 x^5+65610 x^6+(590490 x^3-393660 x^4+65610 x^5) \log (x)) \log ^3(x+\log (x))+(-98415 x^4+32805 x^5+(-98415 x^3+32805 x^4) \log (x)) \log ^4(x+\log (x))+(6561 x^4+6561 x^3 \log (x)) \log ^5(x+\log (x))} \, dx\)

Optimal. Leaf size=24 \[ \frac {(-2+8 x)^2}{6561 x^2 (-3+x+\log (x+\log (x)))^4} \]

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Rubi [F]  time = 5.86, 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 {-16+136 x-248 x^2-96 x^3-256 x^4+\left (24-120 x+160 x^2-256 x^3\right ) \log (x)+\left (-8 x+32 x^2+(-8+32 x) \log (x)\right ) \log (x+\log (x))}{-1594323 x^4+2657205 x^5-1771470 x^6+590490 x^7-98415 x^8+6561 x^9+\left (-1594323 x^3+2657205 x^4-1771470 x^5+590490 x^6-98415 x^7+6561 x^8\right ) \log (x)+\left (2657205 x^4-3542940 x^5+1771470 x^6-393660 x^7+32805 x^8+\left (2657205 x^3-3542940 x^4+1771470 x^5-393660 x^6+32805 x^7\right ) \log (x)\right ) \log (x+\log (x))+\left (-1771470 x^4+1771470 x^5-590490 x^6+65610 x^7+\left (-1771470 x^3+1771470 x^4-590490 x^5+65610 x^6\right ) \log (x)\right ) \log ^2(x+\log (x))+\left (590490 x^4-393660 x^5+65610 x^6+\left (590490 x^3-393660 x^4+65610 x^5\right ) \log (x)\right ) \log ^3(x+\log (x))+\left (-98415 x^4+32805 x^5+\left (-98415 x^3+32805 x^4\right ) \log (x)\right ) \log ^4(x+\log (x))+\left (6561 x^4+6561 x^3 \log (x)\right ) \log ^5(x+\log (x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-16 + 136*x - 248*x^2 - 96*x^3 - 256*x^4 + (24 - 120*x + 160*x^2 - 256*x^3)*Log[x] + (-8*x + 32*x^2 + (-8
+ 32*x)*Log[x])*Log[x + Log[x]])/(-1594323*x^4 + 2657205*x^5 - 1771470*x^6 + 590490*x^7 - 98415*x^8 + 6561*x^
9 + (-1594323*x^3 + 2657205*x^4 - 1771470*x^5 + 590490*x^6 - 98415*x^7 + 6561*x^8)*Log[x] + (2657205*x^4 - 354
2940*x^5 + 1771470*x^6 - 393660*x^7 + 32805*x^8 + (2657205*x^3 - 3542940*x^4 + 1771470*x^5 - 393660*x^6 + 3280
5*x^7)*Log[x])*Log[x + Log[x]] + (-1771470*x^4 + 1771470*x^5 - 590490*x^6 + 65610*x^7 + (-1771470*x^3 + 177147
0*x^4 - 590490*x^5 + 65610*x^6)*Log[x])*Log[x + Log[x]]^2 + (590490*x^4 - 393660*x^5 + 65610*x^6 + (590490*x^3
- 393660*x^4 + 65610*x^5)*Log[x])*Log[x + Log[x]]^3 + (-98415*x^4 + 32805*x^5 + (-98415*x^3 + 32805*x^4)*Log[
x])*Log[x + Log[x]]^4 + (6561*x^4 + 6561*x^3*Log[x])*Log[x + Log[x]]^5),x]

[Out]

