3.8.65 \(\int \frac {162+54 x+4 x^2+2 x^3-2 x^4+(-18 x-2 x^2-2 x^3) \log (2 x)+(81+36 x-11 x^2-4 x^3+x^4+(-18 x-4 x^2+2 x^3) \log (2 x)+x^2 \log ^2(2 x)) \log (\frac {486+216 x-66 x^2-24 x^3+6 x^4+(-108 x-24 x^2+12 x^3) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2})}{(81+36 x-11 x^2-4 x^3+x^4+(-18 x-4 x^2+2 x^3) \log (2 x)+x^2 \log ^2(2 x)) \log ^2(\frac {486+216 x-66 x^2-24 x^3+6 x^4+(-108 x-24 x^2+12 x^3) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2})} \, dx\)
Optimal. Leaf size=27 \[ \frac {x}{\log \left (6 \left (3+\left (2+\frac {9}{x}-x-\log (2 x)\right )^2\right )\right )} \]
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Rubi [F] time = 38.13, 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 {162+54 x+4 x^2+2 x^3-2 x^4+\left (-18 x-2 x^2-2 x^3\right ) \log (2 x)+\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log \left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )}{\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(162 + 54*x + 4*x^2 + 2*x^3 - 2*x^4 + (-18*x - 2*x^2 - 2*x^3)*Log[2*x] + (81 + 36*x - 11*x^2 - 4*x^3 + x^4
+ (-18*x - 4*x^2 + 2*x^3)*Log[2*x] + x^2*Log[2*x]^2)*Log[(486 + 216*x - 66*x^2 - 24*x^3 + 6*x^4 + (-108*x - 2
4*x^2 + 12*x^3)*Log[2*x] + 6*x^2*Log[2*x]^2)/x^2])/((81 + 36*x - 11*x^2 - 4*x^3 + x^4 + (-18*x - 4*x^2 + 2*x^3
)*Log[2*x] + x^2*Log[2*x]^2)*Log[(486 + 216*x - 66*x^2 - 24*x^3 + 6*x^4 + (-108*x - 24*x^2 + 12*x^3)*Log[2*x]
+ 6*x^2*Log[2*x]^2)/x^2]^2),x]
[Out]
162*Defer[Int][1/((81 + 36*x - 11*x^2 - 4*x^3 + x^4 - 18*x*Log[2*x] - 4*x^2*Log[2*x] + 2*x^3*Log[2*x] + x^2*Lo
g[2*x]^2)*Log[(6*(81 + 36*x - 11*x^2 - 4*x^3 + x^4 + 2*x*(-9 - 2*x + x^2)*Log[2*x] + x^2*Log[2*x]^2))/x^2]^2),
x] + 54*Defer[Int][x/((81 + 36*x - 11*x^2 - 4*x^3 + x^4 - 18*x*Log[2*x] - 4*x^2*Log[2*x] + 2*x^3*Log[2*x] + x
^2*Log[2*x]^2)*Log[(6*(81 + 36*x - 11*x^2 - 4*x^3 + x^4 + 2*x*(-9 - 2*x + x^2)*Log[2*x] + x^2*Log[2*x]^2))/x^2
]^2), x] + 4*Defer[Int][x^2/((81 + 36*x - 11*x^2 - 4*x^3 + x^4 - 18*x*Log[2*x] - 4*x^2*Log[2*x] + 2*x^3*Log[2*
x] + x^2*Log[2*x]^2)*Log[(6*(81 + 36*x - 11*x^2 - 4*x^3 + x^4 + 2*x*(-9 - 2*x + x^2)*Log[2*x] + x^2*Log[2*x]^2
))/x^2]^2), x] + 2*Defer[Int][x^3/((81 + 36*x - 11*x^2 - 4*x^3 + x^4 - 18*x*Log[2*x] - 4*x^2*Log[2*x] + 2*x^3*
Log[2*x] + x^2*Log[2*x]^2)*Log[(6*(81 + 36*x - 11*x^2 - 4*x^3 + x^4 + 2*x*(-9 - 2*x + x^2)*Log[2*x] + x^2*Log[
2*x]^2))/x^2]^2), x] - 2*Defer[Int][x^4/((81 + 36*x - 11*x^2 - 4*x^3 + x^4 - 18*x*Log[2*x] - 4*x^2*Log[2*x] +
2*x^3*Log[2*x] + x^2*Log[2*x]^2)*Log[(6*(81 + 36*x - 11*x^2 - 4*x^3 + x^4 + 2*x*(-9 - 2*x + x^2)*Log[2*x] + x^
2*Log[2*x]^2))/x^2]^2), x] - 18*Defer[Int][(x*Log[2*x])/((81 + 36*x - 11*x^2 - 4*x^3 + x^4 - 18*x*Log[2*x] - 4
*x^2*Log[2*x] + 2*x^3*Log[2*x] + x^2*Log[2*x]^2)*Log[(6*(81 + 36*x - 11*x^2 - 4*x^3 + x^4 + 2*x*(-9 - 2*x + x^
