3.33.57 \(\int \frac {-11520+13248 x-1335 x^2-186 x^3-3 x^4+(81 x^2-144 x^3+82 x^4-16 x^5+x^6) \log (3)+(-6144+2880 x+204 x^2+(108 x^2-132 x^3+44 x^4-4 x^5) \log (3)) \log (x)+(-768+3 x^2+(54 x^2-40 x^3+6 x^4) \log (3)) \log ^2(x)+(12 x^2-4 x^3) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)}{(81 x^2-144 x^3+82 x^4-16 x^5+x^6) \log (3)+(108 x^2-132 x^3+44 x^4-4 x^5) \log (3) \log (x)+(54 x^2-40 x^3+6 x^4) \log (3) \log ^2(x)+(12 x^2-4 x^3) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)} \, dx\)

Optimal. Leaf size=31 \[ x+\frac {3 (16+x)^2}{x \log (3) \left (-2 x+(3-x+\log (x))^2\right )} \]

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Rubi [F]  time = 3.95, 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 {-11520+13248 x-1335 x^2-186 x^3-3 x^4+\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (-6144+2880 x+204 x^2+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3)\right ) \log (x)+\left (-768+3 x^2+\left (54 x^2-40 x^3+6 x^4\right ) \log (3)\right ) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)}{\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3) \log (x)+\left (54 x^2-40 x^3+6 x^4\right ) \log (3) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-11520 + 13248*x - 1335*x^2 - 186*x^3 - 3*x^4 + (81*x^2 - 144*x^3 + 82*x^4 - 16*x^5 + x^6)*Log[3] + (-614
4 + 2880*x + 204*x^2 + (108*x^2 - 132*x^3 + 44*x^4 - 4*x^5)*Log[3])*Log[x] + (-768 + 3*x^2 + (54*x^2 - 40*x^3
+ 6*x^4)*Log[3])*Log[x]^2 + (12*x^2 - 4*x^3)*Log[3]*Log[x]^3 + x^2*Log[3]*Log[x]^4)/((81*x^2 - 144*x^3 + 82*x^
4 - 16*x^5 + x^6)*Log[3] + (108*x^2 - 132*x^3 + 44*x^4 - 4*x^5)*Log[3]*Log[x] + (54*x^2 - 40*x^3 + 6*x^4)*Log[
3]*Log[x]^2 + (12*x^2 - 4*x^3)*Log[3]*Log[x]^3 + x^2*Log[3]*Log[x]^4),x]

[Out]

