3.17.74 \(\int \frac {300 x^3+300 x^4+(-3600 x^2-4500 x^3-900 x^4) \log (\frac {1+x}{3})+(14400 x+21600 x^2+8100 x^3+900 x^4) \log ^2(\frac {1+x}{3})+(-19200-33600 x-18000 x^2-3900 x^3-300 x^4) \log ^3(\frac {1+x}{3})+\log ^2(x^2) (-30 x^4+(120 x^3+30 x^4) \log (\frac {1+x}{3})+(120 x^2+120 x^3) \log ^2(\frac {1+x}{3})+(-480 x-600 x^2-120 x^3) \log ^3(\frac {1+x}{3}))+\log ^3(x^2) (-6 x^4 \log (\frac {1+x}{3})+(24 x^2+24 x^3) \log ^3(\frac {1+x}{3}))+\log (x^2) ((60 x^3+60 x^4) \log (\frac {1+x}{3})+(-480 x^2-600 x^3-120 x^4) \log ^2(\frac {1+x}{3})+(960 x+1440 x^2+540 x^3+60 x^4) \log ^3(\frac {1+x}{3}))}{\log ^3(x^2) (-5 x^4-5 x^5+(60 x^3+75 x^4+15 x^5) \log (\frac {1+x}{3})+(-240 x^2-360 x^3-135 x^4-15 x^5) \log ^2(\frac {1+x}{3})+(320 x+560 x^2+300 x^3+65 x^4+5 x^5) \log ^3(\frac {1+x}{3}))} \, dx\)

Optimal. Leaf size=40 \[ 3 \left (1+\frac {1}{5} \left (\frac {5}{\log \left (x^2\right )}+\frac {x}{-4-x+\frac {x}{\log \left (\frac {1+x}{3}\right )}}\right )^2\right ) \]

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Rubi [F]  time = 50.26, 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 {300 x^3+300 x^4+\left (-3600 x^2-4500 x^3-900 x^4\right ) \log \left (\frac {1+x}{3}\right )+\left (14400 x+21600 x^2+8100 x^3+900 x^4\right ) \log ^2\left (\frac {1+x}{3}\right )+\left (-19200-33600 x-18000 x^2-3900 x^3-300 x^4\right ) \log ^3\left (\frac {1+x}{3}\right )+\log ^2\left (x^2\right ) \left (-30 x^4+\left (120 x^3+30 x^4\right ) \log \left (\frac {1+x}{3}\right )+\left (120 x^2+120 x^3\right ) \log ^2\left (\frac {1+x}{3}\right )+\left (-480 x-600 x^2-120 x^3\right ) \log ^3\left (\frac {1+x}{3}\right )\right )+\log ^3\left (x^2\right ) \left (-6 x^4 \log \left (\frac {1+x}{3}\right )+\left (24 x^2+24 x^3\right ) \log ^3\left (\frac {1+x}{3}\right )\right )+\log \left (x^2\right ) \left (\left (60 x^3+60 x^4\right ) \log \left (\frac {1+x}{3}\right )+\left (-480 x^2-600 x^3-120 x^4\right ) \log ^2\left (\frac {1+x}{3}\right )+\left (960 x+1440 x^2+540 x^3+60 x^4\right ) \log ^3\left (\frac {1+x}{3}\right )\right )}{\log ^3\left (x^2\right ) \left (-5 x^4-5 x^5+\left (60 x^3+75 x^4+15 x^5\right ) \log \left (\frac {1+x}{3}\right )+\left (-240 x^2-360 x^3-135 x^4-15 x^5\right ) \log ^2\left (\frac {1+x}{3}\right )+\left (320 x+560 x^2+300 x^3+65 x^4+5 x^5\right ) \log ^3\left (\frac {1+x}{3}\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(300*x^3 + 300*x^4 + (-3600*x^2 - 4500*x^3 - 900*x^4)*Log[(1 + x)/3] + (14400*x + 21600*x^2 + 8100*x^3 + 9
00*x^4)*Log[(1 + x)/3]^2 + (-19200 - 33600*x - 18000*x^2 - 3900*x^3 - 300*x^4)*Log[(1 + x)/3]^3 + Log[x^2]^2*(
-30*x^4 + (120*x^3 + 30*x^4)*Log[(1 + x)/3] + (120*x^2 + 120*x^3)*Log[(1 + x)/3]^2 + (-480*x - 600*x^2 - 120*x
^3)*Log[(1 + x)/3]^3) + Log[x^2]^3*(-6*x^4*Log[(1 + x)/3] + (24*x^2 + 24*x^3)*Log[(1 + x)/3]^3) + Log[x^2]*((6
0*x^3 + 60*x^4)*Log[(1 + x)/3] + (-480*x^2 - 600*x^3 - 120*x^4)*Log[(1 + x)/3]^2 + (960*x + 1440*x^2 + 540*x^3
+ 60*x^4)*Log[(1 + x)/3]^3))/(Log[x^2]^3*(-5*x^4 - 5*x^5 + (60*x^3 + 75*x^4 + 15*x^5)*Log[(1 + x)/3] + (-240*
x^2 - 360*x^3 - 135*x^4 - 15*x^5)*Log[(1 + x)/3]^2 + (320*x + 560*x^2 + 300*x^3 + 65*x^4 + 5*x^5)*Log[(1 + x)/
3]^3)),x]

[Out]