2)*Log[2*x] + x^2*Log[2*x]^2))/x^2]^2), x] - 2*Defer[Int][(x^2*Log[2*x])/((81 + 36*x - 11*x^2 - 4*x^3 + x^4 -
18*x*Log[2*x] - 4*x^2*Log[2*x] + 2*x^3*Log[2*x] + x^2*Log[2*x]^2)*Log[(6*(81 + 36*x - 11*x^2 - 4*x^3 + x^4 + 2
*x*(-9 - 2*x + x^2)*Log[2*x] + x^2*Log[2*x]^2))/x^2]^2), x] - 2*Defer[Int][(x^3*Log[2*x])/((81 + 36*x - 11*x^2
- 4*x^3 + x^4 - 18*x*Log[2*x] - 4*x^2*Log[2*x] + 2*x^3*Log[2*x] + x^2*Log[2*x]^2)*Log[(6*(81 + 36*x - 11*x^2
- 4*x^3 + x^4 + 2*x*(-9 - 2*x + x^2)*Log[2*x] + x^2*Log[2*x]^2))/x^2]^2), x] + Defer[Int][Log[(6*(81 + 36*x -
11*x^2 - 4*x^3 + x^4 + 2*x*(-9 - 2*x + x^2)*Log[2*x] + x^2*Log[2*x]^2))/x^2]^(-1), x]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {162+54 x+4 x^2+2 x^3-2 x^4+\left (-18 x-2 x^2-2 x^3\right ) \log (2 x)+\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log \left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )}{\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (-66+\frac {486}{x^2}+\frac {216}{x}-24 x+6 x^2+\frac {\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)}{x^2}+6 \log ^2(2 x)\right )} \, dx\\ &=\int \left (\frac {162}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )}+\frac {54 x}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )}+\frac {4 x^2}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )}+\frac {2 x^3}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )}-\frac {2 x^4}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )}-\frac {2 x \left (9+x+x^2\right ) \log (2 x)}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )}+\frac {1}{\log \left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )}\right ) \, dx\\ &=2 \int \frac {x^3}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx-2 \int \frac {x^4}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx-2 \int \frac {x \left (9+x+x^2\right ) \log (2 x)}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx+4 \int \frac {x^2}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx+54 \int \frac {x}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx+162 \int \frac {1}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx+\int \frac {1}{\log \left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.16, size = 53, normalized size = 1.96 \begin {gather*} \frac {x}{\log \left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(162 + 54*x + 4*x^2 + 2*x^3 - 2*x^4 + (-18*x - 2*x^2 - 2*x^3)*Log[2*x] + (81 + 36*x - 11*x^2 - 4*x^3
+ x^4 + (-18*x - 4*x^2 + 2*x^3)*Log[2*x] + x^2*Log[2*x]^2)*Log[(486 + 216*x - 66*x^2 - 24*x^3 + 6*x^4 + (-108
*x - 24*x^2 + 12*x^3)*Log[2*x] + 6*x^2*Log[2*x]^2)/x^2])/((81 + 36*x - 11*x^2 - 4*x^3 + x^4 + (-18*x - 4*x^2 +
2*x^3)*Log[2*x] + x^2*Log[2*x]^2)*Log[(486 + 216*x - 66*x^2 - 24*x^3 + 6*x^4 + (-108*x - 24*x^2 + 12*x^3)*Log