x + 96/(Log[3]*(9 - 8*x + x^2 + 6*Log[x] - 2*x*Log[x] + Log[x]^2)) - (1554*Defer[Int][(9 - 8*x + x^2 + 6*Log[x
] - 2*x*Log[x] + Log[x]^2)^(-2), x])/Log[3] - (4608*Defer[Int][1/(x^2*(9 - 8*x + x^2 + 6*Log[x] - 2*x*Log[x] +
Log[x]^2)^2), x])/Log[3] + (7680*Defer[Int][1/(x*(9 - 8*x + x^2 + 6*Log[x] - 2*x*Log[x] + Log[x]^2)^2), x])/L
og[3] + (30*Defer[Int][x/(9 - 8*x + x^2 + 6*Log[x] - 2*x*Log[x] + Log[x]^2)^2, x])/Log[3] - (6*Defer[Int][x^2/
(9 - 8*x + x^2 + 6*Log[x] - 2*x*Log[x] + Log[x]^2)^2, x])/Log[3] - (6*Defer[Int][Log[x]/(9 - 8*x + x^2 + 6*Log
[x] - 2*x*Log[x] + Log[x]^2)^2, x])/Log[3] - (1536*Defer[Int][Log[x]/(x^2*(9 - 8*x + x^2 + 6*Log[x] - 2*x*Log[
x] + Log[x]^2)^2), x])/Log[3] + (1536*Defer[Int][Log[x]/(x*(9 - 8*x + x^2 + 6*Log[x] - 2*x*Log[x] + Log[x]^2)^
2), x])/Log[3] + (6*Defer[Int][(x*Log[x])/(9 - 8*x + x^2 + 6*Log[x] - 2*x*Log[x] + Log[x]^2)^2, x])/Log[3] + (
3*Defer[Int][(9 - 8*x + x^2 + 6*Log[x] - 2*x*Log[x] + Log[x]^2)^(-1), x])/Log[3] - (768*Defer[Int][1/(x^2*(9 -
8*x + x^2 + 6*Log[x] - 2*x*Log[x] + Log[x]^2)), x])/Log[3]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-11520+13248 x-16 x^5 \log (3)+x^6 \log (3)-6 x^3 (31+24 \log (3))+3 x^2 (-445+27 \log (3))+x^4 (-3+82 \log (3))-4 \left (1536-720 x+33 x^3 \log (3)-11 x^4 \log (3)+x^5 \log (3)-3 x^2 (17+9 \log (3))\right ) \log (x)+\left (-768-40 x^3 \log (3)+6 x^4 \log (3)+x^2 (3+54 \log (3))\right ) \log ^2(x)-4 (-3+x) x^2 \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)}{x^2 \log (3) \left (9-8 x+x^2-2 (-3+x) \log (x)+\log ^2(x)\right )^2} \, dx\\ &=\frac {\int \frac {-11520+13248 x-16 x^5 \log (3)+x^6 \log (3)-6 x^3 (31+24 \log (3))+3 x^2 (-445+27 \log (3))+x^4 (-3+82 \log (3))-4 \left (1536-720 x+33 x^3 \log (3)-11 x^4 \log (3)+x^5 \log (3)-3 x^2 (17+9 \log (3))\right ) \log (x)+\left (-768-40 x^3 \log (3)+6 x^4 \log (3)+x^2 (3+54 \log (3))\right ) \log ^2(x)-4 (-3+x) x^2 \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)}{x^2 \left (9-8 x+x^2-2 (-3+x) \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}\\ &=\frac {\int \left (\log (3)-\frac {6 (16+x)^2 \left (3-5 x+x^2+\log (x)-x \log (x)\right )}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}+\frac {3 \left (-256+x^2\right )}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )}\right ) \, dx}{\log (3)}\\ &=x+\frac {3 \int \frac {-256+x^2}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )} \, dx}{\log (3)}-\frac {6 \int \frac {(16+x)^2 \left (3-5 x+x^2+\log (x)-x \log (x)\right )}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}\\ &=x+\frac {3 \int \left (\frac {1}{9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)}-\frac {256}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )}\right ) \, dx}{\log (3)}-\frac {6 \int \left (\frac {3-5 x+x^2+\log (x)-x \log (x)}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}+\frac {256 \left (3-5 x+x^2+\log (x)-x \log (x)\right )}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}+\frac {32 \left (3-5 x+x^2+\log (x)-x \log (x)\right )}{x \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}\right ) \, dx}{\log (3)}\\ &=x+\frac {3 \int \frac {1}{9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)} \, dx}{\log (3)}-\frac {6 \int \frac {3-5 x+x^2+\log (x)-x \log (x)}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}-\frac {192 \int \frac {3-5 x+x^2+\log (x)-x \log (x)}{x \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}-\frac {768 \int \frac {1}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )} \, dx}{\log (3)}-\frac {1536 \int \frac {3-5 x+x^2+\log (x)-x \log (x)}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}\\ &=x+\frac {96}{\log (3) \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )}+\frac {3 \int \frac {1}{9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)} \, dx}{\log (3)}-\frac {6 \int \left (\frac {3}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}-\frac {5 x}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}+\frac {x^2}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}+\frac {\log (x)}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}-\frac {x \log (x)}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}\right ) \, dx}{\log (3)}-\frac {768 \int \frac {1}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )} \, dx}{\log (3)}-\frac {1536 \int \left (\frac {1}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}+\frac {3}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}-\frac {5}{x \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}+\frac {\log (x)}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}-\frac {\log (x)}{x \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}\right ) \, dx}{\log (3)}\\ &=x+\frac {96}{\log (3) \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )}+\frac {3 \int \frac {1}{9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)} \, dx}{\log (3)}-\frac {6 \int \frac {x^2}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}-\frac {6 \int \frac {\log (x)}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}+\frac {6 \int \frac {x \log (x)}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}-\frac {18 \int \frac {1}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}+\frac {30 \int \frac {x}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}-\frac {768 \int \frac {1}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )} \, dx}{\log (3)}-\frac {1536 \int \frac {1}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}-\frac {1536 \int \frac {\log (x)}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}+\frac {1536 \int \frac {\log (x)}{x \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}-\frac {4608 \int \frac {1}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}+\frac {7680 \int \frac {1}{x \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.10, size = 41, normalized size = 1.32 \begin {gather*} \frac {x \log (3)+\frac {3 (16+x)^2}{x \left (9-8 x+x^2-2 (-3+x) \log (x)+\log ^2(x)\right )}}{\log (3)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-11520 + 13248*x - 1335*x^2 - 186*x^3 - 3*x^4 + (81*x^2 - 144*x^3 + 82*x^4 - 16*x^5 + x^6)*Log[3] +
(-6144 + 2880*x + 204*x^2 + (108*x^2 - 132*x^3 + 44*x^4 - 4*x^5)*Log[3])*Log[x] + (-768 + 3*x^2 + (54*x^2 - 4
0*x^3 + 6*x^4)*Log[3])*Log[x]^2 + (12*x^2 - 4*x^3)*Log[3]*Log[x]^3 + x^2*Log[3]*Log[x]^4)/((81*x^2 - 144*x^3 +
82*x^4 - 16*x^5 + x^6)*Log[3] + (108*x^2 - 132*x^3 + 44*x^4 - 4*x^5)*Log[3]*Log[x] + (54*x^2 - 40*x^3 + 6*x^4
)*Log[3]*Log[x]^2 + (12*x^2 - 4*x^3)*Log[3]*Log[x]^3 + x^2*Log[3]*Log[x]^4),x]