(3*x^2)/(5*(4 + x)^2) + 15/Log[x^2]^2 + 12*Defer[Int][1/((4 + x)*Log[x^2]^2), x] - 24*Defer[Int][1/((4 + x)^2*
Log[x^2]), x] - (2*Defer[Int][1/((1 + x)*(-x + 4*Log[(1 + x)/3] + x*Log[(1 + x)/3])^3), x])/5 + (6144*Defer[In
t][1/((4 + x)^3*(-x + 4*Log[(1 + x)/3] + x*Log[(1 + x)/3])^3), x])/5 + (2816*Defer[Int][1/((4 + x)*(-x + 4*Log
[(1 + x)/3] + x*Log[(1 + x)/3])^3), x])/5 + (1152*Defer[Int][1/((4 + x)^3*(-x + 4*Log[(1 + x)/3] + x*Log[(1 +
x)/3])), x])/5 + (72*Defer[Int][1/((4 + x)*(-x + 4*Log[(1 + x)/3] + x*Log[(1 + x)/3])), x])/5 - 48*Defer[Int][
1/((4 + x)*Log[x^2]^2*(-x + 4*Log[(1 + x)/3] + x*Log[(1 + x)/3])), x] - 48*Defer[Int][1/((4 + x)*Log[x^2]*(-x
+ 4*Log[(1 + x)/3] + x*Log[(1 + x)/3])), x] + (102*Defer[Int][(x - (4 + x)*Log[(1 + x)/3])^(-2), x])/5 - (6*De
fer[Int][x/(x - (4 + x)*Log[(1 + x)/3])^2, x])/5 + (2*Defer[Int][1/((1 + x)*(x - (4 + x)*Log[(1 + x)/3])^2), x
])/5 - (4608*Defer[Int][1/((4 + x)^3*(x - (4 + x)*Log[(1 + x)/3])^2), x])/5 + (3456*Defer[Int][1/((4 + x)^2*(x
- (4 + x)*Log[(1 + x)/3])^2), x])/5 - (992*Defer[Int][1/((4 + x)*(x - (4 + x)*Log[(1 + x)/3])^2), x])/5 - 30*
Defer[Int][1/(Log[x^2]*(x - (4 + x)*Log[(1 + x)/3])^2), x] + 6*Defer[Int][x/(Log[x^2]*(x - (4 + x)*Log[(1 + x)
/3])^2), x] + 6*Defer[Int][1/((1 + x)*Log[x^2]*(x - (4 + x)*Log[(1 + x)/3])^2), x] - 384*Defer[Int][1/((4 + x)
^2*Log[x^2]*(x - (4 + x)*Log[(1 + x)/3])^2), x] + 192*Defer[Int][1/((4 + x)*Log[x^2]*(x - (4 + x)*Log[(1 + x)/
3])^2), x] - (414*Defer[Int][(-x + (4 + x)*Log[(1 + x)/3])^(-3), x])/5 + (54*Defer[Int][x/(-x + (4 + x)*Log[(1
+ x)/3])^3, x])/5 - (6*Defer[Int][x^2/(-x + (4 + x)*Log[(1 + x)/3])^3, x])/5 - (6144*Defer[Int][1/((4 + x)^2*
(-x + (4 + x)*Log[(1 + x)/3])^3), x])/5 - (576*Defer[Int][1/((4 + x)^2*(-x + (4 + x)*Log[(1 + x)/3])), x])/5 +
12*Defer[Int][1/(Log[x^2]^2*(-x + (4 + x)*Log[(1 + x)/3])), x] + 192*Defer[Int][1/((4 + x)^2*Log[x^2]*(-x + (
4 + x)*Log[(1 + x)/3])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {6 \left (-10 x (1+x) \log \left (x^2\right ) \log \left (\frac {1+x}{3}\right ) \left (x-(4+x) \log \left (\frac {1+x}{3}\right )\right )^2+50 (1+x) \left (-x+(4+x) \log \left (\frac {1+x}{3}\right )\right )^3+x^2 \log ^3\left (x^2\right ) \log \left (\frac {1+x}{3}\right ) \left (x^2-4 (1+x) \log ^2\left (\frac {1+x}{3}\right )\right )-5 x \log ^2\left (x^2\right ) \left (-x^3+x^2 (4+x) \log \left (\frac {1+x}{3}\right )+4 x (1+x) \log ^2\left (\frac {1+x}{3}\right )-4 \left (4+5 x+x^2\right ) \log ^3\left (\frac {1+x}{3}\right )\right )\right )}{5 x (1+x) \log ^3\left (x^2\right ) \left (x-(4+x) \log \left (\frac {1+x}{3}\right )\right )^3} \, dx\\ &=\frac {6}{5} \int \frac {-10 x (1+x) \log \left (x^2\right ) \log \left (\frac {1+x}{3}\right ) \left (x-(4+x) \log \left (\frac {1+x}{3}\right )\right )^2+50 (1+x) \left (-x+(4+x) \log \left (\frac {1+x}{3}\right )\right )^3+x^2 \log ^3\left (x^2\right ) \log \left (\frac {1+x}{3}\right ) \left (x^2-4 (1+x) \log ^2\left (\frac {1+x}{3}\right )\right )-5 x \log ^2\left (x^2\right ) \left (-x^3+x^2 (4+x) \log \left (\frac {1+x}{3}\right )+4 x (1+x) \log ^2\left (\frac {1+x}{3}\right )-4 \left (4+5 x+x^2\right ) \log ^3\left (\frac {1+x}{3}\right )\right )}{x (1+x) \log ^3\left (x^2\right ) \left (x-(4+x) \log \left (\frac {1+x}{3}\right )\right )^3} \, dx\\ &=\frac {6}{5} \int \left (\frac {2 \left (-1600-1200 x-300 x^2-25 x^3+80 x \log \left (x^2\right )+40 x^2 \log \left (x^2\right )+5 x^3 \log \left (x^2\right )-40 x \log ^2\left (x^2\right )-10 x^2 \log ^2\left (x^2\right )+2 x^2 \log ^3\left (x^2\right )\right )}{x (4+x)^3 \log ^3\left (x^2\right )}-\frac {x^4 \left (12+4 x+x^2\right )}{(1+x) (4+x)^3 \left (-x+4 \log \left (\frac {1+x}{3}\right )+x \log \left (\frac {1+x}{3}\right )\right )^3}-\frac {x^2 \left (-240-140 x-40 x^2-5 x^3+4 x \log \left (x^2\right )-4 x^2 \log \left (x^2\right )+x^3 \log \left (x^2\right )\right )}{(1+x) (4+x)^3 \log \left (x^2\right ) \left (-x+4 \log \left (\frac {1+x}{3}\right )+x \log \left (\frac {1+x}{3}\right )\right )^2}+\frac {2 x \left (80+40 x+5 