[2*x] + 6*x^2*Log[2*x]^2)/x^2]^2),x]
[Out]
x/Log[(6*(81 + 36*x - 11*x^2 - 4*x^3 + x^4 + 2*x*(-9 - 2*x + x^2)*Log[2*x] + x^2*Log[2*x]^2))/x^2]
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fricas [B] time = 0.89, size = 56, normalized size = 2.07 \begin {gather*} \frac {x}{\log \left (\frac {6 \, {\left (x^{4} + x^{2} \log \left (2 \, x\right )^{2} - 4 \, x^{3} - 11 \, x^{2} + 2 \, {\left (x^{3} - 2 \, x^{2} - 9 \, x\right )} \log \left (2 \, x\right ) + 36 \, x + 81\right )}}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((x^2*log(2*x)^2+(2*x^3-4*x^2-18*x)*log(2*x)+x^4-4*x^3-11*x^2+36*x+81)*log((6*x^2*log(2*x)^2+(12*x^3
-24*x^2-108*x)*log(2*x)+6*x^4-24*x^3-66*x^2+216*x+486)/x^2)+(-2*x^3-2*x^2-18*x)*log(2*x)-2*x^4+2*x^3+4*x^2+54*
x+162)/(x^2*log(2*x)^2+(2*x^3-4*x^2-18*x)*log(2*x)+x^4-4*x^3-11*x^2+36*x+81)/log((6*x^2*log(2*x)^2+(12*x^3-24*
x^2-108*x)*log(2*x)+6*x^4-24*x^3-66*x^2+216*x+486)/x^2)^2,x, algorithm="fricas")
[Out]
x/log(6*(x^4 + x^2*log(2*x)^2 - 4*x^3 - 11*x^2 + 2*(x^3 - 2*x^2 - 9*x)*log(2*x) + 36*x + 81)/x^2)
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giac [B] time = 18.70, size = 3434, normalized size = 127.19 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((x^2*log(2*x)^2+(2*x^3-4*x^2-18*x)*log(2*x)+x^4-4*x^3-11*x^2+36*x+81)*log((6*x^2*log(2*x)^2+(12*x^3
-24*x^2-108*x)*log(2*x)+6*x^4-24*x^3-66*x^2+216*x+486)/x^2)+(-2*x^3-2*x^2-18*x)*log(2*x)-2*x^4+2*x^3+4*x^2+54*
x+162)/(x^2*log(2*x)^2+(2*x^3-4*x^2-18*x)*log(2*x)+x^4-4*x^3-11*x^2+36*x+81)/log((6*x^2*log(2*x)^2+(12*x^3-24*
x^2-108*x)*log(2*x)+6*x^4-24*x^3-66*x^2+216*x+486)/x^2)^2,x, algorithm="giac")
[Out]
(x^7 + x^6*log(2) + 2*x^6*log(2*x) + 2*x^5*log(2)*log(2*x) + x^5*log(2*x)^2 + x^4*log(2)*log(2*x)^2 + x^6*log(
x) + 2*x^5*log(2*x)*log(x) + x^4*log(2*x)^2*log(x) - 6*x^6 - 4*x^5*log(2) - 8*x^5*log(2*x) - 4*x^4*log(2)*log(
2*x) - 2*x^4*log(2*x)^2 - 4*x^5*log(x) - 4*x^4*log(2*x)*log(x) - 12*x^5 - 11*x^4*log(2) - 28*x^4*log(2*x) - 18
*x^3*log(2)*log(2*x) - 9*x^3*log(2*x)^2 - 11*x^4*log(x) - 18*x^3*log(2*x)*log(x) + 94*x^4 + 36*x^3*log(2) + 72
*x^3*log(2*x) + 36*x^3*log(x) + 108*x^3 + 81*x^2*log(2) + 162*x^2*log(2*x) + 81*x^2*log(x) - 486*x^2 - 729*x)/
(x^6*log(2) + 2*x^5*log(2)^2 + x^4*log(2)^3 + x^6*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*
x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243) + 2*x^5*log(2)*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x
)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243) + x^4*log(2)^2*log(3*x^4 + 6*x^3*log(2*
x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243) + x^5*log(2)*log(2*x)
+ 2*x^4*log(2)^2*log(2*x) + x^3*log(2)^3*log(2*x) + x^5*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^