64/(6561*(3 - x - Log[x + Log[x]])^4) + (128*Defer[Int][1/((x + Log[x])*(-3 + x + Log[x + Log[x]])^5), x])/656
1 - (16*Defer[Int][1/(x^3*(x + Log[x])*(-3 + x + Log[x + Log[x]])^5), x])/6561 + (112*Defer[Int][1/(x^2*(x + L
og[x])*(-3 + x + Log[x + Log[x]])^5), x])/6561 + (112*Defer[Int][1/(x*(x + Log[x])*(-3 + x + Log[x + Log[x]])^
5), x])/6561 - (16*Defer[Int][Log[x]/(x^2*(x + Log[x])*(-3 + x + Log[x + Log[x]])^5), x])/6561 + (128*Defer[In
t][Log[x]/(x*(x + Log[x])*(-3 + x + Log[x + Log[x]])^5), x])/6561 - (8*Defer[Int][1/(x^3*(-3 + x + Log[x + Log
[x]])^4), x])/6561 + (32*Defer[Int][1/(x^2*(-3 + x + Log[x + Log[x]])^4), x])/6561

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {8 (1-4 x) \left (2-9 x-5 x^2-8 x^3-\log (x) \left (3-3 x+8 x^2-\log (x+\log (x))\right )+x \log (x+\log (x))\right )}{6561 x^3 (x+\log (x)) (3-x-\log (x+\log (x)))^5} \, dx\\ &=\frac {8 \int \frac {(1-4 x) \left (2-9 x-5 x^2-8 x^3-\log (x) \left (3-3 x+8 x^2-\log (x+\log (x))\right )+x \log (x+\log (x))\right )}{x^3 (x+\log (x)) (3-x-\log (x+\log (x)))^5} \, dx}{6561}\\ &=\frac {8 \int \left (-\frac {2 (-1+4 x)^2 \left (1+x+x^2+x \log (x)\right )}{x^3 (x+\log (x)) (-3+x+\log (x+\log (x)))^5}+\frac {-1+4 x}{x^3 (-3+x+\log (x+\log (x)))^4}\right ) \, dx}{6561}\\ &=\frac {8 \int \frac {-1+4 x}{x^3 (-3+x+\log (x+\log (x)))^4} \, dx}{6561}-\frac {16 \int \frac {(-1+4 x)^2 \left (1+x+x^2+x \log (x)\right )}{x^3 (x+\log (x)) (-3+x+\log (x+\log (x)))^5} \, dx}{6561}\\ &=\frac {8 \int \left (-\frac {1}{x^3 (-3+x+\log (x+\log (x)))^4}+\frac {4}{x^2 (-3+x+\log (x+\log (x)))^4}\right ) \, dx}{6561}-\frac {16 \int \left (\frac {1+x+x^2+x \log (x)}{x^3 (x+\log (x)) (-3+x+\log (x+\log (x)))^5}-\frac {8 \left (1+x+x^2+x \log (x)\right )}{x^2 (x+\log (x)) (-3+x+\log (x+\log (x)))^5}+\frac {16 \left (1+x+x^2+x \log (x)\right )}{x (x+\log (x)) (-3+x+\log (x+\log (x)))^5}\right ) \, dx}{6561}\\ &=-\frac {8 \int \frac {1}{x^3 (-3+x+\log (x+\log (x)))^4} \, dx}{6561}-\frac {16 \int \frac {1+x+x^2+x \log (x)}{x^3 (x+\log (x)) (-3+x+\log (x+\log (x)))^5} \, dx}{6561}+\frac {32 \int \frac {1}{x^2 (-3+x+\log (x+\log (x)))^4} \, dx}{6561}+\frac {128 \int \frac {1+x+x^2+x \log (x)}{x^2 (x+\log (x)) (-3+x+\log (x+\log (x)))^5} \, dx}{6561}-\frac {256 \int \frac {1+x+x^2+x \log (x)}{x (x+\log (x)) (-3+x+\log (x+\log (x)))^5} \, dx}{6561}\\ &=\frac {64}{6561 (3-x-\log (x+\log (x)))^4}-\frac {8 \int \frac {1}{x^3 (-3+x+\log (x+\log (x)))^4} \, dx}{6561}-\frac {16 \int \left (\frac {1}{x^3 (x+\log (x)) (-3+x+\log (x+\log (x)))^5}+\frac {1}{x^2 (x+\log (x)) (-3+x+\log (x+\log (x)))^5}+\frac {1}{x (x+\log (x)) (-3+x+\log (x+\log (x)))^5}+\frac {\log (x)}{x^2 (x+\log (x)) (-3+x+\log (x+\log (x)))^5}\right ) \, dx}{6561}+\frac {32 \int \frac {1}{x^2 (-3+x+\log (x+\log (x)))^4} \, dx}{6561}+\frac {128 \int \left (\frac {1}{(x+\log (x)) (-3+x+\log (x+\log (x)))^5}+\frac {1}{x^2 (x+\log (x)) (-3+x+\log (x+\log (x)))^5}+\frac {1}{x (x+\log (x)) (-3+x+\log (x+\log (x)))^5}+\frac {\log (x)}{x (x+\log (x)) (-3+x+\log (x+\log (x)))^5}\right ) \, dx}{6561}\\ &=\frac {64}{6561 (3-x-\log (x+\log (x)))^4}-\frac {8 \int \frac {1}{x^3 (-3+x+\log (x+\log (x)))^4} \, dx}{6561}-\frac {16 \int \frac {1}{x^3 (x+\log (x)) (-3+x+\log (x+\log (x)))^5} \, dx}{6561}-\frac {16 \int \frac {1}{x^2 (x+\log (x)) (-3+x+\log (x+\log (x)))^5} \, dx}{6561}-\frac {16 \int \frac {1}{x (x+\log (x)) (-3+x+\log (x+\log (x)))^5} \, dx}{6561}-\frac {16 \int \frac {\log (x)}{x^2 (x+\log (x)) (-3+x+\log (x+\log (x)))^5} \, dx}{6561}+\frac {32 \int \frac {1}{x^2 (-3+x+\log (x+\log (x)))^4} \, dx}{6561}+\frac {128 \int \frac {1}{(x+\log (x)) (-3+x+\log (x+\log (x)))^5} \, dx}{6561}+\frac {128 \int \frac {1}{x^2 (x+\log (x)) (-3+x+\log (x+\log (x)))^5} \, dx}{6561}+\frac {128 \int \frac {1}{x (x+\log (x)) (-3+x+\log (x+\log (x)))^5} \, dx}{6561}+\frac {128 \int \frac {\log (x)}{x (x+\log (x)) (-3+x+\log (x+\log (x)))^5} \, dx}{6561}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 5.07, size = 24, normalized size = 1.00 \begin {gather*} \frac {4 (-1+4 x)^2}{6561 x^2 (-3+x+\log (x+\log (x)))^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-16 + 136*x - 248*x^2 - 96*x^3 - 256*x^4 + (24 - 120*x + 160*x^2 - 256*x^3)*Log[x] + (-8*x + 32*x^2
+ (-8 + 32*x)*Log[x])*Log[x + Log[x]])/(-1594323*x^4 + 2657205*x^5 - 1771470*x^6 + 590490*x^7 - 98415*x^8 + 6
561*x^9 + (-1594323*x^3 + 2657205*x^4 - 1771470*x^5 + 590490*x^6 - 98415*x^7 + 6561*x^8)*Log[x] + (2657205*x^4
- 3542940*x^5 + 1771470*x^6 - 393660*x^7 + 32805*x^8 + (2657205*x^3 - 3542940*x^4 + 1771470*x^5 - 393660*x^6
+ 32805*x^7)*Log[x])*Log[x + Log[x]] + (-1771470*x^4 + 1771470*x^5 - 590490*x^6 + 65610*x^7 + (-1771470*x^3 +
1771470*x^4 - 590490*x^5 + 65610*x^6)*Log[x])*Log[x + Log[x]]^2 + (590490*x^4 - 393660*x^5 + 65610*x^6 + (5904
90*x^3 - 393660*x^4 + 65610*x^5)*Log[x])*Log[x + Log[x]]^3 + (-98415*x^4 + 32805*x^5 + (-98415*x^3 + 32805*x^4
)*Log[x])*Log[x + Log[x]]^4 + (6561*x^4 + 6561*x^3*Log[x])*Log[x + Log[x]]^5),x]

[Out]

(4*(-1 + 4*x)^2)/(6561*x^2*(-3 + x + Log[x + Log[x]])^4)