x^2-80 \log \left (x^2\right )-20 x \log \left (x^2\right )+6 x \log ^2\left (x^2\right )\right )}{(4+x)^3 \log ^2\left (x^2\right ) \left (-x+4 \log \left (\frac {1+x}{3}\right )+x \log \left (\frac {1+x}{3}\right )\right )}\right ) \, dx\\ &=-\left (\frac {6}{5} \int \frac {x^4 \left (12+4 x+x^2\right )}{(1+x) (4+x)^3 \left (-x+4 \log \left (\frac {1+x}{3}\right )+x \log \left (\frac {1+x}{3}\right )\right )^3} \, dx\right )-\frac {6}{5} \int \frac {x^2 \left (-240-140 x-40 x^2-5 x^3+4 x \log \left (x^2\right )-4 x^2 \log \left (x^2\right )+x^3 \log \left (x^2\right )\right )}{(1+x) (4+x)^3 \log \left (x^2\right ) \left (-x+4 \log \left (\frac {1+x}{3}\right )+x \log \left (\frac {1+x}{3}\right )\right )^2} \, dx+\frac {12}{5} \int \frac {-1600-1200 x-300 x^2-25 x^3+80 x \log \left (x^2\right )+40 x^2 \log \left (x^2\right )+5 x^3 \log \left (x^2\right )-40 x \log ^2\left (x^2\right )-10 x^2 \log ^2\left (x^2\right )+2 x^2 \log ^3\left (x^2\right )}{x (4+x)^3 \log ^3\left (x^2\right )} \, dx+\frac {12}{5} \int \frac {x \left (80+40 x+5 x^2-80 \log \left (x^2\right )-20 x \log \left (x^2\right )+6 x \log ^2\left (x^2\right )\right )}{(4+x)^3 \log ^2\left (x^2\right ) \left (-x+4 \log \left (\frac {1+x}{3}\right )+x \log \left (\frac {1+x}{3}\right )\right )} \, dx\\ &=-\left (\frac {6}{5} \int \frac {x^2 \left (-5 \left (48+28 x+8 x^2+x^3\right )+(-2+x)^2 x \log \left (x^2\right )\right )}{(1+x) (4+x)^3 \log \left (x^2\right ) \left (x-(4+x) \log \left (\frac {1+x}{3}\right )\right )^2} \, dx\right )-\frac {6}{5} \int \left (\frac {69}{\left (-x+4 \log \left (\frac {1+x}{3}\right )+x \log \left (\frac {1+x}{3}\right )\right )^3}-\frac {9 x}{\left (-x+4 \log \left (\frac {1+x}{3}\right )+x \log \left (\frac {1+x}{3}\right )\right )^3}+\frac {x^2}{\left (-x+4 \log \left (\frac {1+x}{3}\right )+x \log \left (\frac {1+x}{3}\right )\right )^3}+\frac {1}{3 (1+x) \left (-x+4 \log \left (\frac {1+x}{3}\right )+x \log \left (\frac {1+x}{3}\right )\right )^3}-\frac {1024}{(4+x)^3 \left (-x+4 \log \left (\frac {1+x}{3}\right )+x \log \left (\frac {1+x}{3}\right )\right )^3}+\frac {1024}{(4+x)^2 \left (-x+4 \log \left (\frac {1+x}{3}\right )+x \log \left (\frac {1+x}{3}\right )\right )^3}-\frac {1408}{3 (4+x) \left (-x+4 \log \left (\frac {1+x}{3}\right )+x \log \left (\frac {1+x}{3}\right )\right )^3}\right ) \, dx+\frac {12}{5} \int \left (\frac {2 x}{(4+x)^3}-\frac {25}{x \log ^3\left (x^2\right )}+\frac {5}{(4+x) \log ^2\left (x^2\right )}-\frac {10}{(4+x)^2 \log \left (x^2\right )}\right ) \, dx+\frac {12}{5} \int \frac {x \left (-5 (4+x)^2+20 (4+x) \log \left (x^2\right )-6 x \log ^2\left (x^2\right )\right )}{(4+x)^3 \log ^2\left (x^2\right ) \left (x-(4+x) \log \left (\frac {1+x}{3}\right )\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.33, size = 104, normalized size = 2.60 \begin {gather*} -\frac {6}{5} \left (-\frac {25}{2 \log ^2\left (x^2\right )}+\frac {5 x \log \left (\frac {1+x}{3}\right )}{\log \left (x^2\right ) \left (-x+(4+x) \log \left (\frac {1+x}{3}\right )\right )}+\frac {x^2-2 x (4+x) \log \left (\frac {1+x}{3}\right )+8 (2+x) \log ^2\left (\frac {1+x}{3}\right )}{2 \left (x-(4+x) \log \left (\frac {1+x}{3}\right )\right )^2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(300*x^3 + 300*x^4 + (-3600*x^2 - 4500*x^3 - 900*x^4)*Log[(1 + x)/3] + (14400*x + 21600*x^2 + 8100*x
^3 + 900*x^4)*Log[(1 + x)/3]^2 + (-19200 - 33600*x - 18000*x^2 - 3900*x^3 - 300*x^4)*Log[(1 + x)/3]^3 + Log[x^
2]^2*(-30*x^4 + (120*x^3 + 30*x^4)*Log[(1 + x)/3] + (120*x^2 + 120*x^3)*Log[(1 + x)/3]^2 + (-480*x - 600*x^2 -
120*x^3)*Log[(1 + x)/3]^3) + Log[x^2]^3*(-6*x^4*Log[(1 + x)/3] + (24*x^2 + 24*x^3)*Log[(1 + x)/3]^3) + Log[x^
2]*((60*x^3 + 60*x^4)*Log[(1 + x)/3] + (-480*x^2 - 600*x^3 - 120*x^4)*Log[(1 + x)/3]^2 + (960*x + 1440*x^2 + 5
40*x^3 + 60*x^4)*Log[(1 + x)/3]^3))/(Log[x^2]^3*(-5*x^4 - 5*x^5 + (60*x^3 + 75*x^4 + 15*x^5)*Log[(1 + x)/3] +
(-240*x^2 - 360*x^3 - 135*x^4 - 15*x^5)*Log[(1 + x)/3]^2 + (320*x + 560*x^2 + 300*x^3 + 65*x^4 + 5*x^5)*Log[(1
+ x)/3]^3)),x]

