3.80.13 \(\int \frac {1250 x^4-200 x^6+6 x^8+(1000 x^3-40 x^5) \log (x) \log (12 x)+(500 x^3-20 x^5+(500 x^3-60 x^5) \log (x)) \log ^2(12 x)+(600 x^2-8 x^4) \log ^2(x) \log ^3(12 x)+((300 x^2-4 x^4) \log (x)-4 x^4 \log ^2(x)) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+(60 x \log ^2(x)-20 x \log ^3(x)) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+(4 \log ^3(x)-2 \log ^4(x)) \log ^8(12 x)}{x^3} \, dx\)

Optimal. Leaf size=28 \[ x^2 \left (-x^2+\left (5+\frac {\log (x) \log ^2(12 x)}{x}\right )^2\right )^2 \]

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Rubi [F]  time = 54.72, 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 {1250 x^4-200 x^6+6 x^8+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (500 x^3-20 x^5+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)}{x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(1250*x^4 - 200*x^6 + 6*x^8 + (1000*x^3 - 40*x^5)*Log[x]*Log[12*x] + (500*x^3 - 20*x^5 + (500*x^3 - 60*x^5
)*Log[x])*Log[12*x]^2 + (600*x^2 - 8*x^4)*Log[x]^2*Log[12*x]^3 + ((300*x^2 - 4*x^4)*Log[x] - 4*x^4*Log[x]^2)*L
og[12*x]^4 + 120*x*Log[x]^3*Log[12*x]^5 + (60*x*Log[x]^2 - 20*x*Log[x]^3)*Log[12*x]^6 + 8*Log[x]^4*Log[12*x]^7
+ (4*Log[x]^3 - 2*Log[x]^4)*Log[12*x]^8)/x^3,x]

[Out]

625*x^2 - 50*x^4 + x^6 + 1000*x*Log[x] - (40*x^3*Log[x])/9 - (40*(225*x - x^3)*Log[x])/9 + 1000*x*Log[12*x] -
(40*x^3*Log[12*x])/9 - (40*(225*x - x^3)*Log[12*x])/9 + 500*x*Log[x]*Log[12*x]^2 - 20*x^3*Log[x]*Log[12*x]^2 -
2*x^2*Log[x]^2*Log[12*x]^4 + 60*Log[x]*Log[12*x]^5 - 10*Log[12*x]^6 + (20*Log[x]^3*Log[12*x]^6)/x + (Log[x]^4
*Log[12*x]^8)/x^2 + 600*Defer[Int][(Log[x]^2*Log[12*x]^3)/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (2 x \left (625-100 x^2+3 x^4\right )-40 (-5+x) (5+x) \log (x) \log (12 x)-20 \left (-25+x^2-25 \log (x)+3 x^2 \log (x)\right ) \log ^2(12 x)-\frac {8 \left (-75+x^2\right ) \log ^2(x) \log ^3(12 x)}{x}-\frac {4 \log (x) \left (-75+x^2+x^2 \log (x)\right ) \log ^4(12 x)}{x}+\frac {120 \log ^3(x) \log ^5(12 x)}{x^2}-\frac {20 (-3+\log (x)) \log ^2(x) \log ^6(12 x)}{x^2}+\frac {8 \log ^4(x) \log ^7(12 x)}{x^3}-\frac {2 (-2+\log (x)) \log ^3(x) \log ^8(12 x)}{x^3}\right ) \, dx\\ &=2 \int x \left (625-100 x^2+3 x^4\right ) \, dx-2 \int \frac {(-2+\log (x)) \log ^3(x) \log ^8(12 x)}{x^3} \, dx-4 \int \frac {\log (x) \left (-75+x^2+x^2 \log (x)\right ) \log ^4(12 x)}{x} \, dx-8 \int \frac {\left (-75+x^2\right ) \log ^2(x) \log ^3(12 x)}{x} \, dx+8 \int \frac {\log ^4(x) \log ^7(12 x)}{x^3} \, dx-20 \int \left (-25+x^2-25 \log (x)+3 x^2 \log (x)\right ) \log ^2(12 x) \, dx-20 \int \frac {(-3+\log (x)) \log ^2(x) \log ^6(12 x)}{x^2} \, dx-40 \int (-5+x) (5+x) \log (x) \log (12 x) \, dx+120 \int \frac {\log ^3(x) \log ^5(12 x)}{x^2} \, dx\\ &=1000 x \log (x) \log (12 x)-\frac {40}{3} x^3 \log (x) \log (12 x)-\frac {120 \log ^3(x) \log ^5(12 x)}{x}-\frac {4 \log ^4(x) \log ^7(12 x)}{x^2}+2 \int \left (625 x-100 x^3+3 x^5\right ) \, dx-2 \int \left (-\frac {2 \log ^3(x) \log ^8(12 x)}{x^3}+\frac {\log ^4(x) \log ^8(12 x)}{x^3}\right ) \, dx-4 \int \left (-\frac {75 \log (x) \log ^4(12 x)}{x}+x \log (x) \log ^4(12 x)+x \log ^2(x) \log ^4(12 x)\right ) \, dx-8 \int \left (-\frac {75 \log ^2(x) \log ^3(12 x)}{x}+x \log ^2(x) \log ^3(12 x)\right ) \, dx+16 \int \frac {\log ^3(x) \log ^7(12 x)}{x^3} \, dx-20 \int \left (-25 \log ^2(12 x)+x^2 \log ^2(12 x)-25 \log (x) \log ^2(12 x)+3 x^2 \log (x) \log ^2(12 x)\right ) \, dx-20 \int \left (-\frac {3 \log ^2(x) \log ^6(12 x)}{x^2}+\frac {\log ^3(x) \log ^6(12 x)}{x^2}\right ) \, dx+28 \int \frac {\log ^4(x) \log ^6(12 x)}{x^3} \, dx+40 \int \frac {1}{3} \left (-75+x^2\right ) \log (x) \, dx+40 \int \frac {1}{3} \left (-75+x^2\right ) \log (12 x) \, dx+360 \int \frac {\log ^2(x) \log ^5(12 x)}{x^2} \, dx+600 \int \frac {\log ^3(x) \log ^4(12 x)}{x^2} \, dx\\ &=625 x^2-50 x^4+x^6+1000 x \log (x) \log (12 x)-\frac {40}{3} x^3 \log (x) \log (12 x)-\frac {600 \log ^3(x) \log ^4(12 x)}{x}-\frac {360 \log ^2(x) \log ^5(12 x)}{x}-\frac {120 \log ^3(x) \log ^5(12 x)}{x}-\frac {14 \log ^4(x) \log ^6(12 x)}{x^2}-\frac {8 \log ^3(x) \log ^7(12 x)}{x^2}-\frac {4 \log ^4(x) \log ^7(12 x)}{x^2}-2 \int \frac {\log ^4(x) \log ^8(12 x)}{x^3} \, dx-4 \int x \log (x) \log ^4(12 x) \, dx-4 \int x \log ^2(x) \log ^4(12 x) \, dx+4 \int \frac {\log ^3(x) \log ^8(12 x)}{x^3} \, dx-8 \int x \log ^2(x) \log ^3(12 x) \, dx+\frac {40}{3} \int \left (-75+x^2\right ) \log (x) \, dx+\frac {40}{3} \int \left (-75+x^2\right ) \log (12 x) \, dx-20 \int x^2 \log ^2(12 x) \, dx-20 \int \frac {\log ^3(x) \log ^6(12 x)}{x^2} \, dx+24 \int \frac {\log ^2(x) \log ^7(12 x)}{x^3} \, dx+2 \left (56 \int \frac {\log ^3(x) \log ^6(12 x)}{x^3} \, dx\right )-60 \int x^2 \log (x) \log ^2(12 x) \, dx+60 \int \frac {\log ^2(x) \log ^6(12 x)}{x^2} \, dx+84 \int \frac {\log ^4(x) \log ^5(12 x)}{x^3} \, dx+300 \int \frac {\log (x) \log ^4(12 x)}{x} \, dx+500 \int \log ^2(12 x) \, dx+500 \int \log (x) \log ^2(12 x) \, dx+600 \int \frac {\log ^2(x) \log ^3(12 x)}{x} \, dx+720 \int \frac {\log (x) \log ^5(12 x)}{x^2} \, dx+2 \left (1800 \int \frac {\log ^2(x) \log ^4(12 x)}{x^2} \, dx\right )+2400 \int \frac {\log ^3(x) \log ^3(12 x)}{x^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.46, size = 39, normalized size = 1.39 \begin {gather*} \frac {\left (25 x^2-x^4+10 x \log (x) \log ^2(12 x)+\log ^2(x) \log ^4(12 x)\right )^2}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1250*x^4 - 200*x^6 + 6*x^8 + (1000*x^3 - 40*x^5)*Log[x]*Log[12*x] + (500*x^3 - 20*x^5 + (500*x^3 -
60*x^5)*Log[x])*Log[12*x]^2 + (600*x^2 - 8*x^4)*Log[x]^2*Log[12*x]^3 + ((300*x^2 - 4*x^4)*Log[x] - 4*x^4*Log[x
]^2)*Log[12*x]^4 + 120*x*Log[x]^3*Log[12*x]^5 + (60*x*Log[x]^2 - 20*x*Log[x]^3)*Log[12*x]^6 + 8*Log[x]^4*Log[1
2*x]^7 + (4*Log[x]^3 - 2*Log[x]^4)*Log[12*x]^8)/x^3,x]