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fricas [B]  time = 0.72, size = 116, normalized size = 4.83 \begin {gather*} \frac {4 \, {\left (16 \, x^{2} - 8 \, x + 1\right )}}{6561 \, {\left (x^{6} + x^{2} \log \left (x + \log \relax (x)\right )^{4} - 12 \, x^{5} + 54 \, x^{4} + 4 \, {\left (x^{3} - 3 \, x^{2}\right )} \log \left (x + \log \relax (x)\right )^{3} - 108 \, x^{3} + 6 \, {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} \log \left (x + \log \relax (x)\right )^{2} + 81 \, x^{2} + 4 \, {\left (x^{5} - 9 \, x^{4} + 27 \, x^{3} - 27 \, x^{2}\right )} \log \left (x + \log \relax (x)\right )\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((32*x-8)*log(x)+32*x^2-8*x)*log(x+log(x))+(-256*x^3+160*x^2-120*x+24)*log(x)-256*x^4-96*x^3-248*x^
2+136*x-16)/((6561*x^3*log(x)+6561*x^4)*log(x+log(x))^5+((32805*x^4-98415*x^3)*log(x)+32805*x^5-98415*x^4)*log
(x+log(x))^4+((65610*x^5-393660*x^4+590490*x^3)*log(x)+65610*x^6-393660*x^5+590490*x^4)*log(x+log(x))^3+((6561
0*x^6-590490*x^5+1771470*x^4-1771470*x^3)*log(x)+65610*x^7-590490*x^6+1771470*x^5-1771470*x^4)*log(x+log(x))^2
+((32805*x^7-393660*x^6+1771470*x^5-3542940*x^4+2657205*x^3)*log(x)+32805*x^8-393660*x^7+1771470*x^6-3542940*x
^5+2657205*x^4)*log(x+log(x))+(6561*x^8-98415*x^7+590490*x^6-1771470*x^5+2657205*x^4-1594323*x^3)*log(x)+6561*
x^9-98415*x^8+590490*x^7-1771470*x^6+2657205*x^5-1594323*x^4),x, algorithm="fricas")

[Out]

4/6561*(16*x^2 - 8*x + 1)/(x^6 + x^2*log(x + log(x))^4 - 12*x^5 + 54*x^4 + 4*(x^3 - 3*x^2)*log(x + log(x))^3 -
108*x^3 + 6*(x^4 - 6*x^3 + 9*x^2)*log(x + log(x))^2 + 81*x^2 + 4*(x^5 - 9*x^4 + 27*x^3 - 27*x^2)*log(x + log(
x)))