[Out]

(-6*(-25/(2*Log[x^2]^2) + (5*x*Log[(1 + x)/3])/(Log[x^2]*(-x + (4 + x)*Log[(1 + x)/3])) + (x^2 - 2*x*(4 + x)*L
og[(1 + x)/3] + 8*(2 + x)*Log[(1 + x)/3]^2)/(2*(x - (4 + x)*Log[(1 + x)/3])^2)))/5

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fricas [B]  time = 0.92, size = 158, normalized size = 3.95 \begin {gather*} -\frac {3 \, {\left ({\left (8 \, {\left (x + 2\right )} \log \left (\frac {1}{3} \, x + \frac {1}{3}\right )^{2} + x^{2} - 2 \, {\left (x^{2} + 4 \, x\right )} \log \left (\frac {1}{3} \, x + \frac {1}{3}\right )\right )} \log \left (x^{2}\right )^{2} - 25 \, {\left (x^{2} + 8 \, x + 16\right )} \log \left (\frac {1}{3} \, x + \frac {1}{3}\right )^{2} - 25 \, x^{2} - 10 \, {\left (x^{2} \log \left (\frac {1}{3} \, x + \frac {1}{3}\right ) - {\left (x^{2} + 4 \, x\right )} \log \left (\frac {1}{3} \, x + \frac {1}{3}\right )^{2}\right )} \log \left (x^{2}\right ) + 50 \, {\left (x^{2} + 4 \, x\right )} \log \left (\frac {1}{3} \, x + \frac {1}{3}\right )\right )}}{5 \, {\left ({\left (x^{2} + 8 \, x + 16\right )} \log \left (\frac {1}{3} \, x + \frac {1}{3}\right )^{2} + x^{2} - 2 \, {\left (x^{2} + 4 \, x\right )} \log \left (\frac {1}{3} \, x + \frac {1}{3}\right )\right )} \log \left (x^{2}\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((24*x^3+24*x^2)*log(1/3*x+1/3)^3-6*x^4*log(1/3*x+1/3))*log(x^2)^3+((-120*x^3-600*x^2-480*x)*log(1/
3*x+1/3)^3+(120*x^3+120*x^2)*log(1/3*x+1/3)^2+(30*x^4+120*x^3)*log(1/3*x+1/3)-30*x^4)*log(x^2)^2+((60*x^4+540*
x^3+1440*x^2+960*x)*log(1/3*x+1/3)^3+(-120*x^4-600*x^3-480*x^2)*log(1/3*x+1/3)^2+(60*x^4+60*x^3)*log(1/3*x+1/3
))*log(x^2)+(-300*x^4-3900*x^3-18000*x^2-33600*x-19200)*log(1/3*x+1/3)^3+(900*x^4+8100*x^3+21600*x^2+14400*x)*
log(1/3*x+1/3)^2+(-900*x^4-4500*x^3-3600*x^2)*log(1/3*x+1/3)+300*x^4+300*x^3)/((5*x^5+65*x^4+300*x^3+560*x^2+3
20*x)*log(1/3*x+1/3)^3+(-15*x^5-135*x^4-360*x^3-240*x^2)*log(1/3*x+1/3)^2+(15*x^5+75*x^4+60*x^3)*log(1/3*x+1/3
)-5*x^5-5*x^4)/log(x^2)^3,x, algorithm="fricas")

[Out]

-3/5*((8*(x + 2)*log(1/3*x + 1/3)^2 + x^2 - 2*(x^2 + 4*x)*log(1/3*x + 1/3))*log(x^2)^2 - 25*(x^2 + 8*x + 16)*l
og(1/3*x + 1/3)^2 - 25*x^2 - 10*(x^2*log(1/3*x + 1/3) - (x^2 + 4*x)*log(1/3*x + 1/3)^2)*log(x^2) + 50*(x^2 + 4
*x)*log(1/3*x + 1/3))/(((x^2 + 8*x + 16)*log(1/3*x + 1/3)^2 + x^2 - 2*(x^2 + 4*x)*log(1/3*x + 1/3))*log(x^2)^2
)

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giac [B]  time = 1.23, size = 485, normalized size = 12.12 \begin {gather*} -\frac {3 \, {\left (2 \, x^{4} \log \relax (3) \log \left (x^{2}\right ) - 2 \, x^{4} \log \left (x^{2}\right ) \log \left (x + 1\right ) - 10 \, x^{4} \log \relax (3) + x^{4} \log \left (x^{2}\right ) + 8 \, x^{3} \log \relax (3) \log \left (x^{2}\right ) + 10 \, x^{4} \log \left (x + 1\right ) - 8 \, x^{3} \log \left (x^{2}\right ) \log \left (x + 1\right ) - 10 \, x^{4} - 80 \, x^{3} \log \relax (3) + 80 \, x^{3} \log \left (x + 1\right ) - 40 \, x^{3} - 160 \, x^{2} \log \relax (3) + 160 \, x^{2} \log \left (x + 1\right )\right )}}{5 \, {\left (x^{4} \log \relax (3)^{2} \log \left (x^{2}\right ) - 2 \, x^{4} \log \relax (3) \log \left (x^{2}\right ) \log \left (x + 1\right ) + x^{4} \log \left (x^{2}\right ) \log \left (x + 1\right )^{2} + 2 \, x^{4} \log \relax (3) \log \left (x^{2}\right ) + 16 \, x^{3} \log \relax (3)^{2} \log \left (x^{2}\right ) - 2 \, x^{4} \log \left (x^{2}\right ) \log \left (x + 1\right ) - 32 \, x^{3} \log \relax (3) \log \left (x^{2}\right ) \log \left (x + 1\right ) + 16 \, x^{3} \log \left (x^{2}\right ) \log \left (x + 1\right )^{2} + x^{4} \log \left (x^{2}\right ) + 24 \, x^{3} \log \relax (3) \log \left (x^{2}\right ) + 96 \, x^{2} \log \relax (3)^{2} \log \left (x^{2}\right ) - 24 \, x^{3} \log \left (x^{2}\right ) \log \left (x + 1\right ) - 192 \, x^{2} \log \relax (3) \log \left (x^{2}\right ) \log \left (x + 1\right ) + 96 \, x^{2} \log \left (x^{2}\right ) \log \left (x + 1\right )^{2} + 8 \, x^{3} \log \left (x^{2}\right ) + 96 \, x^{2} \log \relax (3) \log \left (x^{2}\right ) + 256 \, x \log \relax (3)^{2} \log \left (x^{2}\right ) - 96 \, x^{2} \log \left (x^{2}\right ) \log \left (x + 1\right ) - 512 \, x \log \relax (3) \log \left (x^{2}\right ) \log \left (x + 1\right ) + 256 \, x \log \left (x^{2}\right ) \log \left (x + 1\right )^{2} + 16 \, x^{2} \log \left (x^{2}\right ) + 128 \, x \log \relax (3) \log \left (x^{2}\right ) + 256 \, \log \relax (3)^{2} \log \left (x^{2}\right ) - 128 \, x \log \left (x^{2}\right ) \log \left (x + 1\right ) - 512 \, \log \relax (3) \log \left (x^{2}\right ) \log \left (x + 1\right ) + 256 \, \log \left (x^{2}\right ) \log \left (x + 1\right )^{2}\right )}} - \frac {3 \, {\left (2 \, x \log \left (x^{2}\right ) - 5 \, x - 20\right )}}{x \log \left (x^{2}\right )^{2} + 4 \, \log \left (x^{2}\right )^{2}} - \frac {24 \, {\left (x + 2\right )}}{5 \, {\left (x^{2} + 8 \, x + 16\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((24*x^3+24*x^2)*log(1/3*x+1/3)^3-6*x^4*log(1/3*x+1/3))*log(x^2)^3+((-120*x^3-600*x^2-480*x)*log(1/
3*x+1/3)^3+(120*x^3+120*x^2)*log(1/3*x+1/3)^2+(30*x^4+120*x^3)*log(1/3*x+1/3)-30*x^4)*log(x^2)^2+((60*x^4+540*
x^3+1440*x^2+960*x)*log(1/3*x+1/3)^3+(-120*x^4-600*x^3-480*x^2)*log(1/3*x+1/3)^2+(60*x^4+60*x^3)*log(1/3*x+1/3
))*log(x^2)+(-300*x^4-3900*x^3-18000*x^2-33600*x-19200)*log(1/3*x+1/3)^3+(900*x^4+8100*x^3+21600*x^2+14400*x)*
log(1/3*x+1/3)^2+(-900*x^4-4500*x^3-3600*x^2)*log(1/3*x+1/3)+300*x^4+300*x^3)/((5*x^5+65*x^4+300*x^3+560*x^2+3
20*x)*log(1/3*x+1/3)^3+(-15*x^5-135*x^4-360*x^3-240*x^2)*log(1/3*x+1/3)^2+(15*x^5+75*x^4+60*x^3)*log(1/3*x+1/3
)-5*x^5-5*x^4)/log(x^2)^3,x, algorithm="giac")