[Out]

(25*x^2 - x^4 + 10*x*Log[x]*Log[12*x]^2 + Log[x]^2*Log[12*x]^4)^2/x^2

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fricas [B]  time = 0.57, size = 279, normalized size = 9.96 \begin {gather*} \frac {28 \, \log \left (12\right )^{2} \log \relax (x)^{10} + 8 \, \log \left (12\right ) \log \relax (x)^{11} + \log \relax (x)^{12} + 4 \, {\left (14 \, \log \left (12\right )^{3} + 5 \, x\right )} \log \relax (x)^{9} + 10 \, {\left (7 \, \log \left (12\right )^{4} + 12 \, x \log \left (12\right )\right )} \log \relax (x)^{8} + x^{8} + 4 \, {\left (14 \, \log \left (12\right )^{5} + 75 \, x \log \left (12\right )^{2}\right )} \log \relax (x)^{7} + 2 \, {\left (14 \, \log \left (12\right )^{6} - x^{4} + 200 \, x \log \left (12\right )^{3} + 75 \, x^{2}\right )} \log \relax (x)^{6} - 50 \, x^{6} + 4 \, {\left (2 \, \log \left (12\right )^{7} + 75 \, x \log \left (12\right )^{4} - 2 \, {\left (x^{4} - 75 \, x^{2}\right )} \log \left (12\right )\right )} \log \relax (x)^{5} + {\left (\log \left (12\right )^{8} + 120 \, x \log \left (12\right )^{5} - 12 \, {\left (x^{4} - 75 \, x^{2}\right )} \log \left (12\right )^{2}\right )} \log \relax (x)^{4} + 625 \, x^{4} - 20 \, {\left (x^{5} - 25 \, x^{3}\right )} \log \left (12\right )^{2} \log \relax (x) + 4 \, {\left (5 \, x \log \left (12\right )^{6} - 5 \, x^{5} - 2 \, {\left (x^{4} - 75 \, x^{2}\right )} \log \left (12\right )^{3} + 125 \, x^{3}\right )} \log \relax (x)^{3} - 2 \, {\left ({\left (x^{4} - 75 \, x^{2}\right )} \log \left (12\right )^{4} + 20 \, {\left (x^{5} - 25 \, x^{3}\right )} \log \left (12\right )\right )} \log \relax (x)^{2}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*log(x)^4+4*log(x)^3)*log(12*x)^8+8*log(x)^4*log(12*x)^7+(-20*x*log(x)^3+60*x*log(x)^2)*log(12*x
)^6+120*x*log(x)^3*log(12*x)^5+(-4*x^4*log(x)^2+(-4*x^4+300*x^2)*log(x))*log(12*x)^4+(-8*x^4+600*x^2)*log(x)^2
*log(12*x)^3+((-60*x^5+500*x^3)*log(x)-20*x^5+500*x^3)*log(12*x)^2+(-40*x^5+1000*x^3)*log(x)*log(12*x)+6*x^8-2
00*x^6+1250*x^4)/x^3,x, algorithm="fricas")

[Out]

(28*log(12)^2*log(x)^10 + 8*log(12)*log(x)^11 + log(x)^12 + 4*(14*log(12)^3 + 5*x)*log(x)^9 + 10*(7*log(12)^4
+ 12*x*log(12))*log(x)^8 + x^8 + 4*(14*log(12)^5 + 75*x*log(12)^2)*log(x)^7 + 2*(14*log(12)^6 - x^4 + 200*x*lo
g(12)^3 + 75*x^2)*log(x)^6 - 50*x^6 + 4*(2*log(12)^7 + 75*x*log(12)^4 - 2*(x^4 - 75*x^2)*log(12))*log(x)^5 + (
log(12)^8 + 120*x*log(12)^5 - 12*(x^4 - 75*x^2)*log(12)^2)*log(x)^4 + 625*x^4 - 20*(x^5 - 25*x^3)*log(12)^2*lo
g(x) + 4*(5*x*log(12)^6 - 5*x^5 - 2*(x^4 - 75*x^2)*log(12)^3 + 125*x^3)*log(x)^3 - 2*((x^4 - 75*x^2)*log(12)^4
+ 20*(x^5 - 25*x^3)*log(12))*log(x)^2)/x^2