3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243)*log(2*x) + 2*x^4*log(2)*log(3*x^4 + 6*x^3*log(2*x)
+ 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243)*log(2*x) + x^3*log(2)^2
*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 2
43)*log(2*x) - 2*x^6*log(x) - 2*x^5*log(2)*log(x) + 2*x^5*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x
^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243)*log(x) + 2*x^4*log(2)*log(3*x^4 + 6*x^3*log(2*x)
+ 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243)*log(x) - 2*x^5*log(2*x)*
log(x) - 2*x^4*log(2)*log(2*x)*log(x) + 2*x^4*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*
log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243)*log(2*x)*log(x) + 2*x^3*log(2)*log(3*x^4 + 6*x^3*log(2*x) + 3
*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243)*log(2*x)*log(x) - 4*x^5*log
(x)^2 - 3*x^4*log(2)*log(x)^2 + x^4*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) -
33*x^2 - 54*x*log(2*x) + 108*x + 243)*log(x)^2 - 4*x^4*log(2*x)*log(x)^2 - 3*x^3*log(2)*log(2*x)*log(x)^2 + x
^3*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x +
243)*log(2*x)*log(x)^2 - 2*x^4*log(x)^3 - 2*x^3*log(2*x)*log(x)^3 - 6*x^5*log(2) - 8*x^4*log(2)^2 - 2*x^3*log
(2)^3 - 6*x^5*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x
) + 108*x + 243) - 8*x^4*log(2)*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*
x^2 - 54*x*log(2*x) + 108*x + 243) - 2*x^3*log(2)^2*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 1
2*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243) - 4*x^4*log(2)*log(2*x) - 4*x^3*log(2)^2*log(2*x) - 4*x
^4*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x +
243)*log(2*x) - 4*x^3*log(2)*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^
2 - 54*x*log(2*x) + 108*x + 243)*log(2*x) + 12*x^5*log(x) + 8*x^4*log(2)*log(x) - 8*x^4*log(3*x^4 + 6*x^3*log(
2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243)*log(x) - 4*x^3*log(
2)*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x +
243)*log(x) + 8*x^4*log(2*x)*log(x) + 4*x^3*log(2)*log(2*x)*log(x) - 4*x^3*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2
*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243)*log(2*x)*log(x) + 16*x^4*log(x)
^2 + 6*x^3*log(2)*log(x)^2 - 2*x^3*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) -
33*x^2 - 54*x*log(2*x) + 108*x + 243)*log(x)^2 + 8*x^3*log(2*x)*log(x)^2 + 4*x^3*log(x)^3 - 12*x^4*log(2) - 28
*x^3*log(2)^2 - 9*x^2*log(2)^3 - 12*x^4*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*
x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243) - 28*x^3*log(2)*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*
x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243) - 9*x^2*log(2)^2*log(3*x^4 + 6*x^3*log(2*x) + 3*
x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243) - 11*x^3*log(2)*log(2*x) - 1