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giac [B]  time = 2.37, size = 432, normalized size = 18.00 \begin {gather*} \frac {4 \, {\left (16 \, x^{4} + 16 \, x^{3} \log \relax (x) + 8 \, x^{3} - 8 \, x^{2} \log \relax (x) + 9 \, x^{2} + x \log \relax (x) - 7 \, x + 1\right )}}{6561 \, {\left (x^{8} + 4 \, x^{7} \log \left (x + \log \relax (x)\right ) + 6 \, x^{6} \log \left (x + \log \relax (x)\right )^{2} + 4 \, x^{5} \log \left (x + \log \relax (x)\right )^{3} + x^{4} \log \left (x + \log \relax (x)\right )^{4} + x^{7} \log \relax (x) + 4 \, x^{6} \log \left (x + \log \relax (x)\right ) \log \relax (x) + 6 \, x^{5} \log \left (x + \log \relax (x)\right )^{2} \log \relax (x) + 4 \, x^{4} \log \left (x + \log \relax (x)\right )^{3} \log \relax (x) + x^{3} \log \left (x + \log \relax (x)\right )^{4} \log \relax (x) - 11 \, x^{7} - 32 \, x^{6} \log \left (x + \log \relax (x)\right ) - 30 \, x^{5} \log \left (x + \log \relax (x)\right )^{2} - 8 \, x^{4} \log \left (x + \log \relax (x)\right )^{3} + x^{3} \log \left (x + \log \relax (x)\right )^{4} - 12 \, x^{6} \log \relax (x) - 36 \, x^{5} \log \left (x + \log \relax (x)\right ) \log \relax (x) - 36 \, x^{4} \log \left (x + \log \relax (x)\right )^{2} \log \relax (x) - 12 \, x^{3} \log \left (x + \log \relax (x)\right )^{3} \log \relax (x) + 43 \, x^{6} + 76 \, x^{5} \log \left (x + \log \relax (x)\right ) + 24 \, x^{4} \log \left (x + \log \relax (x)\right )^{2} - 8 \, x^{3} \log \left (x + \log \relax (x)\right )^{3} + x^{2} \log \left (x + \log \relax (x)\right )^{4} + 54 \, x^{5} \log \relax (x) + 108 \, x^{4} \log \left (x + \log \relax (x)\right ) \log \relax (x) + 54 \, x^{3} \log \left (x + \log \relax (x)\right )^{2} \log \relax (x) - 66 \, x^{5} - 36 \, x^{4} \log \left (x + \log \relax (x)\right ) + 18 \, x^{3} \log \left (x + \log \relax (x)\right )^{2} - 12 \, x^{2} \log \left (x + \log \relax (x)\right )^{3} - 108 \, x^{4} \log \relax (x) - 108 \, x^{3} \log \left (x + \log \relax (x)\right ) \log \relax (x) + 27 \, x^{4} + 54 \, x^{2} \log \left (x + \log \relax (x)\right )^{2} + 81 \, x^{3} \log \relax (x) - 27 \, x^{3} - 108 \, x^{2} \log \left (x + \log \relax (x)\right ) + 81 \, x^{2}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((32*x-8)*log(x)+32*x^2-8*x)*log(x+log(x))+(-256*x^3+160*x^2-120*x+24)*log(x)-256*x^4-96*x^3-248*x^
2+136*x-16)/((6561*x^3*log(x)+6561*x^4)*log(x+log(x))^5+((32805*x^4-98415*x^3)*log(x)+32805*x^5-98415*x^4)*log
(x+log(x))^4+((65610*x^5-393660*x^4+590490*x^3)*log(x)+65610*x^6-393660*x^5+590490*x^4)*log(x+log(x))^3+((6561
0*x^6-590490*x^5+1771470*x^4-1771470*x^3)*log(x)+65610*x^7-590490*x^6+1771470*x^5-1771470*x^4)*log(x+log(x))^2
+((32805*x^7-393660*x^6+1771470*x^5-3542940*x^4+2657205*x^3)*log(x)+32805*x^8-393660*x^7+1771470*x^6-3542940*x
^5+2657205*x^4)*log(x+log(x))+(6561*x^8-98415*x^7+590490*x^6-1771470*x^5+2657205*x^4-1594323*x^3)*log(x)+6561*
x^9-98415*x^8+590490*x^7-1771470*x^6+2657205*x^5-1594323*x^4),x, algorithm="giac")

[Out]

4/6561*(16*x^4 + 16*x^3*log(x) + 8*x^3 - 8*x^2*log(x) + 9*x^2 + x*log(x) - 7*x + 1)/(x^8 + 4*x^7*log(x + log(x
)) + 6*x^6*log(x + log(x))^2 + 4*x^5*log(x + log(x))^3 + x^4*log(x + log(x))^4 + x^7*log(x) + 4*x^6*log(x + lo
g(x))*log(x) + 6*x^5*log(x + log(x))^2*log(x) + 4*x^4*log(x + log(x))^3*log(x) + x^3*log(x + log(x))^4*log(x)
- 11*x^7 - 32*x^6*log(x + log(x)) - 30*x^5*log(x + log(x))^2 - 8*x^4*log(x + log(x))^3 + x^3*log(x + log(x))^4
- 12*x^6*log(x) - 36*x^5*log(x + log(x))*log(x) - 36*x^4*log(x + log(x))^2*log(x) - 12*x^3*log(x + log(x))^3*
log(x) + 43*x^6 + 76*x^5*log(x + log(x)) + 24*x^4*log(x + log(x))^2 - 8*x^3*log(x + log(x))^3 + x^2*log(x + lo
g(x))^4 + 54*x^5*log(x) + 108*x^4*log(x + log(x))*log(x) + 54*x^3*log(x + log(x))^2*log(x) - 66*x^5 - 36*x^4*l
og(x + log(x)) + 18*x^3*log(x + log(x))^2 - 12*x^2*log(x + log(x))^3 - 108*x^4*log(x) - 108*x^3*log(x + log(x)
)*log(x) + 27*x^4 + 54*x^2*log(x + log(x))^2 + 81*x^3*log(x) - 27*x^3 - 108*x^2*log(x + log(x)) + 81*x^2)