[Out]

-3/5*(2*x^4*log(3)*log(x^2) - 2*x^4*log(x^2)*log(x + 1) - 10*x^4*log(3) + x^4*log(x^2) + 8*x^3*log(3)*log(x^2)
+ 10*x^4*log(x + 1) - 8*x^3*log(x^2)*log(x + 1) - 10*x^4 - 80*x^3*log(3) + 80*x^3*log(x + 1) - 40*x^3 - 160*x
^2*log(3) + 160*x^2*log(x + 1))/(x^4*log(3)^2*log(x^2) - 2*x^4*log(3)*log(x^2)*log(x + 1) + x^4*log(x^2)*log(x
+ 1)^2 + 2*x^4*log(3)*log(x^2) + 16*x^3*log(3)^2*log(x^2) - 2*x^4*log(x^2)*log(x + 1) - 32*x^3*log(3)*log(x^2
)*log(x + 1) + 16*x^3*log(x^2)*log(x + 1)^2 + x^4*log(x^2) + 24*x^3*log(3)*log(x^2) + 96*x^2*log(3)^2*log(x^2)
- 24*x^3*log(x^2)*log(x + 1) - 192*x^2*log(3)*log(x^2)*log(x + 1) + 96*x^2*log(x^2)*log(x + 1)^2 + 8*x^3*log(
x^2) + 96*x^2*log(3)*log(x^2) + 256*x*log(3)^2*log(x^2) - 96*x^2*log(x^2)*log(x + 1) - 512*x*log(3)*log(x^2)*l
og(x + 1) + 256*x*log(x^2)*log(x + 1)^2 + 16*x^2*log(x^2) + 128*x*log(3)*log(x^2) + 256*log(3)^2*log(x^2) - 12
8*x*log(x^2)*log(x + 1) - 512*log(3)*log(x^2)*log(x + 1) + 256*log(x^2)*log(x + 1)^2) - 3*(2*x*log(x^2) - 5*x
- 20)/(x*log(x^2)^2 + 4*log(x^2)^2) - 24/5*(x + 2)/(x^2 + 8*x + 16)

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maple [C]  time = 2.21, size = 892, normalized size = 22.30

method	result	size
risch	\(-\frac {12 \left (-400-200 x +20 x^{2} \ln \relax (x )+64 \ln \relax (x )^{2}-25 x^{2}+32 x \ln \relax (x )^{2}+80 x \ln \relax (x )-20 i \pi x \mathrm {csgn}\left (i x^{2}\right )^{3}-4 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{6}-32 i \ln \relax (x ) \pi \mathrm {csgn}\left (i x^{2}\right )^{3}-4 \pi ^{2} \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{2}+16 \pi ^{2} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{3}-24 \pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{4}+16 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{5}-20 i \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+40 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-5 i \pi \,x^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+10 i \pi \,x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+64 i \ln \relax (x ) \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-32 i \ln \relax (x ) \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-16 i \pi x \mathrm {csgn}\left (i x^{2}\right )^{3} \ln \relax (x )-2 \pi ^{2} x \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{2}+8 \pi ^{2} x \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{3}-12 \pi ^{2} x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{4}+8 \pi ^{2} x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{5}-5 i \pi \,x^{2} \mathrm {csgn}\left (i x^{2}\right )^{3}-2 \pi ^{2} x \mathrm {csgn}\left (i x^{2}\right )^{6}-16 i \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) \ln \relax (x )+32 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} \ln \relax (x )\right )}{5 \left (4+x \right )^{2} \left (4 \ln \relax (x )-i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x \right )^{2}+2 i \pi \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )-i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}\right )^{2}}+\frac {\frac {6 \pi \,x^{4} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) \ln \left (\frac {x}{3}+\frac {1}{3}\right )}{5}-\frac {12 \pi \,x^{4} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} \ln \left (\frac {x}{3}+\frac {1}{3}\right )}{5}+\frac {6 \pi \,x^{4} \mathrm {csgn}\left (i x^{2}\right )^{3} \ln \left (\frac {x}{3}+\frac {1}{3}\right )}{5}-\frac {3 \pi \,x^{4} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )}{5}+\frac {6 \pi \,x^{4} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}}{5}-\frac {3 \pi \,x^{4} \mathrm {csgn}\left (i x^{2}\right )^{3}}{5}+\frac {24 \pi \,x^{3} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) \ln \left (\frac {x}{3}+\frac {1}{3}\right )}{5}-\frac {48 \pi \,x^{3} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} \ln \left (\frac {x}{3}+\frac {1}{3}\right )}{5}+\frac {24 \pi \,x^{3} \mathrm {csgn}\left (i x^{2}\right )^{3} \ln \left (\frac {x}{3}+\frac {1}{3}\right )}{5}+\frac {24 i x^{4} \ln \relax (x ) \ln \left (\frac {x}{3}+\frac {1}{3}\right )}{5}+48 i x^{3}-192 i x^{2} \ln \left (\frac {x}{3}+\frac {1}{3}\right )+\frac {96 i x^{3} \ln \relax (x ) \ln \left (\frac {x}{3}+\frac {1}{3}\right )}{5}-12 i x^{4} \ln \left (\frac {x}{3}+\frac {1}{3}\right )-96 i x^{3} \ln \left (\frac {x}{3}+\frac {1}{3}\right )-\frac {12 i x^{4} \ln \relax (x )}{5}+12 i x^{4}}{\left (x \ln \left (\frac {x}{3}+\frac {1}{3}\right )-x +4 \ln \left (\frac {x}{3}+\frac {1}{3}\right )\right )^{2} \left (\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}+4 i \ln \relax (x )\right ) \left (x^{2}+8 x +16\right )}\)	\(892\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((24*x^3+24*x^2)*ln(1/3*x+1/3)^3-6*x^4*ln(1/3*x+1/3))*ln(x^2)^3+((-120*x^3-600*x^2-480*x)*ln(1/3*x+1/3)^3
+(120*x^3+120*x^2)*ln(1/3*x+1/3)^2+(30*x^4+120*x^3)*ln(1/3*x+1/3)-30*x^4)*ln(x^2)^2+((60*x^4+540*x^3+1440*x^2+
960*x)*ln(1/3*x+1/3)^3+(-120*x^4-600*x^3-480*x^2)*ln(1/3*x+1/3)^2+(60*x^4+60*x^3)*ln(1/3*x+1/3))*ln(x^2)+(-300
*x^4-3900*x^3-18000*x^2-33600*x-19200)*ln(1/3*x+1/3)^3+(900*x^4+8100*x^3+21600*x^2+14400*x)*ln(1/3*x+1/3)^2+(-
900*x^4-4500*x^3-3600*x^2)*ln(1/3*x+1/3)+300*x^4+300*x^3)/((5*x^5+65*x^4+300*x^3+560*x^2+320*x)*ln(1/3*x+1/3)^
3+(-15*x^5-135*x^4-360*x^3-240*x^2)*ln(1/3*x+1/3)^2+(15*x^5+75*x^4+60*x^3)*ln(1/3*x+1/3)-5*x^5-5*x^4)/ln(x^2)^
3,x,method=_RETURNVERBOSE)