8*x^2*log(2)^2*log(2*x) - 11*x^3*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33
*x^2 - 54*x*log(2*x) + 108*x + 243)*log(2*x) - 18*x^2*log(2)*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 1
2*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243)*log(2*x) + 24*x^4*log(x) + 28*x^3*log(2)*log(x
) - 28*x^3*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) +
108*x + 243)*log(x) - 18*x^2*log(2)*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x)
- 33*x^2 - 54*x*log(2*x) + 108*x + 243)*log(x) + 22*x^3*log(2*x)*log(x) + 18*x^2*log(2)*log(2*x)*log(x) - 18*x
^2*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x +
243)*log(2*x)*log(x) + 56*x^3*log(x)^2 + 27*x^2*log(2)*log(x)^2 - 9*x^2*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*lo
g(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243)*log(x)^2 + 36*x^2*log(2*x)*log(x)^
2 + 18*x^2*log(x)^3 + 94*x^3*log(2) + 72*x^2*log(2)^2 + 94*x^3*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 -
12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243) + 72*x^2*log(2)*log(3*x^4 + 6*x^3*log(2*x) +
3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243) + 36*x^2*log(2)*log(2*x)
+ 36*x^2*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 1
08*x + 243)*log(2*x) - 188*x^3*log(x) - 72*x^2*log(2)*log(x) + 72*x^2*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2
*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243)*log(x) - 72*x^2*log(2*x)*log(x) - 144
*x^2*log(x)^2 + 108*x^2*log(2) + 162*x*log(2)^2 + 108*x^2*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x
^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243) + 162*x*log(2)*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2
*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243) + 81*x*log(2)*log(2*x) + 81*x*l
og(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243
)*log(2*x) - 216*x^2*log(x) - 162*x*log(2)*log(x) + 162*x*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x
^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243)*log(x) - 162*x*log(2*x)*log(x) - 324*x*log(x)^2 -
486*x*log(2) - 486*x*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x
*log(2*x) + 108*x + 243) + 972*x*log(x) - 729*log(2) - 729*log(3*x^4 + 6*x^3*log(2*x) + 3*x^2*log(2*x)^2 - 12*
x^3 - 12*x^2*log(2*x) - 33*x^2 - 54*x*log(2*x) + 108*x + 243) + 1458*log(x))