[Out]

(x*Log[3] + (3*(16 + x)^2)/(x*(9 - 8*x + x^2 - 2*(-3 + x)*Log[x] + Log[x]^2)))/Log[3]

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fricas [B]  time = 0.66, size = 92, normalized size = 2.97 \begin {gather*} \frac {x^{2} \log \relax (3) \log \relax (x)^{2} - 2 \, {\left (x^{3} - 3 \, x^{2}\right )} \log \relax (3) \log \relax (x) + 3 \, x^{2} + {\left (x^{4} - 8 \, x^{3} + 9 \, x^{2}\right )} \log \relax (3) + 96 \, x + 768}{x \log \relax (3) \log \relax (x)^{2} - 2 \, {\left (x^{2} - 3 \, x\right )} \log \relax (3) \log \relax (x) + {\left (x^{3} - 8 \, x^{2} + 9 \, x\right )} \log \relax (3)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^2*log(3)*log(x)^4+(-4*x^3+12*x^2)*log(3)*log(x)^3+((6*x^4-40*x^3+54*x^2)*log(3)+3*x^2-768)*log(x)
^2+((-4*x^5+44*x^4-132*x^3+108*x^2)*log(3)+204*x^2+2880*x-6144)*log(x)+(x^6-16*x^5+82*x^4-144*x^3+81*x^2)*log(
3)-3*x^4-186*x^3-1335*x^2+13248*x-11520)/(x^2*log(3)*log(x)^4+(-4*x^3+12*x^2)*log(3)*log(x)^3+(6*x^4-40*x^3+54
*x^2)*log(3)*log(x)^2+(-4*x^5+44*x^4-132*x^3+108*x^2)*log(3)*log(x)+(x^6-16*x^5+82*x^4-144*x^3+81*x^2)*log(3))
,x, algorithm="fricas")

[Out]

(x^2*log(3)*log(x)^2 - 2*(x^3 - 3*x^2)*log(3)*log(x) + 3*x^2 + (x^4 - 8*x^3 + 9*x^2)*log(3) + 96*x + 768)/(x*l
og(3)*log(x)^2 - 2*(x^2 - 3*x)*log(3)*log(x) + (x^3 - 8*x^2 + 9*x)*log(3))

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giac [A]  time = 0.52, size = 57, normalized size = 1.84 \begin {gather*} x + \frac {3 \, {\left (x^{2} + 32 \, x + 256\right )}}{x^{3} \log \relax (3) - 2 \, x^{2} \log \relax (3) \log \relax (x) + x \log \relax (3) \log \relax (x)^{2} - 8 \, x^{2} \log \relax (3) + 6 \, x \log \relax (3) \log \relax (x) + 9 \, x \log \relax (3)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^2*log(3)*log(x)^4+(-4*x^3+12*x^2)*log(3)*log(x)^3+((6*x^4-40*x^3+54*x^2)*log(3)+3*x^2-768)*log(x)
^2+((-4*x^5+44*x^4-132*x^3+108*x^2)*log(3)+204*x^2+2880*x-6144)*log(x)+(x^6-16*x^5+82*x^4-144*x^3+81*x^2)*log(
3)-3*x^4-186*x^3-1335*x^2+13248*x-11520)/(x^2*log(3)*log(x)^4+(-4*x^3+12*x^2)*log(3)*log(x)^3+(6*x^4-40*x^3+54
*x^2)*log(3)*log(x)^2+(-4*x^5+44*x^4-132*x^3+108*x^2)*log(3)*log(x)+(x^6-16*x^5+82*x^4-144*x^3+81*x^2)*log(3))
,x, algorithm="giac")