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maple [A]  time = 0.05, size = 26, normalized size = 1.08

method	result	size
risch	\(\frac {\frac {64}{6561} x^{2}-\frac {32}{6561} x +\frac {4}{6561}}{x^{2} \left (x +\ln \left (x +\ln \relax (x )\right )-3\right )^{4}}\)	\(26\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((32*x-8)*ln(x)+32*x^2-8*x)*ln(x+ln(x))+(-256*x^3+160*x^2-120*x+24)*ln(x)-256*x^4-96*x^3-248*x^2+136*x-16
)/((6561*x^3*ln(x)+6561*x^4)*ln(x+ln(x))^5+((32805*x^4-98415*x^3)*ln(x)+32805*x^5-98415*x^4)*ln(x+ln(x))^4+((6
5610*x^5-393660*x^4+590490*x^3)*ln(x)+65610*x^6-393660*x^5+590490*x^4)*ln(x+ln(x))^3+((65610*x^6-590490*x^5+17
71470*x^4-1771470*x^3)*ln(x)+65610*x^7-590490*x^6+1771470*x^5-1771470*x^4)*ln(x+ln(x))^2+((32805*x^7-393660*x^
6+1771470*x^5-3542940*x^4+2657205*x^3)*ln(x)+32805*x^8-393660*x^7+1771470*x^6-3542940*x^5+2657205*x^4)*ln(x+ln
(x))+(6561*x^8-98415*x^7+590490*x^6-1771470*x^5+2657205*x^4-1594323*x^3)*ln(x)+6561*x^9-98415*x^8+590490*x^7-1
771470*x^6+2657205*x^5-1594323*x^4),x,method=_RETURNVERBOSE)

[Out]

4/6561*(16*x^2-8*x+1)/x^2/(x+ln(x+ln(x))-3)^4

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maxima [B]  time = 0.58, size = 116, normalized size = 4.83 \begin {gather*} \frac {4 \, {\left (16 \, x^{2} - 8 \, x + 1\right )}}{6561 \, {\left (x^{6} + x^{2} \log \left (x + \log \relax (x)\right )^{4} - 12 \, x^{5} + 54 \, x^{4} + 4 \, {\left (x^{3} - 3 \, x^{2}\right )} \log \left (x + \log \relax (x)\right )^{3} - 108 \, x^{3} + 6 \, {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} \log \left (x + \log \relax (x)\right )^{2} + 81 \, x^{2} + 4 \, {\left (x^{5} - 9 \, x^{4} + 27 \, x^{3} - 27 \, x^{2}\right )} \log \left (x + \log \relax (x)\right )\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((32*x-8)*log(x)+32*x^2-8*x)*log(x+log(x))+(-256*x^3+160*x^2-120*x+24)*log(x)-256*x^4-96*x^3-248*x^
2+136*x-16)/((6561*x^3*log(x)+6561*x^4)*log(x+log(x))^5+((32805*x^4-98415*x^3)*log(x)+32805*x^5-98415*x^4)*log
(x+log(x))^4+((65610*x^5-393660*x^4+590490*x^3)*log(x)+65610*x^6-393660*x^5+590490*x^4)*log(x+log(x))^3+((6561
0*x^6-590490*x^5+1771470*x^4-1771470*x^3)*log(x)+65610*x^7-590490*x^6+1771470*x^5-1771470*x^4)*log(x+log(x))^2
+((32805*x^7-393660*x^6+1771470*x^5-3542940*x^4+2657205*x^3)*log(x)+32805*x^8-393660*x^7+1771470*x^6-3542940*x
^5+2657205*x^4)*log(x+log(x))+(6561*x^8-98415*x^7+590490*x^6-1771470*x^5+2657205*x^4-1594323*x^3)*log(x)+6561*
x^9-98415*x^8+590490*x^7-1771470*x^6+2657205*x^5-1594323*x^4),x, algorithm="maxima")