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giac [B]  time = 1.26, size = 2318, normalized size = 82.79 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*log(x)^4+4*log(x)^3)*log(12*x)^8+8*log(x)^4*log(12*x)^7+(-20*x*log(x)^3+60*x*log(x)^2)*log(12*x
)^6+120*x*log(x)^3*log(12*x)^5+(-4*x^4*log(x)^2+(-4*x^4+300*x^2)*log(x))*log(12*x)^4+(-8*x^4+600*x^2)*log(x)^2
*log(12*x)^3+((-60*x^5+500*x^3)*log(x)-20*x^5+500*x^3)*log(12*x)^2+(-40*x^5+1000*x^3)*log(x)*log(12*x)+6*x^8-2
00*x^6+1250*x^4)/x^3,x, algorithm="giac")

[Out]

log(x)^12/x^2 + 1/2*(2*log(x)^4/x^2 + 4*log(x)^3/x^2 + 6*log(x)^2/x^2 + 6*log(x)/x^2 + 3/x^2)*log(12)^8 - 1/2*
(4*log(x)^3/x^2 + 6*log(x)^2/x^2 + 6*log(x)/x^2 + 3/x^2)*log(12)^8 + 2*(4*log(x)^5/x^2 + 10*log(x)^4/x^2 + 20*
log(x)^3/x^2 + 30*log(x)^2/x^2 + 30*log(x)/x^2 + 15/x^2)*log(12)^7 - 10*(2*log(x)^4/x^2 + 4*log(x)^3/x^2 + 6*l
og(x)^2/x^2 + 6*log(x)/x^2 + 3/x^2)*log(12)^7 - 2*x^2*log(x)^6 + 20*log(x)^9/x + 7*(4*log(x)^6/x^2 + 12*log(x)
^5/x^2 + 30*log(x)^4/x^2 + 60*log(x)^3/x^2 + 90*log(x)^2/x^2 + 90*log(x)/x^2 + 45/x^2)*log(12)^6 - 21*(4*log(x
)^5/x^2 + 10*log(x)^4/x^2 + 20*log(x)^3/x^2 + 30*log(x)^2/x^2 + 30*log(x)/x^2 + 15/x^2)*log(12)^6 + 20*(log(x)
^3/x + 3*log(x)^2/x + 6*log(x)/x + 6/x)*log(12)^6 - 60*(log(x)^2/x + 2*log(x)/x + 2/x)*log(12)^6 + x^6 + 7*(8*
log(x)^7/x^2 + 28*log(x)^6/x^2 + 84*log(x)^5/x^2 + 210*log(x)^4/x^2 + 420*log(x)^3/x^2 + 630*log(x)^2/x^2 + 63
0*log(x)/x^2 + 315/x^2)*log(12)^5 - 49*(4*log(x)^6/x^2 + 12*log(x)^5/x^2 + 30*log(x)^4/x^2 + 60*log(x)^3/x^2 +
90*log(x)^2/x^2 + 90*log(x)/x^2 + 45/x^2)*log(12)^5 + 120*(log(x)^4/x + 4*log(x)^3/x + 12*log(x)^2/x + 24*log
(x)/x + 24/x)*log(12)^5 - 480*(log(x)^3/x + 3*log(x)^2/x + 6*log(x)/x + 6/x)*log(12)^5 + 150*log(12)^4*log(x)^
2 - 20*x^3*log(x)^3 + 600*log(12)^3*log(x)^3 + 900*log(12)^2*log(x)^4 + 600*log(12)*log(x)^5 + 150*log(x)^6 -
20/3*x^3*log(12)^2 + 35*(2*log(x)^8/x^2 + 8*log(x)^7/x^2 + 28*log(x)^6/x^2 + 84*log(x)^5/x^2 + 210*log(x)^4/x^
2 + 420*log(x)^3/x^2 + 630*log(x)^2/x^2 + 630*log(x)/x^2 + 315/x^2)*log(12)^4 - 35*(8*log(x)^7/x^2 + 28*log(x)
^6/x^2 + 84*log(x)^5/x^2 + 210*log(x)^4/x^2 + 420*log(x)^3/x^2 + 630*log(x)^2/x^2 + 630*log(x)/x^2 + 315/x^2)*
log(12)^4 - (2*x^2*log(x)^2 - 2*x^2*log(x) + x^2)*log(12)^4 + 300*(log(x)^5/x + 5*log(x)^4/x + 20*log(x)^3/x +
60*log(x)^2/x + 120*log(x)/x + 120/x)*log(12)^4 - (2*x^2*log(x) - x^2)*log(12)^4 - 1500*(log(x)^4/x + 4*log(x
)^3/x + 12*log(x)^2/x + 24*log(x)/x + 24/x)*log(12)^4 - 50*x^4 + 14*(4*log(x)^9/x^2 + 18*log(x)^8/x^2 + 72*log
(x)^7/x^2 + 252*log(x)^6/x^2 + 756*log(x)^5/x^2 + 1890*log(x)^4/x^2 + 3780*log(x)^3/x^2 + 5670*log(x)^2/x^2 +
5670*log(x)/x^2 + 2835/x^2)*log(12)^3 - 126*(2*log(x)^8/x^2 + 8*log(x)^7/x^2 + 28*log(x)^6/x^2 + 84*log(x)^5/x
^2 + 210*log(x)^4/x^2 + 420*log(x)^3/x^2 + 630*log(x)^2/x^2 + 630*log(x)/x^2 + 315/x^2)*log(12)^3 - 2*(4*x^2*l
og(x)^3 - 6*x^2*log(x)^2 + 6*x^2*log(x) - 3*x^2)*log(12)^3 + 400*(log(x)^6/x + 6*log(x)^5/x + 30*log(x)^4/x +
120*log(x)^3/x + 360*log(x)^2/x + 720*log(x)/x + 720/x)*log(12)^3 - 6*(2*x^2*log(x)^2 - 2*x^2*log(x) + x^2)*lo
g(12)^3 - 2400*(log(x)^5/x + 5*log(x)^4/x + 20*log(x)^3/x + 60*log(x)^2/x + 120*log(x)/x + 120/x)*log(12)^3 +
500*x*log(x)^3 + 7*(4*log(x)^10/x^2 + 20*log(x)^9/x^2 + 90*log(x)^8/x^2 + 360*log(x)^7/x^2 + 1260*log(x)^6/x^2
+ 3780*log(x)^5/x^2 + 9450*log(x)^4/x^2 + 18900*log(x)^3/x^2 + 28350*log(x)^2/x^2 + 28350*log(x)/x^2 + 14175/
x^2)*log(12)^2 - 35*(4*log(x)^9/x^2 + 18*log(x)^8/x^2 + 72*log(x)^7/x^2 + 252*log(x)^6/x^2 + 756*log(x)^5/x^2
+ 1890*log(x)^4/x^2 + 3780*log(x)^3/x^2 + 5670*log(x)^2/x^2 + 5670*log(x)/x^2 + 2835/x^2)*log(12)^2 - 6*(2*x^2
*log(x)^4 - 4*x^2*log(x)^3 + 6*x^2*log(x)^2 - 6*x^2*log(x) + 3*x^2)*log(12)^2 + 300*(log(x)^7/x + 7*log(x)^6/x
+ 42*log(x)^5/x + 210*log(x)^4/x + 840*log(x)^3/x + 2520*log(x)^2/x + 5040*log(x)/x + 5040/x)*log(12)^2 - 6*(
4*x^2*log(x)^3 - 6*x^2*log(x)^2 + 6*x^2*log(x) - 3*x^2)*log(12)^2 - 2100*(log(x)^6/x + 6*log(x)^5/x + 30*log(x
)^4/x + 120*log(x)^3/x + 360*log(x)^2/x + 720*log(x)/x + 720/x)*log(12)^2 - 20/3*(3*x^3*log(x) - x^3)*log(12)^
2 + 500*(x*log(x) - x)*log(12)^2 + 500*x*log(12)^2 + 625*x^2 + (8*log(x)^11/x^2 + 44*log(x)^10/x^2 + 220*log(x
)^9/x^2 + 990*log(x)^8/x^2 + 3960*log(x)^7/x^2 + 13860*log(x)^6/x^2 + 41580*log(x)^5/x^2 + 103950*log(x)^4/x^2
+ 207900*log(x)^3/x^2 + 311850*log(x)^2/x^2 + 311850*log(x)/x^2 + 155925/x^2)*log(12) - 11*(4*log(x)^10/x^2 +
20*log(x)^9/x^2 + 90*log(x)^8/x^2 + 360*log(x)^7/x^2 + 1260*log(x)^6/x^2 + 3780*log(x)^5/x^2 + 9450*log(x)^4/
x^2 + 18900*log(x)^3/x^2 + 28350*log(x)^2/x^2 + 28350*log(x)/x^2 + 14175/x^2)*log(12) - 2*(4*x^2*log(x)^5 - 10
*x^2*log(x)^4 + 20*x^2*log(x)^3 - 30*x^2*log(x)^2 + 30*x^2*log(x) - 15*x^2)*log(12) + 120*(log(x)^8/x + 8*log(
x)^7/x + 56*log(x)^6/x + 336*log(x)^5/x + 1680*log(x)^4/x + 6720*log(x)^3/x + 20160*log(x)^2/x + 40320*log(x)/
x + 40320/x)*log(12) - 10*(2*x^2*log(x)^4 - 4*x^2*log(x)^3 + 6*x^2*log(x)^2 - 6*x^2*log(x) + 3*x^2)*log(12) -
960*(log(x)^7/x + 7*log(x)^6/x + 42*log(x)^5/x + 210*log(x)^4/x + 840*log(x)^3/x + 2520*log(x)^2/x + 5040*log(
x)/x + 5040/x)*log(12) - 40/9*(9*x^3*log(x)^2 - 6*x^3*log(x) + 2*x^3)*log(12) - 80/9*(3*x^3*log(x) - x^3)*log(
12) + 1000*(x*log(x)^2 - 2*x*log(x) + 2*x)*log(12) + 2000*(x*log(x) - x)*log(12)