[Out]

x + 3*(x^2 + 32*x + 256)/(x^3*log(3) - 2*x^2*log(3)*log(x) + x*log(3)*log(x)^2 - 8*x^2*log(3) + 6*x*log(3)*log
(x) + 9*x*log(3))

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maple [A]  time = 0.04, size = 43, normalized size = 1.39

method	result	size
risch	\(x +\frac {3 x^{2}+96 x +768}{x \ln \relax (3) \left (\ln \relax (x )^{2}-2 x \ln \relax (x )+x^{2}+6 \ln \relax (x )-8 x +9\right )}\)	\(43\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x^2*ln(3)*ln(x)^4+(-4*x^3+12*x^2)*ln(3)*ln(x)^3+((6*x^4-40*x^3+54*x^2)*ln(3)+3*x^2-768)*ln(x)^2+((-4*x^5+
44*x^4-132*x^3+108*x^2)*ln(3)+204*x^2+2880*x-6144)*ln(x)+(x^6-16*x^5+82*x^4-144*x^3+81*x^2)*ln(3)-3*x^4-186*x^
3-1335*x^2+13248*x-11520)/(x^2*ln(3)*ln(x)^4+(-4*x^3+12*x^2)*ln(3)*ln(x)^3+(6*x^4-40*x^3+54*x^2)*ln(3)*ln(x)^2
+(-4*x^5+44*x^4-132*x^3+108*x^2)*ln(3)*ln(x)+(x^6-16*x^5+82*x^4-144*x^3+81*x^2)*ln(3)),x,method=_RETURNVERBOSE
)

[Out]

x+3*(x^2+32*x+256)/x/ln(3)/(ln(x)^2-2*x*ln(x)+x^2+6*ln(x)-8*x+9)

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maxima [B]  time = 0.66, size = 103, normalized size = 3.32 \begin {gather*} \frac {x^{4} \log \relax (3) + x^{2} \log \relax (3) \log \relax (x)^{2} - 8 \, x^{3} \log \relax (3) + 3 \, x^{2} {\left (3 \, \log \relax (3) + 1\right )} - 2 \, {\left (x^{3} \log \relax (3) - 3 \, x^{2} \log \relax (3)\right )} \log \relax (x) + 96 \, x + 768}{x^{3} \log \relax (3) + x \log \relax (3) \log \relax (x)^{2} - 8 \, x^{2} \log \relax (3) + 9 \, x \log \relax (3) - 2 \, {\left (x^{2} \log \relax (3) - 3 \, x \log \relax (3)\right )} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^2*log(3)*log(x)^4+(-4*x^3+12*x^2)*log(3)*log(x)^3+((6*x^4-40*x^3+54*x^2)*log(3)+3*x^2-768)*log(x)
^2+((-4*x^5+44*x^4-132*x^3+108*x^2)*log(3)+204*x^2+2880*x-6144)*log(x)+(x^6-16*x^5+82*x^4-144*x^3+81*x^2)*log(
3)-3*x^4-186*x^3-1335*x^2+13248*x-11520)/(x^2*log(3)*log(x)^4+(-4*x^3+12*x^2)*log(3)*log(x)^3+(6*x^4-40*x^3+54
*x^2)*log(3)*log(x)^2+(-4*x^5+44*x^4-132*x^3+108*x^2)*log(3)*log(x)+(x^6-16*x^5+82*x^4-144*x^3+81*x^2)*log(3))
,x, algorithm="maxima")

[Out]