[Out]

4/6561*(16*x^2 - 8*x + 1)/(x^6 + x^2*log(x + log(x))^4 - 12*x^5 + 54*x^4 + 4*(x^3 - 3*x^2)*log(x + log(x))^3 -
108*x^3 + 6*(x^4 - 6*x^3 + 9*x^2)*log(x + log(x))^2 + 81*x^2 + 4*(x^5 - 9*x^4 + 27*x^3 - 27*x^2)*log(x + log(
x)))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {248\,x^2-\ln \left (x+\ln \relax (x)\right )\,\left (\ln \relax (x)\,\left (32\,x-8\right )-8\,x+32\,x^2\right )-136\,x+96\,x^3+256\,x^4+\ln \relax (x)\,\left (256\,x^3-160\,x^2+120\,x-24\right )+16}{{\ln \left (x+\ln \relax (x)\right )}^3\,\left (\ln \relax (x)\,\left (65610\,x^5-393660\,x^4+590490\,x^3\right )+590490\,x^4-393660\,x^5+65610\,x^6\right )+{\ln \left (x+\ln \relax (x)\right )}^5\,\left (6561\,x^3\,\ln \relax (x)+6561\,x^4\right )-{\ln \left (x+\ln \relax (x)\right )}^2\,\left (\ln \relax (x)\,\left (-65610\,x^6+590490\,x^5-1771470\,x^4+1771470\,x^3\right )+1771470\,x^4-1771470\,x^5+590490\,x^6-65610\,x^7\right )+\ln \left (x+\ln \relax (x)\right )\,\left (\ln \relax (x)\,\left (32805\,x^7-393660\,x^6+1771470\,x^5-3542940\,x^4+2657205\,x^3\right )+2657205\,x^4-3542940\,x^5+1771470\,x^6-393660\,x^7+32805\,x^8\right )-{\ln \left (x+\ln \relax (x)\right )}^4\,\left (\ln \relax (x)\,\left (98415\,x^3-32805\,x^4\right )+98415\,x^4-32805\,x^5\right )-1594323\,x^4+2657205\,x^5-1771470\,x^6+590490\,x^7-98415\,x^8+6561\,x^9-\ln \relax (x)\,\left (-6561\,x^8+98415\,x^7-590490\,x^6+1771470\,x^5-2657205\,x^4+1594323\,x^3\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(248*x^2 - log(x + log(x))*(log(x)*(32*x - 8) - 8*x + 32*x^2) - 136*x + 96*x^3 + 256*x^4 + log(x)*(120*x
- 160*x^2 + 256*x^3 - 24) + 16)/(log(x + log(x))^3*(log(x)*(590490*x^3 - 393660*x^4 + 65610*x^5) + 590490*x^4
- 393660*x^5 + 65610*x^6) + log(x + log(x))^5*(6561*x^3*log(x) + 6561*x^4) - log(x + log(x))^2*(log(x)*(177147
0*x^3 - 1771470*x^4 + 590490*x^5 - 65610*x^6) + 1771470*x^4 - 1771470*x^5 + 590490*x^6 - 65610*x^7) + log(x +
log(x))*(log(x)*(2657205*x^3 - 3542940*x^4 + 1771470*x^5 - 393660*x^6 + 32805*x^7) + 2657205*x^4 - 3542940*x^5
+ 1771470*x^6 - 393660*x^7 + 32805*x^8) - log(x + log(x))^4*(log(x)*(98415*x^3 - 32805*x^4) + 98415*x^4 - 328
05*x^5) - 1594323*x^4 + 2657205*x^5 - 1771470*x^6 + 590490*x^7 - 98415*x^8 + 6561*x^9 - log(x)*(1594323*x^3 -
2657205*x^4 + 1771470*x^5 - 590490*x^6 + 98415*x^7 - 6561*x^8)),x)