________________________________________________________________________________________

maple [B]  time = 3.85, size = 1024, normalized size = 36.57

method	result	size
risch	\(\frac {\ln \relax (x )^{12}}{x^{2}}+\frac {4 \left (4 \ln \relax (2)+2 \ln \relax (3)\right ) \ln \relax (x )^{11}}{x^{2}}+\frac {7 \left (16 \ln \relax (2)^{2}+16 \ln \relax (2) \ln \relax (3)+4 \ln \relax (3)^{2}\right ) \ln \relax (x )^{10}}{x^{2}}+\frac {\left (20 x +56 \ln \relax (3)^{3}+448 \ln \relax (2)^{3}+672 \ln \relax (2)^{2} \ln \relax (3)+336 \ln \relax (2) \ln \relax (3)^{2}\right ) \ln \relax (x )^{9}}{x^{2}}+\frac {5 \left (112 \ln \relax (3)^{4}+1792 \ln \relax (2)^{4}+2688 \ln \relax (3)^{2} \ln \relax (2)^{2}+192 x \ln \relax (3)+384 x \ln \relax (2)+3584 \ln \relax (2)^{3} \ln \relax (3)+896 \ln \relax (2) \ln \relax (3)^{3}\right ) \ln \relax (x )^{8}}{8 x^{2}}+\frac {\left (4800 x \ln \relax (2)^{2}+1200 x \ln \relax (3)^{2}+7168 \ln \relax (2)^{5}+4800 x \ln \relax (2) \ln \relax (3)+224 \ln \relax (3)^{5}+17920 \ln \relax (2)^{4} \ln \relax (3)+17920 \ln \relax (2)^{3} \ln \relax (3)^{2}+8960 \ln \relax (2)^{2} \ln \relax (3)^{3}+2240 \ln \relax (2) \ln \relax (3)^{4}\right ) \ln \relax (x )^{7}}{4 x^{2}}+\frac {\left (-32 x^{4}+2400 x^{2}+38400 x \ln \relax (2) \ln \relax (3)^{2}+107520 \ln \relax (3)^{2} \ln \relax (2)^{4}+6400 x \ln \relax (3)^{3}+51200 x \ln \relax (2)^{3}+28672 \ln \relax (2)^{6}+448 \ln \relax (3)^{6}+76800 \ln \relax (2)^{2} \ln \relax (3) x +86016 \ln \relax (2)^{5} \ln \relax (3)+71680 \ln \relax (2)^{3} \ln \relax (3)^{3}+26880 \ln \relax (2)^{2} \ln \relax (3)^{4}+5376 \ln \relax (2) \ln \relax (3)^{5}\right ) \ln \relax (x )^{6}}{16 x^{2}}+\frac {\left (153600 x \ln \relax (3) \ln \relax (2)^{3}+9600 x^{2} \ln \relax (3)+76800 x \ln \relax (2)^{4}-256 x^{4} \ln \relax (2)+4800 x \ln \relax (3)^{4}+19200 x^{2} \ln \relax (2)-128 x^{4} \ln \relax (3)+35840 \ln \relax (2)^{3} \ln \relax (3)^{4}+10752 \ln \relax (2)^{2} \ln \relax (3)^{5}+1792 \ln \relax (2) \ln \relax (3)^{6}+128 \ln \relax (3)^{7}+16384 \ln \relax (2)^{7}+115200 \ln \relax (2)^{2} \ln \relax (3)^{2} x +38400 \ln \relax (2) \ln \relax (3)^{3} x +57344 \ln \relax (2)^{6} \ln \relax (3)+86016 \ln \relax (2)^{5} \ln \relax (3)^{2}+71680 \ln \relax (2)^{4} \ln \relax (3)^{3}\right ) \ln \relax (x )^{5}}{16 x^{2}}+\frac {\left (65536 \ln \relax (2)^{8}+286720 \ln \relax (3)^{4} \ln \relax (2)^{4}-12288 x^{4} \ln \relax (2)^{2}+921600 x^{2} \ln \relax (2)^{2}+230400 x^{2} \ln \relax (3)^{2}-3072 x^{4} \ln \relax (3)^{2}+30720 x \ln \relax (3)^{5}+983040 x \ln \relax (2)^{5}+262144 \ln \relax (2)^{7} \ln \relax (3)+458752 \ln \relax (2)^{6} \ln \relax (3)^{2}+458752 \ln \relax (2)^{5} \ln \relax (3)^{3}+114688 \ln \relax (2)^{3} \ln \relax (3)^{5}+28672 \ln \relax (2)^{2} \ln \relax (3)^{6}+4096 \ln \relax (2) \ln \relax (3)^{7}+256 \ln \relax (3)^{8}+2457600 \ln \relax (2)^{4} \ln \relax (3) x +2457600 \ln \relax (2)^{3} \ln \relax (3)^{2} x +1228800 \ln \relax (2)^{2} \ln \relax (3)^{3} x +307200 \ln \relax (2) \ln \relax (3)^{4} x -12288 \ln \relax (2) \ln \relax (3) x^{4}+921600 \ln \relax (2) \ln \relax (3) x^{2}\right ) \ln \relax (x )^{4}}{256 x^{2}}+\frac {\left (-128 x^{3} \ln \relax (3)^{3}-1024 x^{3} \ln \relax (2)^{3}-320 x^{4}+8000 x^{2}+57600 x \ln \relax (2) \ln \relax (3)^{2}+76800 \ln \relax (3)^{2} \ln \relax (2)^{4}+9600 x \ln \relax (3)^{3}+76800 x \ln \relax (2)^{3}+20480 \ln \relax (2)^{6}+320 \ln \relax (3)^{6}+115200 \ln \relax (2)^{2} \ln \relax (3) x -1536 \ln \relax (2)^{2} \ln \relax (3) x^{3}-768 \ln \relax (2) \ln \relax (3)^{2} x^{3}+61440 \ln \relax (2)^{5} \ln \relax (3)+51200 \ln \relax (2)^{3} \ln \relax (3)^{3}+19200 \ln \relax (2)^{2} \ln \relax (3)^{4}+3840 \ln \relax (2) \ln \relax (3)^{5}\right ) \ln \relax (x )^{3}}{16 x}+\left (-48 x^{2} \ln \relax (3)^{2} \ln \relax (2)^{2}-32 x^{2} \ln \relax (2)^{4}+150 \ln \relax (3)^{4}+2400 \ln \relax (2)^{4}+3600 \ln \relax (3)^{2} \ln \relax (2)^{2}-40 x^{3} \ln \relax (3)+1000 x \ln \relax (3)+2000 x \ln \relax (2)-80 x^{3} \ln \relax (2)-2 x^{2} \ln \relax (3)^{4}-64 \ln \relax (2)^{3} \ln \relax (3) x^{2}-16 \ln \relax (2) \ln \relax (3)^{3} x^{2}+4800 \ln \relax (2)^{3} \ln \relax (3)+1200 \ln \relax (2) \ln \relax (3)^{3}\right ) \ln \relax (x )^{2}+\left (-80 x^{3} \ln \relax (3) \ln \relax (2)-20 x^{3} \ln \relax (3)^{2}-80 x^{3} \ln \relax (2)^{2}+2000 x \ln \relax (2)^{2}+500 x \ln \relax (3)^{2}+2000 x \ln \relax (2) \ln \relax (3)\right ) \ln \relax (x )+x^{6}-50 x^{4}+625 x^{2}\)	\(1024\)
default	\(\text {Expression too large to display}\)	\(2336\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-2*ln(x)^4+4*ln(x)^3)*ln(12*x)^8+8*ln(x)^4*ln(12*x)^7+(-20*x*ln(x)^3+60*x*ln(x)^2)*ln(12*x)^6+120*x*ln(x
)^3*ln(12*x)^5+(-4*x^4*ln(x)^2+(-4*x^4+300*x^2)*ln(x))*ln(12*x)^4+(-8*x^4+600*x^2)*ln(x)^2*ln(12*x)^3+((-60*x^
5+500*x^3)*ln(x)-20*x^5+500*x^3)*ln(12*x)^2+(-40*x^5+1000*x^3)*ln(x)*ln(12*x)+6*x^8-200*x^6+1250*x^4)/x^3,x,me
thod=_RETURNVERBOSE)

[Out]

1/x^2*ln(x)^12+4*(4*ln(2)+2*ln(3))/x^2*ln(x)^11+7*(16*ln(2)^2+16*ln(2)*ln(3)+4*ln(3)^2)/x^2*ln(x)^10+(20*x+56*
ln(3)^3+448*ln(2)^3+672*ln(2)^2*ln(3)+336*ln(2)*ln(3)^2)/x^2*ln(x)^9+5/8*(112*ln(3)^4+1792*ln(2)^4+2688*ln(3)^
2*ln(2)^2+192*x*ln(3)+384*x*ln(2)+3584*ln(2)^3*ln(3)+896*ln(2)*ln(3)^3)/x^2*ln(x)^8+1/4*(4800*x*ln(2)^2+1200*x
*ln(3)^2+7168*ln(2)^5+4800*x*ln(2)*ln(3)+224*ln(3)^5+17920*ln(2)^4*ln(3)+17920*ln(2)^3*ln(3)^2+8960*ln(2)^2*ln
(3)^3+2240*ln(2)*ln(3)^4)/x^2*ln(x)^7+1/16*(-32*x^4+2400*x^2+38400*x*ln(2)*ln(3)^2+107520*ln(3)^2*ln(2)^4+6400
*x*ln(3)^3+51200*x*ln(2)^3+28672*ln(2)^6+448*ln(3)^6+76800*ln(2)^2*ln(3)*x+86016*ln(2)^5*ln(3)+71680*ln(2)^3*l
n(3)^3+26880*ln(2)^2*ln(3)^4+5376*ln(2)*ln(3)^5)/x^2*ln(x)^6+1/16*(153600*x*ln(3)*ln(2)^3+9600*x^2*ln(3)+76800
*x*ln(2)^4-256*x^4*ln(2)+4800*x*ln(3)^4+19200*x^2*ln(2)-128*x^4*ln(3)+35840*ln(2)^3*ln(3)^4+10752*ln(2)^2*ln(3
)^5+1792*ln(2)*ln(3)^6+128*ln(3)^7+16384*ln(2)^7+115200*ln(2)^2*ln(3)^2*x+38400*ln(2)*ln(3)^3*x+57344*ln(2)^6*
ln(3)+86016*ln(2)^5*ln(3)^2+71680*ln(2)^4*ln(3)^3)/x^2*ln(x)^5+1/256*(65536*ln(2)^8+286720*ln(3)^4*ln(2)^4-122
88*x^4*ln(2)^2+921600*x^2*ln(2)^2+230400*x^2*ln(3)^2-3072*x^4*ln(3)^2+30720*x*ln(3)^5+983040*x*ln(2)^5+262144*
ln(2)^7*ln(3)+458752*ln(2)^6*ln(3)^2+458752*ln(2)^5*ln(3)^3+114688*ln(2)^3*ln(3)^5+28672*ln(2)^2*ln(3)^6+4096*
ln(2)*ln(3)^7+256*ln(3)^8+2457600*ln(2)^4*ln(3)*x+2457600*ln(2)^3*ln(3)^2*x+1228800*ln(2)^2*ln(3)^3*x+307200*l
n(2)*ln(3)^4*x-12288*ln(2)*ln(3)*x^4+921600*ln(2)*ln(3)*x^2)/x^2*ln(x)^4+1/16*(-128*x^3*ln(3)^3-1024*x^3*ln(2)
^3-320*x^4+8000*x^2+57600*x*ln(2)*ln(3)^2+76800*ln(3)^2*ln(2)^4+9600*x*ln(3)^3+76800*x*ln(2)^3+20480*ln(2)^6+3
20*ln(3)^6+115200*ln(2)^2*ln(3)*x-1536*ln(2)^2*ln(3)*x^3-768*ln(2)*ln(3)^2*x^3+61440*ln(2)^5*ln(3)+51200*ln(2)
^3*ln(3)^3+19200*ln(2)^2*ln(3)^4+3840*ln(2)*ln(3)^5)/x*ln(x)^3+(-48*x^2*ln(3)^2*ln(2)^2-32*x^2*ln(2)^4+150*ln(
3)^4+2400*ln(2)^4+3600*ln(3)^2*ln(2)^2-40*x^3*ln(3)+1000*x*ln(3)+2000*x*ln(2)-80*x^3*ln(2)-2*x^2*ln(3)^4-64*ln
(2)^3*ln(3)*x^2-16*ln(2)*ln(3)^3*x^2+4800*ln(2)^3*ln(3)+1200*ln(2)*ln(3)^3)*ln(x)^2+(-80*x^3*ln(3)*ln(2)-20*x^
3*ln(3)^2-80*x^3*ln(2)^2+2000*x*ln(2)^2+500*x*ln(3)^2+2000*x*ln(2)*ln(3))*ln(x)+x^6-50*x^4+625*x^2