[Out]

-12/5*(-400-200*x+20*x^2*ln(x)+64*ln(x)^2-25*x^2+32*x*ln(x)^2+80*x*ln(x)-4*Pi^2*csgn(I*x^2)^6-4*Pi^2*csgn(I*x)
^4*csgn(I*x^2)^2+16*Pi^2*csgn(I*x)^3*csgn(I*x^2)^3-24*Pi^2*csgn(I*x)^2*csgn(I*x^2)^4+16*Pi^2*csgn(I*x)*csgn(I*
x^2)^5-16*I*Pi*x*csgn(I*x)^2*csgn(I*x^2)*ln(x)+32*I*Pi*x*csgn(I*x)*csgn(I*x^2)^2*ln(x)-2*Pi^2*x*csgn(I*x^2)^6-
2*Pi^2*x*csgn(I*x)^4*csgn(I*x^2)^2+8*Pi^2*x*csgn(I*x)^3*csgn(I*x^2)^3-12*Pi^2*x*csgn(I*x)^2*csgn(I*x^2)^4+8*Pi
^2*x*csgn(I*x)*csgn(I*x^2)^5-5*I*Pi*x^2*csgn(I*x^2)^3-20*I*Pi*x*csgn(I*x^2)^3-32*I*ln(x)*Pi*csgn(I*x^2)^3-5*I*
Pi*x^2*csgn(I*x)^2*csgn(I*x^2)+10*I*Pi*x^2*csgn(I*x)*csgn(I*x^2)^2-20*I*Pi*x*csgn(I*x)^2*csgn(I*x^2)+64*I*ln(x
)*Pi*csgn(I*x)*csgn(I*x^2)^2+40*I*Pi*x*csgn(I*x)*csgn(I*x^2)^2-32*I*ln(x)*Pi*csgn(I*x)^2*csgn(I*x^2)-16*I*Pi*x
*csgn(I*x^2)^3*ln(x))/(4+x)^2/(4*ln(x)-I*Pi*csgn(I*x^2)*csgn(I*x)^2+2*I*Pi*csgn(I*x^2)^2*csgn(I*x)-I*Pi*csgn(I
*x^2)^3)^2+3/5*(2*Pi*x^4*csgn(I*x)^2*csgn(I*x^2)*ln(1/3*x+1/3)-4*Pi*x^4*csgn(I*x)*csgn(I*x^2)^2*ln(1/3*x+1/3)+
2*Pi*x^4*csgn(I*x^2)^3*ln(1/3*x+1/3)-Pi*x^4*csgn(I*x)^2*csgn(I*x^2)+2*Pi*x^4*csgn(I*x)*csgn(I*x^2)^2-Pi*x^4*cs
gn(I*x^2)^3+8*Pi*x^3*csgn(I*x)^2*csgn(I*x^2)*ln(1/3*x+1/3)-16*Pi*x^3*csgn(I*x)*csgn(I*x^2)^2*ln(1/3*x+1/3)+8*P
i*x^3*csgn(I*x^2)^3*ln(1/3*x+1/3)+8*I*x^4*ln(x)*ln(1/3*x+1/3)+80*I*x^3-320*I*x^2*ln(1/3*x+1/3)+32*I*x^3*ln(x)*
ln(1/3*x+1/3)-20*I*x^4*ln(1/3*x+1/3)-160*I*x^3*ln(1/3*x+1/3)-4*I*x^4*ln(x)+20*I*x^4)/(x*ln(1/3*x+1/3)-x+4*ln(1
/3*x+1/3))^2/(Pi*csgn(I*x)^2*csgn(I*x^2)-2*Pi*csgn(I*x)*csgn(I*x^2)^2+Pi*csgn(I*x^2)^3+4*I*ln(x))/(x^2+8*x+16)