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maple [F] time = 0.03, size = 0, normalized size = 0.00 \[\int \frac {\left (x^{2} \ln \left (2 x \right )^{2}+\left (2 x^{3}-4 x^{2}-18 x \right ) \ln \left (2 x \right )+x^{4}-4 x^{3}-11 x^{2}+36 x +81\right ) \ln \left (\frac {6 x^{2} \ln \left (2 x \right )^{2}+\left (12 x^{3}-24 x^{2}-108 x \right ) \ln \left (2 x \right )+6 x^{4}-24 x^{3}-66 x^{2}+216 x +486}{x^{2}}\right )+\left (-2 x^{3}-2 x^{2}-18 x \right ) \ln \left (2 x \right )-2 x^{4}+2 x^{3}+4 x^{2}+54 x +162}{\left (x^{2} \ln \left (2 x \right )^{2}+\left (2 x^{3}-4 x^{2}-18 x \right ) \ln \left (2 x \right )+x^{4}-4 x^{3}-11 x^{2}+36 x +81\right ) \ln \left (\frac {6 x^{2} \ln \left (2 x \right )^{2}+\left (12 x^{3}-24 x^{2}-108 x \right ) \ln \left (2 x \right )+6 x^{4}-24 x^{3}-66 x^{2}+216 x +486}{x^{2}}\right )^{2}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((x^2*ln(2*x)^2+(2*x^3-4*x^2-18*x)*ln(2*x)+x^4-4*x^3-11*x^2+36*x+81)*ln((6*x^2*ln(2*x)^2+(12*x^3-24*x^2-10
8*x)*ln(2*x)+6*x^4-24*x^3-66*x^2+216*x+486)/x^2)+(-2*x^3-2*x^2-18*x)*ln(2*x)-2*x^4+2*x^3+4*x^2+54*x+162)/(x^2*
ln(2*x)^2+(2*x^3-4*x^2-18*x)*ln(2*x)+x^4-4*x^3-11*x^2+36*x+81)/ln((6*x^2*ln(2*x)^2+(12*x^3-24*x^2-108*x)*ln(2*
x)+6*x^4-24*x^3-66*x^2+216*x+486)/x^2)^2,x)
[Out]
int(((x^2*ln(2*x)^2+(2*x^3-4*x^2-18*x)*ln(2*x)+x^4-4*x^3-11*x^2+36*x+81)*ln((6*x^2*ln(2*x)^2+(12*x^3-24*x^2-10
8*x)*ln(2*x)+6*x^4-24*x^3-66*x^2+216*x+486)/x^2)+(-2*x^3-2*x^2-18*x)*ln(2*x)-2*x^4+2*x^3+4*x^2+54*x+162)/(x^2*
ln(2*x)^2+(2*x^3-4*x^2-18*x)*ln(2*x)+x^4-4*x^3-11*x^2+36*x+81)/ln((6*x^2*ln(2*x)^2+(12*x^3-24*x^2-108*x)*ln(2*
x)+6*x^4-24*x^3-66*x^2+216*x+486)/x^2)^2,x)
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maxima [B] time = 0.84, size = 76, normalized size = 2.81 \begin {gather*} \frac {x}{\log \relax (3) + \log \relax (2) + \log \left (x^{4} + 2 \, x^{3} {\left (\log \relax (2) - 2\right )} + x^{2} \log \relax (x)^{2} + {\left (\log \relax (2)^{2} - 4 \, \log \relax (2) - 11\right )} x^{2} - 18 \, x {\left (\log \relax (2) - 2\right )} + 2 \, {\left (x^{3} + x^{2} {\left (\log \relax (2) - 2\right )} - 9 \, x\right )} \log \relax (x) + 81\right ) - 2 \, \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((x^2*log(2*x)^2+(2*x^3-4*x^2-18*x)*log(2*x)+x^4-4*x^3-11*x^2+36*x+81)*log((6*x^2*log(2*x)^2+(12*x^3
-24*x^2-108*x)*log(2*x)+6*x^4-24*x^3-66*x^2+216*x+486)/x^2)+(-2*x^3-2*x^2-18*x)*log(2*x)-2*x^4+2*x^3+4*x^2+54*
x+162)/(x^2*log(2*x)^2+(2*x^3-4*x^2-18*x)*log(2*x)+x^4-4*x^3-11*x^2+36*x+81)/log((6*x^2*log(2*x)^2+(12*x^3-24*
x^2-108*x)*log(2*x)+6*x^4-24*x^3-66*x^2+216*x+486)/x^2)^2,x, algorithm="maxima")
[Out]
x/(log(3) + log(2) + log(x^4 + 2*x^3*(log(2) - 2) + x^2*log(x)^2 + (log(2)^2 - 4*log(2) - 11)*x^2 - 18*x*(log(
2) - 2) + 2*(x^3 + x^2*(log(2) - 2) - 9*x)*log(x) + 81) - 2*log(x))