________________________________________________________________________________________

maxima [B]  time = 0.54, size = 1994, normalized size = 71.21 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*log(x)^4+4*log(x)^3)*log(12*x)^8+8*log(x)^4*log(12*x)^7+(-20*x*log(x)^3+60*x*log(x)^2)*log(12*x
)^6+120*x*log(x)^3*log(12*x)^5+(-4*x^4*log(x)^2+(-4*x^4+300*x^2)*log(x))*log(12*x)^4+(-8*x^4+600*x^2)*log(x)^2
*log(12*x)^3+((-60*x^5+500*x^3)*log(x)-20*x^5+500*x^3)*log(12*x)^2+(-40*x^5+1000*x^3)*log(x)*log(12*x)+6*x^8-2
00*x^6+1250*x^4)/x^3,x, algorithm="maxima")

[Out]

x^6 + 150*log(12*x)^4*log(x)^2 - 20/9*(9*log(12*x)^2 - 6*log(12*x) + 2)*x^3*log(x) - (2*log(12*x)^4 - 4*log(12
*x)^3 + 6*log(12*x)^2 - 6*log(12*x) + 3)*x^2*log(x)^2 - (4*log(12*x)^3 - 6*log(12*x)^2 + 6*log(12*x) - 3)*x^2*
log(x)^2 - 20/27*(9*log(12*x)^2 - 6*log(12*x) + 2)*x^3 + 20/9*(3*log(12*x)^2 - 4*log(12*x) + 2)*x^3 - 50*x^4 +
40/27*x^3*(3*log(3) + 6*log(2) - 2) - (2*log(12*x)^4 - 4*log(12*x)^3 + 6*log(12*x)^2 - 6*log(12*x) + 3)*x^2*l
og(x) + (2*log(12*x)^4 - 8*log(12*x)^3 + 18*log(12*x)^2 - 24*log(12*x) + 15)*x^2*log(x) + 2*(2*log(12*x)^3 - 6
*log(12*x)^2 + 9*log(12*x) - 6)*x^2*log(x) + 40/9*x^3*log(x) + 1/2*(2*log(12*x)^4 - 8*log(12*x)^3 + 18*log(12*
x)^2 - 24*log(12*x) + 15)*x^2 - 1/2*(2*log(12*x)^4 - 12*log(12*x)^3 + 36*log(12*x)^2 - 60*log(12*x) + 45)*x^2
- (2*log(12*x)^3 - 9*log(12*x)^2 + 18*log(12*x) - 15)*x^2 + 500*(log(12*x)^2 - 2*log(12*x) + 2)*x*log(x) + 20*
(log(12*x)^6 + 6*log(12*x)^5 + 30*log(12*x)^4 + 120*log(12*x)^3 + 360*log(12*x)^2 + 720*log(12*x) + 720)*log(x
)^3/x - 120*(log(12*x)^5 + 5*log(12*x)^4 + 20*log(12*x)^3 + 60*log(12*x)^2 + 120*log(12*x) + 120)*log(x)^3/x +
1/2*(2*log(12*x)^8 + 8*log(12*x)^7 + 28*log(12*x)^6 + 84*log(12*x)^5 + 210*log(12*x)^4 + 420*log(12*x)^3 + 63
0*log(12*x)^2 + 630*log(12*x) + 315)*log(x)^4/x^2 - 1/2*(8*log(12*x)^7 + 28*log(12*x)^6 + 84*log(12*x)^5 + 210
*log(12*x)^4 + 420*log(12*x)^3 + 630*log(12*x)^2 + 630*log(12*x) + 315)*log(x)^4/x^2 + 625*x^2 - 1000*x*(log(3
) + 2*log(2) - 2) + 1000*x*log(12*x) - 40/9*(3*x^3*log(12*x) - x^3)*log(x) + 1000*(x*log(12*x) - x)*log(x) - 1
000*x*log(x) + 60*(log(12*x)^6 + 12*log(12*x)^5 + 90*log(12*x)^4 + 480*log(12*x)^3 + 1800*log(12*x)^2 + 4320*l
og(12*x) + 5040)*log(x)^2/x - 60*(log(12*x)^6 + 6*log(12*x)^5 + 30*log(12*x)^4 + 120*log(12*x)^3 + 360*log(12*
x)^2 + 720*log(12*x) + 720)*log(x)^2/x - 360*(log(12*x)^5 + 10*log(12*x)^4 + 60*log(12*x)^3 + 240*log(12*x)^2
+ 600*log(12*x) + 720)*log(x)^2/x + (2*log(12*x)^8 + 16*log(12*x)^7 + 84*log(12*x)^6 + 336*log(12*x)^5 + 1050*
log(12*x)^4 + 2520*log(12*x)^3 + 4410*log(12*x)^2 + 5040*log(12*x) + 2835)*log(x)^3/x^2 - (2*log(12*x)^8 + 8*l
og(12*x)^7 + 28*log(12*x)^6 + 84*log(12*x)^5 + 210*log(12*x)^4 + 420*log(12*x)^3 + 630*log(12*x)^2 + 630*log(1
2*x) + 315)*log(x)^3/x^2 - 2*(4*log(12*x)^7 + 28*log(12*x)^6 + 126*log(12*x)^5 + 420*log(12*x)^4 + 1050*log(12
*x)^3 + 1890*log(12*x)^2 + 2205*log(12*x) + 1260)*log(x)^3/x^2 - 2000*x + 120*(log(12*x)^6 + 18*log(12*x)^5 +
180*log(12*x)^4 + 1200*log(12*x)^3 + 5400*log(12*x)^2 + 15120*log(12*x) + 20160)*log(x)/x - 120*(log(12*x)^6 +
12*log(12*x)^5 + 90*log(12*x)^4 + 480*log(12*x)^3 + 1800*log(12*x)^2 + 4320*log(12*x) + 5040)*log(x)/x - 720*
(log(12*x)^5 + 15*log(12*x)^4 + 120*log(12*x)^3 + 600*log(12*x)^2 + 1800*log(12*x) + 2520)*log(x)/x + 3/2*(2*l
og(12*x)^8 + 24*log(12*x)^7 + 168*log(12*x)^6 + 840*log(12*x)^5 + 3150*log(12*x)^4 + 8820*log(12*x)^3 + 17640*
log(12*x)^2 + 22680*log(12*x) + 14175)*log(x)^2/x^2 - 3/2*(2*log(12*x)^8 + 16*log(12*x)^7 + 84*log(12*x)^6 + 3
36*log(12*x)^5 + 1050*log(12*x)^4 + 2520*log(12*x)^3 + 4410*log(12*x)^2 + 5040*log(12*x) + 2835)*log(x)^2/x^2