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maxima [B]  time = 0.81, size = 290, normalized size = 7.25 \begin {gather*} \frac {3 \, {\left (25 \, {\left (\log \relax (3)^{2} + 2 \, \log \relax (3) + 1\right )} x^{2} - {\left (32 \, {\left (x + 2\right )} \log \relax (x)^{2} - 25 \, x^{2} + 20 \, {\left (x^{2} + 4 \, x\right )} \log \relax (x) - 200 \, x - 400\right )} \log \left (x + 1\right )^{2} - 4 \, {\left (x^{2} {\left (2 \, \log \relax (3) + 1\right )} + 8 \, {\left (\log \relax (3)^{2} + \log \relax (3)\right )} x + 16 \, \log \relax (3)^{2}\right )} \log \relax (x)^{2} + 200 \, {\left (\log \relax (3)^{2} + \log \relax (3)\right )} x + 400 \, \log \relax (3)^{2} - 2 \, {\left (25 \, x^{2} {\left (\log \relax (3) + 1\right )} - 4 \, {\left (x^{2} + 4 \, x {\left (2 \, \log \relax (3) + 1\right )} + 16 \, \log \relax (3)\right )} \log \relax (x)^{2} + 100 \, x {\left (2 \, \log \relax (3) + 1\right )} - 10 \, {\left (x^{2} {\left (2 \, \log \relax (3) + 1\right )} + 8 \, x \log \relax (3)\right )} \log \relax (x) + 400 \, \log \relax (3)\right )} \log \left (x + 1\right ) - 20 \, {\left ({\left (\log \relax (3)^{2} + \log \relax (3)\right )} x^{2} + 4 \, x \log \relax (3)^{2}\right )} \log \relax (x)\right )}}{20 \, {\left ({\left (x^{2} + 8 \, x + 16\right )} \log \left (x + 1\right )^{2} \log \relax (x)^{2} - 2 \, {\left (x^{2} {\left (\log \relax (3) + 1\right )} + 4 \, x {\left (2 \, \log \relax (3) + 1\right )} + 16 \, \log \relax (3)\right )} \log \left (x + 1\right ) \log \relax (x)^{2} + {\left ({\left (\log \relax (3)^{2} + 2 \, \log \relax (3) + 1\right )} x^{2} + 8 \, {\left (\log \relax (3)^{2} + \log \relax (3)\right )} x + 16 \, \log \relax (3)^{2}\right )} \log \relax (x)^{2}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((24*x^3+24*x^2)*log(1/3*x+1/3)^3-6*x^4*log(1/3*x+1/3))*log(x^2)^3+((-120*x^3-600*x^2-480*x)*log(1/
3*x+1/3)^3+(120*x^3+120*x^2)*log(1/3*x+1/3)^2+(30*x^4+120*x^3)*log(1/3*x+1/3)-30*x^4)*log(x^2)^2+((60*x^4+540*
x^3+1440*x^2+960*x)*log(1/3*x+1/3)^3+(-120*x^4-600*x^3-480*x^2)*log(1/3*x+1/3)^2+(60*x^4+60*x^3)*log(1/3*x+1/3
))*log(x^2)+(-300*x^4-3900*x^3-18000*x^2-33600*x-19200)*log(1/3*x+1/3)^3+(900*x^4+8100*x^3+21600*x^2+14400*x)*
log(1/3*x+1/3)^2+(-900*x^4-4500*x^3-3600*x^2)*log(1/3*x+1/3)+300*x^4+300*x^3)/((5*x^5+65*x^4+300*x^3+560*x^2+3
20*x)*log(1/3*x+1/3)^3+(-15*x^5-135*x^4-360*x^3-240*x^2)*log(1/3*x+1/3)^2+(15*x^5+75*x^4+60*x^3)*log(1/3*x+1/3
)-5*x^5-5*x^4)/log(x^2)^3,x, algorithm="maxima")

[Out]

3/20*(25*(log(3)^2 + 2*log(3) + 1)*x^2 - (32*(x + 2)*log(x)^2 - 25*x^2 + 20*(x^2 + 4*x)*log(x) - 200*x - 400)*
log(x + 1)^2 - 4*(x^2*(2*log(3) + 1) + 8*(log(3)^2 + log(3))*x + 16*log(3)^2)*log(x)^2 + 200*(log(3)^2 + log(3
))*x + 400*log(3)^2 - 2*(25*x^2*(log(3) + 1) - 4*(x^2 + 4*x*(2*log(3) + 1) + 16*log(3))*log(x)^2 + 100*x*(2*lo
g(3) + 1) - 10*(x^2*(2*log(3) + 1) + 8*x*log(3))*log(x) + 400*log(3))*log(x + 1) - 20*((log(3)^2 + log(3))*x^2
+ 4*x*log(3)^2)*log(x))/((x^2 + 8*x + 16)*log(x + 1)^2*log(x)^2 - 2*(x^2*(log(3) + 1) + 4*x*(2*log(3) + 1) +
16*log(3))*log(x + 1)*log(x)^2 + ((log(3)^2 + 2*log(3) + 1)*x^2 + 8*(log(3)^2 + log(3))*x + 16*log(3)^2)*log(x
)^2)

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mupad [B]  time = 1.64, size = 366, normalized size = 9.15 \begin {gather*} \frac {\frac {6\,x\,{\ln \left (x^2\right )}^2}{{\left (x+4\right )}^2}-\frac {3\,x\,\ln \left (x^2\right )}{x+4}+15}{{\ln \left (x^2\right )}^2}-\frac {\frac {3\,x}{x+4}-\frac {6\,x\,\ln \left (x^2\right )}{{\left (x+4\right )}^2}+\frac {3\,x\,{\ln \left (x^2\right )}^2\,\left (x-4\right )}{{\left (x+4\right )}^3}}{\ln \left (x^2\right )}-\frac {\frac {84\,x}{5}+\frac {48}{5}}{x^2+8\,x+16}-\frac {\ln \left (x^2\right )\,\left (12\,x-3\,x^2\right )}{x^3+12\,x^2+48\,x+64}+\frac {6\,\left (-x^6\,{\ln \left (x^2\right )}^2+5\,x^6\,\ln \left (x^2\right )-5\,x^5\,{\ln \left (x^2\right )}^2+45\,x^5\,\ln \left (x^2\right )-16\,x^4\,{\ln \left (x^2\right )}^2+180\,x^4\,\ln \left (x^2\right )-12\,x^3\,{\ln \left (x^2\right )}^2+380\,x^3\,\ln \left (x^2\right )+240\,x^2\,\ln \left (x^2\right )\right )}{5\,{\ln \left (x^2\right )}^2\,\left (x-\ln \left (\frac {x}{3}+\frac {1}{3}\right )\,\left (x+4\right )\right )\,{\left (x+4\right )}^2\,\left (x^3+5\,x^2+16\,x+12\right )}+\frac {3\,\left (x^7\,{\ln \left (x^2\right )}^2+5\,x^6\,{\ln \left (x^2\right )}^2+16\,x^5\,{\ln \left (x^2\right )}^2+12\,x^4\,{\ln \left (x^2\right )}^2\right )}{5\,{\ln \left (x^2\right )}^2\,{\left (x+4\right )}^2\,\left ({\ln \left (\frac {x}{3}+\frac {1}{3}\right )}^2\,{\left (x+4\right )}^2+x^2-2\,x\,\ln \left (\frac {x}{3}+\frac {1}{3}\right )\,\left (x+4\right )\right )\,\left (x^3+5\,x^2+16\,x+12\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x/3 + 1/3)^2*(14400*x + 21600*x^2 + 8100*x^3 + 900*x^4) - log(x/3 + 1/3)*(3600*x^2 + 4500*x^3 + 900*
x^4) - log(x/3 + 1/3)^3*(33600*x + 18000*x^2 + 3900*x^3 + 300*x^4 + 19200) + log(x^2)^3*(log(x/3 + 1/3)^3*(24*
x^2 + 24*x^3) - 6*x^4*log(x/3 + 1/3)) + log(x^2)*(log(x/3 + 1/3)^3*(960*x + 1440*x^2 + 540*x^3 + 60*x^4) - log
(x/3 + 1/3)^2*(480*x^2 + 600*x^3 + 120*x^4) + log(x/3 + 1/3)*(60*x^3 + 60*x^4)) - log(x^2)^2*(log(x/3 + 1/3)^3
*(480*x + 600*x^2 + 120*x^3) - log(x/3 + 1/3)^2*(120*x^2 + 120*x^3) - log(x/3 + 1/3)*(120*x^3 + 30*x^4) + 30*x
^4) + 300*x^3 + 300*x^4)/(log(x^2)^3*(log(x/3 + 1/3)^2*(240*x^2 + 360*x^3 + 135*x^4 + 15*x^5) - log(x/3 + 1/3)
^3*(320*x + 560*x^2 + 300*x^3 + 65*x^4 + 5*x^5) - log(x/3 + 1/3)*(60*x^3 + 75*x^4 + 15*x^5) + 5*x^4 + 5*x^5)),
x)