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mupad [B] time = 1.42, size = 295, normalized size = 10.93 \begin {gather*} \frac {x}{2}+\frac {\ln \relax (x)}{2}+\frac {x+\frac {x\,\ln \left (\frac {216\,x-\ln \left (2\,x\right )\,\left (-12\,x^3+24\,x^2+108\,x\right )-66\,x^2-24\,x^3+6\,x^4+6\,x^2\,{\ln \left (2\,x\right )}^2+486}{x^2}\right )\,\left (x^4+2\,x^3\,\ln \left (2\,x\right )-4\,x^3+x^2\,{\ln \left (2\,x\right )}^2-4\,x^2\,\ln \left (2\,x\right )-11\,x^2-18\,x\,\ln \left (2\,x\right )+36\,x+81\right )}{2\,\left (x^2+x+9\right )\,\left (2\,x-x\,\ln \left (2\,x\right )-x^2+9\right )}}{\ln \left (\frac {216\,x-\ln \left (2\,x\right )\,\left (-12\,x^3+24\,x^2+108\,x\right )-66\,x^2-24\,x^3+6\,x^4+6\,x^2\,{\ln \left (2\,x\right )}^2+486}{x^2}\right )}-\frac {\frac {15\,x}{2}-\frac {27}{2}}{x^2+x+9}-\frac {3\,\left (x^7+2\,x^6+19\,x^5+18\,x^4+81\,x^3\right )}{2\,{\left (x^2+x+9\right )}^3\,\left (2\,x-x\,\ln \left (2\,x\right )-x^2+9\right )}-\frac {\ln \left (2\,x\right )\,\left (\frac {x}{2}+\frac {9}{2}\right )}{x^2+x+9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((54*x - log(2*x)*(18*x + 2*x^2 + 2*x^3) + log((216*x - log(2*x)*(108*x + 24*x^2 - 12*x^3) - 66*x^2 - 24*x^
3 + 6*x^4 + 6*x^2*log(2*x)^2 + 486)/x^2)*(36*x - log(2*x)*(18*x + 4*x^2 - 2*x^3) - 11*x^2 - 4*x^3 + x^4 + x^2*
log(2*x)^2 + 81) + 4*x^2 + 2*x^3 - 2*x^4 + 162)/(log((216*x - log(2*x)*(108*x + 24*x^2 - 12*x^3) - 66*x^2 - 24
*x^3 + 6*x^4 + 6*x^2*log(2*x)^2 + 486)/x^2)^2*(36*x - log(2*x)*(18*x + 4*x^2 - 2*x^3) - 11*x^2 - 4*x^3 + x^4 +
x^2*log(2*x)^2 + 81)),x)
[Out]
x/2 + log(x)/2 + (x + (x*log((216*x - log(2*x)*(108*x + 24*x^2 - 12*x^3) - 66*x^2 - 24*x^3 + 6*x^4 + 6*x^2*log
(2*x)^2 + 486)/x^2)*(36*x - 18*x*log(2*x) - 4*x^2*log(2*x) + 2*x^3*log(2*x) - 11*x^2 - 4*x^3 + x^4 + x^2*log(2
*x)^2 + 81))/(2*(x + x^2 + 9)*(2*x - x*log(2*x) - x^2 + 9)))/log((216*x - log(2*x)*(108*x + 24*x^2 - 12*x^3) -
66*x^2 - 24*x^3 + 6*x^4 + 6*x^2*log(2*x)^2 + 486)/x^2) - ((15*x)/2 - 27/2)/(x + x^2 + 9) - (3*(81*x^3 + 18*x^
4 + 19*x^5 + 2*x^6 + x^7))/(2*(x + x^2 + 9)^3*(2*x - x*log(2*x) - x^2 + 9)) - (log(2*x)*(x/2 + 9/2))/(x + x^2
+ 9)
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sympy [B] time = 0.82, size = 56, normalized size = 2.07 \begin {gather*} \frac {x}{\log {\left (\frac {6 x^{4} - 24 x^{3} + 6 x^{2} \log {\left (2 x \right )}^{2} - 66 x^{2} + 216 x + \left (12 x^{3} - 24 x^{2} - 108 x\right ) \log {\left (2 x \right )} + 486}{x^{2}} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((x**2*ln(2*x)**2+(2*x**3-4*x**2-18*x)*ln(2*x)+x**4-4*x**3-11*x**2+36*x+81)*ln((6*x**2*ln(2*x)**2+(1
2*x**3-24*x**2-108*x)*ln(2*x)+6*x**4-24*x**3-66*x**2+216*x+486)/x**2)+(-2*x**3-2*x**2-18*x)*ln(2*x)-2*x**4+2*x
**3+4*x**2+54*x+162)/(x**2*ln(2*x)**2+(2*x**3-4*x**2-18*x)*ln(2*x)+x**4-4*x**3-11*x**2+36*x+81)/ln((6*x**2*ln(
2*x)**2+(12*x**3-24*x**2-108*x)*ln(2*x)+6*x**4-24*x**3-66*x**2+216*x+486)/x**2)**2,x)
[Out]
x/log((6*x**4 - 24*x**3 + 6*x**2*log(2*x)**2 - 66*x**2 + 216*x + (12*x**3 - 24*x**2 - 108*x)*log(2*x) + 486)/x
**2)
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