- 3*(4*log(12*x)^7 + 42*log(12*x)^6 + 252*log(12*x)^5 + 1050*log(12*x)^4 + 3150*log(12*x)^3 + 6615*log(12*x)^2
+ 8820*log(12*x) + 5670)*log(x)^2/x^2 + 120*(log(12*x)^6 + 24*log(12*x)^5 + 300*log(12*x)^4 + 2400*log(12*x)^
3 + 12600*log(12*x)^2 + 40320*log(12*x) + 60480)/x - 120*(log(12*x)^6 + 18*log(12*x)^5 + 180*log(12*x)^4 + 120
0*log(12*x)^3 + 5400*log(12*x)^2 + 15120*log(12*x) + 20160)/x - 720*(log(12*x)^5 + 20*log(12*x)^4 + 200*log(12
*x)^3 + 1200*log(12*x)^2 + 4200*log(12*x) + 6720)/x + 3/2*(2*log(12*x)^8 + 32*log(12*x)^7 + 280*log(12*x)^6 +
1680*log(12*x)^5 + 7350*log(12*x)^4 + 23520*log(12*x)^3 + 52920*log(12*x)^2 + 75600*log(12*x) + 51975)*log(x)/
x^2 - 3/2*(2*log(12*x)^8 + 24*log(12*x)^7 + 168*log(12*x)^6 + 840*log(12*x)^5 + 3150*log(12*x)^4 + 8820*log(12
*x)^3 + 17640*log(12*x)^2 + 22680*log(12*x) + 14175)*log(x)/x^2 - 6*(2*log(12*x)^7 + 28*log(12*x)^6 + 210*log(
12*x)^5 + 1050*log(12*x)^4 + 3675*log(12*x)^3 + 8820*log(12*x)^2 + 13230*log(12*x) + 9450)*log(x)/x^2 + 3/4*(2
*log(12*x)^8 + 40*log(12*x)^7 + 420*log(12*x)^6 + 2940*log(12*x)^5 + 14700*log(12*x)^4 + 52920*log(12*x)^3 + 1
32300*log(12*x)^2 + 207900*log(12*x) + 155925)/x^2 - 3/4*(2*log(12*x)^8 + 32*log(12*x)^7 + 280*log(12*x)^6 + 1
680*log(12*x)^5 + 7350*log(12*x)^4 + 23520*log(12*x)^3 + 52920*log(12*x)^2 + 75600*log(12*x) + 51975)/x^2 - 3/
2*(4*log(12*x)^7 + 70*log(12*x)^6 + 630*log(12*x)^5 + 3675*log(12*x)^4 + 14700*log(12*x)^3 + 39690*log(12*x)^2
+ 66150*log(12*x) + 51975)/x^2

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mupad [B]  time = 8.41, size = 367, normalized size = 13.11 \begin {gather*} 600\,\ln \left (12\right )\,{\ln \relax (x)}^5+500\,x\,{\ln \relax (x)}^3+150\,{\ln \relax (x)}^6+900\,{\ln \left (12\right )}^2\,{\ln \relax (x)}^4+600\,{\ln \left (12\right )}^3\,{\ln \relax (x)}^3+150\,{\ln \left (12\right )}^4\,{\ln \relax (x)}^2-20\,x^3\,{\ln \relax (x)}^3-2\,x^2\,{\ln \relax (x)}^6+\frac {20\,{\ln \relax (x)}^9}{x}+\frac {{\ln \relax (x)}^{12}}{x^2}+625\,x^2-50\,x^4+x^6-12\,x^2\,{\ln \left (12\right )}^2\,{\ln \relax (x)}^4-8\,x^2\,{\ln \left (12\right )}^3\,{\ln \relax (x)}^3-2\,x^2\,{\ln \left (12\right )}^4\,{\ln \relax (x)}^2+\frac {300\,{\ln \left (12\right )}^2\,{\ln \relax (x)}^7}{x}+\frac {400\,{\ln \left (12\right )}^3\,{\ln \relax (x)}^6}{x}+\frac {300\,{\ln \left (12\right )}^4\,{\ln \relax (x)}^5}{x}+\frac {120\,{\ln \left (12\right )}^5\,{\ln \relax (x)}^4}{x}+\frac {20\,{\ln \left (12\right )}^6\,{\ln \relax (x)}^3}{x}+\frac {28\,{\ln \left (12\right )}^2\,{\ln \relax (x)}^{10}}{x^2}+\frac {56\,{\ln \left (12\right )}^3\,{\ln \relax (x)}^9}{x^2}+\frac {70\,{\ln \left (12\right )}^4\,{\ln \relax (x)}^8}{x^2}+\frac {56\,{\ln \left (12\right )}^5\,{\ln \relax (x)}^7}{x^2}+\frac {28\,{\ln \left (12\right )}^6\,{\ln \relax (x)}^6}{x^2}+\frac {8\,{\ln \left (12\right )}^7\,{\ln \relax (x)}^5}{x^2}+\frac {{\ln \left (12\right )}^8\,{\ln \relax (x)}^4}{x^2}+1000\,x\,\ln \left (12\right )\,{\ln \relax (x)}^2+500\,x\,{\ln \left (12\right )}^2\,\ln \relax (x)-40\,x^3\,\ln \left (12\right )\,{\ln \relax (x)}^2-20\,x^3\,{\ln \left (12\right )}^2\,\ln \relax (x)-8\,x^2\,\ln \left (12\right )\,{\ln \relax (x)}^5+\frac {120\,\ln \left (12\right )\,{\ln \relax (x)}^8}{x}+\frac {8\,\ln \left (12\right )\,{\ln \relax (x)}^{11}}{x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((8*log(12*x)^7*log(x)^4 + log(12*x)^6*(60*x*log(x)^2 - 20*x*log(x)^3) + log(12*x)^8*(4*log(x)^3 - 2*log(x)
^4) + 1250*x^4 - 200*x^6 + 6*x^8 + log(12*x)^2*(log(x)*(500*x^3 - 60*x^5) + 500*x^3 - 20*x^5) + log(12*x)^4*(l
og(x)*(300*x^2 - 4*x^4) - 4*x^4*log(x)^2) + log(12*x)^3*log(x)^2*(600*x^2 - 8*x^4) + log(12*x)*log(x)*(1000*x^
3 - 40*x^5) + 120*x*log(12*x)^5*log(x)^3)/x^3,x)