(x^4*log(3) + x^2*log(3)*log(x)^2 - 8*x^3*log(3) + 3*x^2*(3*log(3) + 1) - 2*(x^3*log(3) - 3*x^2*log(3))*log(x)
+ 96*x + 768)/(x^3*log(3) + x*log(3)*log(x)^2 - 8*x^2*log(3) + 9*x*log(3) - 2*(x^2*log(3) - 3*x*log(3))*log(x
))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {13248\,x+{\ln \relax (x)}^2\,\left (\ln \relax (3)\,\left (6\,x^4-40\,x^3+54\,x^2\right )+3\,x^2-768\right )+\ln \relax (x)\,\left (2880\,x+\ln \relax (3)\,\left (-4\,x^5+44\,x^4-132\,x^3+108\,x^2\right )+204\,x^2-6144\right )-1335\,x^2-186\,x^3-3\,x^4+\ln \relax (3)\,\left (x^6-16\,x^5+82\,x^4-144\,x^3+81\,x^2\right )+\ln \relax (3)\,{\ln \relax (x)}^3\,\left (12\,x^2-4\,x^3\right )+x^2\,\ln \relax (3)\,{\ln \relax (x)}^4-11520}{\ln \relax (3)\,\left (x^6-16\,x^5+82\,x^4-144\,x^3+81\,x^2\right )+\ln \relax (3)\,{\ln \relax (x)}^2\,\left (6\,x^4-40\,x^3+54\,x^2\right )+\ln \relax (3)\,{\ln \relax (x)}^3\,\left (12\,x^2-4\,x^3\right )+x^2\,\ln \relax (3)\,{\ln \relax (x)}^4+\ln \relax (3)\,\ln \relax (x)\,\left (-4\,x^5+44\,x^4-132\,x^3+108\,x^2\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((13248*x + log(x)^2*(log(3)*(54*x^2 - 40*x^3 + 6*x^4) + 3*x^2 - 768) + log(x)*(2880*x + log(3)*(108*x^2 -
132*x^3 + 44*x^4 - 4*x^5) + 204*x^2 - 6144) - 1335*x^2 - 186*x^3 - 3*x^4 + log(3)*(81*x^2 - 144*x^3 + 82*x^4 -
16*x^5 + x^6) + log(3)*log(x)^3*(12*x^2 - 4*x^3) + x^2*log(3)*log(x)^4 - 11520)/(log(3)*(81*x^2 - 144*x^3 + 8
2*x^4 - 16*x^5 + x^6) + log(3)*log(x)^2*(54*x^2 - 40*x^3 + 6*x^4) + log(3)*log(x)^3*(12*x^2 - 4*x^3) + x^2*log
(3)*log(x)^4 + log(3)*log(x)*(108*x^2 - 132*x^3 + 44*x^4 - 4*x^5)),x)

[Out]

int((13248*x + log(x)^2*(log(3)*(54*x^2 - 40*x^3 + 6*x^4) + 3*x^2 - 768) + log(x)*(2880*x + log(3)*(108*x^2 -
132*x^3 + 44*x^4 - 4*x^5) + 204*x^2 - 6144) - 1335*x^2 - 186*x^3 - 3*x^4 + log(3)*(81*x^2 - 144*x^3 + 82*x^4 -
16*x^5 + x^6) + log(3)*log(x)^3*(12*x^2 - 4*x^3) + x^2*log(3)*log(x)^4 - 11520)/(log(3)*(81*x^2 - 144*x^3 + 8
2*x^4 - 16*x^5 + x^6) + log(3)*log(x)^2*(54*x^2 - 40*x^3 + 6*x^4) + log(3)*log(x)^3*(12*x^2 - 4*x^3) + x^2*log
(3)*log(x)^4 + log(3)*log(x)*(108*x^2 - 132*x^3 + 44*x^4 - 4*x^5)), x)

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sympy [B]  time = 0.30, size = 61, normalized size = 1.97 \begin {gather*} x + \frac {3 x^{2} + 96 x + 768}{x^{3} \log {\relax (3 )} - 8 x^{2} \log {\relax (3 )} + x \log {\relax (3 )} \log {\relax (x )}^{2} + 9 x \log {\relax (3 )} + \left (- 2 x^{2} \log {\relax (3 )} + 6 x \log {\relax (3 )}\right ) \log {\relax (x )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x**2*ln(3)*ln(x)**4+(-4*x**3+12*x**2)*ln(3)*ln(x)**3+((6*x**4-40*x**3+54*x**2)*ln(3)+3*x**2-768)*ln
(x)**2+((-4*x**5+44*x**4-132*x**3+108*x**2)*ln(3)+204*x**2+2880*x-6144)*ln(x)+(x**6-16*x**5+82*x**4-144*x**3+8
1*x**2)*ln(3)-3*x**4-186*x**3-1335*x**2+13248*x-11520)/(x**2*ln(3)*ln(x)**4+(-4*x**3+12*x**2)*ln(3)*ln(x)**3+(
6*x**4-40*x**3+54*x**2)*ln(3)*ln(x)**2+(-4*x**5+44*x**4-132*x**3+108*x**2)*ln(3)*ln(x)+(x**6-16*x**5+82*x**4-1
44*x**3+81*x**2)*ln(3)),x)

[Out]

x + (3*x**2 + 96*x + 768)/(x**3*log(3) - 8*x**2*log(3) + x*log(3)*log(x)**2 + 9*x*log(3) + (-2*x**2*log(3) + 6
*x*log(3))*log(x))

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