[Out]

int(-(248*x^2 - log(x + log(x))*(log(x)*(32*x - 8) - 8*x + 32*x^2) - 136*x + 96*x^3 + 256*x^4 + log(x)*(120*x
- 160*x^2 + 256*x^3 - 24) + 16)/(log(x + log(x))^3*(log(x)*(590490*x^3 - 393660*x^4 + 65610*x^5) + 590490*x^4
- 393660*x^5 + 65610*x^6) + log(x + log(x))^5*(6561*x^3*log(x) + 6561*x^4) - log(x + log(x))^2*(log(x)*(177147
0*x^3 - 1771470*x^4 + 590490*x^5 - 65610*x^6) + 1771470*x^4 - 1771470*x^5 + 590490*x^6 - 65610*x^7) + log(x +
log(x))*(log(x)*(2657205*x^3 - 3542940*x^4 + 1771470*x^5 - 393660*x^6 + 32805*x^7) + 2657205*x^4 - 3542940*x^5
+ 1771470*x^6 - 393660*x^7 + 32805*x^8) - log(x + log(x))^4*(log(x)*(98415*x^3 - 32805*x^4) + 98415*x^4 - 328
05*x^5) - 1594323*x^4 + 2657205*x^5 - 1771470*x^6 + 590490*x^7 - 98415*x^8 + 6561*x^9 - log(x)*(1594323*x^3 -
2657205*x^4 + 1771470*x^5 - 590490*x^6 + 98415*x^7 - 6561*x^8)), x)

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sympy [B]  time = 0.70, size = 117, normalized size = 4.88 \begin {gather*} \frac {64 x^{2} - 32 x + 4}{6561 x^{6} - 78732 x^{5} + 354294 x^{4} - 708588 x^{3} + 6561 x^{2} \log {\left (x + \log {\relax (x )} \right )}^{4} + 531441 x^{2} + \left (26244 x^{3} - 78732 x^{2}\right ) \log {\left (x + \log {\relax (x )} \right )}^{3} + \left (39366 x^{4} - 236196 x^{3} + 354294 x^{2}\right ) \log {\left (x + \log {\relax (x )} \right )}^{2} + \left (26244 x^{5} - 236196 x^{4} + 708588 x^{3} - 708588 x^{2}\right ) \log {\left (x + \log {\relax (x )} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((32*x-8)*ln(x)+32*x**2-8*x)*ln(x+ln(x))+(-256*x**3+160*x**2-120*x+24)*ln(x)-256*x**4-96*x**3-248*x
**2+136*x-16)/((6561*x**3*ln(x)+6561*x**4)*ln(x+ln(x))**5+((32805*x**4-98415*x**3)*ln(x)+32805*x**5-98415*x**4
)*ln(x+ln(x))**4+((65610*x**5-393660*x**4+590490*x**3)*ln(x)+65610*x**6-393660*x**5+590490*x**4)*ln(x+ln(x))**
3+((65610*x**6-590490*x**5+1771470*x**4-1771470*x**3)*ln(x)+65610*x**7-590490*x**6+1771470*x**5-1771470*x**4)*
ln(x+ln(x))**2+((32805*x**7-393660*x**6+1771470*x**5-3542940*x**4+2657205*x**3)*ln(x)+32805*x**8-393660*x**7+1
771470*x**6-3542940*x**5+2657205*x**4)*ln(x+ln(x))+(6561*x**8-98415*x**7+590490*x**6-1771470*x**5+2657205*x**4
-1594323*x**3)*ln(x)+6561*x**9-98415*x**8+590490*x**7-1771470*x**6+2657205*x**5-1594323*x**4),x)

[Out]

(64*x**2 - 32*x + 4)/(6561*x**6 - 78732*x**5 + 354294*x**4 - 708588*x**3 + 6561*x**2*log(x + log(x))**4 + 5314
41*x**2 + (26244*x**3 - 78732*x**2)*log(x + log(x))**3 + (39366*x**4 - 236196*x**3 + 354294*x**2)*log(x + log(
x))**2 + (26244*x**5 - 236196*x**4 + 708588*x**3 - 708588*x**2)*log(x + log(x)))

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