[Out]

600*log(12)*log(x)^5 + 500*x*log(x)^3 + 150*log(x)^6 + 900*log(12)^2*log(x)^4 + 600*log(12)^3*log(x)^3 + 150*l
og(12)^4*log(x)^2 - 20*x^3*log(x)^3 - 2*x^2*log(x)^6 + (20*log(x)^9)/x + log(x)^12/x^2 + 625*x^2 - 50*x^4 + x^
6 - 12*x^2*log(12)^2*log(x)^4 - 8*x^2*log(12)^3*log(x)^3 - 2*x^2*log(12)^4*log(x)^2 + (300*log(12)^2*log(x)^7)
/x + (400*log(12)^3*log(x)^6)/x + (300*log(12)^4*log(x)^5)/x + (120*log(12)^5*log(x)^4)/x + (20*log(12)^6*log(
x)^3)/x + (28*log(12)^2*log(x)^10)/x^2 + (56*log(12)^3*log(x)^9)/x^2 + (70*log(12)^4*log(x)^8)/x^2 + (56*log(1
2)^5*log(x)^7)/x^2 + (28*log(12)^6*log(x)^6)/x^2 + (8*log(12)^7*log(x)^5)/x^2 + (log(12)^8*log(x)^4)/x^2 + 100
0*x*log(12)*log(x)^2 + 500*x*log(12)^2*log(x) - 40*x^3*log(12)*log(x)^2 - 20*x^3*log(12)^2*log(x) - 8*x^2*log(
12)*log(x)^5 + (120*log(12)*log(x)^8)/x + (8*log(12)*log(x)^11)/x^2

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sympy [B]  time = 1.24, size = 333, normalized size = 11.89 \begin {gather*} x^{6} - 50 x^{4} + 625 x^{2} + \left (- 20 x^{3} \log {\left (12 \right )}^{2} + 500 x \log {\left (12 \right )}^{2}\right ) \log {\relax (x )} + \left (- 40 x^{3} \log {\left (12 \right )} - 2 x^{2} \log {\left (12 \right )}^{4} + 1000 x \log {\left (12 \right )} + 150 \log {\left (12 \right )}^{4}\right ) \log {\relax (x )}^{2} + \frac {\left (- 20 x^{4} - 8 x^{3} \log {\left (12 \right )}^{3} + 500 x^{2} + 600 x \log {\left (12 \right )}^{3} + 20 \log {\left (12 \right )}^{6}\right ) \log {\relax (x )}^{3}}{x} + \frac {\left (20 x + 56 \log {\left (12 \right )}^{3}\right ) \log {\relax (x )}^{9}}{x^{2}} + \frac {\left (120 x \log {\left (12 \right )} + 70 \log {\left (12 \right )}^{4}\right ) \log {\relax (x )}^{8}}{x^{2}} + \frac {\left (300 x \log {\left (12 \right )}^{2} + 56 \log {\left (12 \right )}^{5}\right ) \log {\relax (x )}^{7}}{x^{2}} + \frac {\left (- 2 x^{4} + 150 x^{2} + 400 x \log {\left (12 \right )}^{3} + 28 \log {\left (12 \right )}^{6}\right ) \log {\relax (x )}^{6}}{x^{2}} + \frac {\left (- 8 x^{4} \log {\left (12 \right )} + 600 x^{2} \log {\left (12 \right )} + 300 x \log {\left (12 \right )}^{4} + 8 \log {\left (12 \right )}^{7}\right ) \log {\relax (x )}^{5}}{x^{2}} + \frac {\left (- 12 x^{4} \log {\left (12 \right )}^{2} + 900 x^{2} \log {\left (12 \right )}^{2} + 120 x \log {\left (12 \right )}^{5} + \log {\left (12 \right )}^{8}\right ) \log {\relax (x )}^{4}}{x^{2}} + \frac {\log {\relax (x )}^{12}}{x^{2}} + \frac {8 \log {\left (12 \right )} \log {\relax (x )}^{11}}{x^{2}} + \frac {28 \log {\left (12 \right )}^{2} \log {\relax (x )}^{10}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*ln(x)**4+4*ln(x)**3)*ln(12*x)**8+8*ln(x)**4*ln(12*x)**7+(-20*x*ln(x)**3+60*x*ln(x)**2)*ln(12*x)
**6+120*x*ln(x)**3*ln(12*x)**5+(-4*x**4*ln(x)**2+(-4*x**4+300*x**2)*ln(x))*ln(12*x)**4+(-8*x**4+600*x**2)*ln(x
)**2*ln(12*x)**3+((-60*x**5+500*x**3)*ln(x)-20*x**5+500*x**3)*ln(12*x)**2+(-40*x**5+1000*x**3)*ln(x)*ln(12*x)+
6*x**8-200*x**6+1250*x**4)/x**3,x)

[Out]

x**6 - 50*x**4 + 625*x**2 + (-20*x**3*log(12)**2 + 500*x*log(12)**2)*log(x) + (-40*x**3*log(12) - 2*x**2*log(1
2)**4 + 1000*x*log(12) + 150*log(12)**4)*log(x)**2 + (-20*x**4 - 8*x**3*log(12)**3 + 500*x**2 + 600*x*log(12)*
*3 + 20*log(12)**6)*log(x)**3/x + (20*x + 56*log(12)**3)*log(x)**9/x**2 + (120*x*log(12) + 70*log(12)**4)*log(
x)**8/x**2 + (300*x*log(12)**2 + 56*log(12)**5)*log(x)**7/x**2 + (-2*x**4 + 150*x**2 + 400*x*log(12)**3 + 28*l
og(12)**6)*log(x)**6/x**2 + (-8*x**4*log(12) + 600*x**2*log(12) + 300*x*log(12)**4 + 8*log(12)**7)*log(x)**5/x
**2 + (-12*x**4*log(12)**2 + 900*x**2*log(12)**2 + 120*x*log(12)**5 + log(12)**8)*log(x)**4/x**2 + log(x)**12/
x**2 + 8*log(12)*log(x)**11/x**2 + 28*log(12)**2*log(x)**10/x**2

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