[Out]

((6*x*log(x^2)^2)/(x + 4)^2 - (3*x*log(x^2))/(x + 4) + 15)/log(x^2)^2 - ((3*x)/(x + 4) - (6*x*log(x^2))/(x + 4
)^2 + (3*x*log(x^2)^2*(x - 4))/(x + 4)^3)/log(x^2) - ((84*x)/5 + 48/5)/(8*x + x^2 + 16) - (log(x^2)*(12*x - 3*
x^2))/(48*x + 12*x^2 + x^3 + 64) + (6*(240*x^2*log(x^2) + 380*x^3*log(x^2) + 180*x^4*log(x^2) + 45*x^5*log(x^2
) + 5*x^6*log(x^2) - 12*x^3*log(x^2)^2 - 16*x^4*log(x^2)^2 - 5*x^5*log(x^2)^2 - x^6*log(x^2)^2))/(5*log(x^2)^2
*(x - log(x/3 + 1/3)*(x + 4))*(x + 4)^2*(16*x + 5*x^2 + x^3 + 12)) + (3*(12*x^4*log(x^2)^2 + 16*x^5*log(x^2)^2
+ 5*x^6*log(x^2)^2 + x^7*log(x^2)^2))/(5*log(x^2)^2*(x + 4)^2*(log(x/3 + 1/3)^2*(x + 4)^2 + x^2 - 2*x*log(x/3
+ 1/3)*(x + 4))*(16*x + 5*x^2 + x^3 + 12))

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sympy [B]  time = 1.19, size = 240, normalized size = 6.00 \begin {gather*} \frac {24 \left (- x - 2\right )}{5 x^{2} + 40 x + 80} + \frac {- 3 x^{4} \log {\left (x^{2} \right )} + 30 x^{4} + 120 x^{3} + \left (6 x^{4} \log {\left (x^{2} \right )} - 30 x^{4} + 24 x^{3} \log {\left (x^{2} \right )} - 240 x^{3} - 480 x^{2}\right ) \log {\left (\frac {x}{3} + \frac {1}{3} \right )}}{5 x^{4} \log {\left (x^{2} \right )} + 40 x^{3} \log {\left (x^{2} \right )} + 80 x^{2} \log {\left (x^{2} \right )} + \left (- 10 x^{4} \log {\left (x^{2} \right )} - 120 x^{3} \log {\left (x^{2} \right )} - 480 x^{2} \log {\left (x^{2} \right )} - 640 x \log {\left (x^{2} \right )}\right ) \log {\left (\frac {x}{3} + \frac {1}{3} \right )} + \left (5 x^{4} \log {\left (x^{2} \right )} + 80 x^{3} \log {\left (x^{2} \right )} + 480 x^{2} \log {\left (x^{2} \right )} + 1280 x \log {\left (x^{2} \right )} + 1280 \log {\left (x^{2} \right )}\right ) \log {\left (\frac {x}{3} + \frac {1}{3} \right )}^{2}} + \frac {- 6 x \log {\left (x^{2} \right )} + 15 x + 60}{\left (x + 4\right ) \log {\left (x^{2} \right )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((24*x**3+24*x**2)*ln(1/3*x+1/3)**3-6*x**4*ln(1/3*x+1/3))*ln(x**2)**3+((-120*x**3-600*x**2-480*x)*l
n(1/3*x+1/3)**3+(120*x**3+120*x**2)*ln(1/3*x+1/3)**2+(30*x**4+120*x**3)*ln(1/3*x+1/3)-30*x**4)*ln(x**2)**2+((6
0*x**4+540*x**3+1440*x**2+960*x)*ln(1/3*x+1/3)**3+(-120*x**4-600*x**3-480*x**2)*ln(1/3*x+1/3)**2+(60*x**4+60*x
**3)*ln(1/3*x+1/3))*ln(x**2)+(-300*x**4-3900*x**3-18000*x**2-33600*x-19200)*ln(1/3*x+1/3)**3+(900*x**4+8100*x*
*3+21600*x**2+14400*x)*ln(1/3*x+1/3)**2+(-900*x**4-4500*x**3-3600*x**2)*ln(1/3*x+1/3)+300*x**4+300*x**3)/((5*x
**5+65*x**4+300*x**3+560*x**2+320*x)*ln(1/3*x+1/3)**3+(-15*x**5-135*x**4-360*x**3-240*x**2)*ln(1/3*x+1/3)**2+(
15*x**5+75*x**4+60*x**3)*ln(1/3*x+1/3)-5*x**5-5*x**4)/ln(x**2)**3,x)

[Out]

24*(-x - 2)/(5*x**2 + 40*x + 80) + (-3*x**4*log(x**2) + 30*x**4 + 120*x**3 + (6*x**4*log(x**2) - 30*x**4 + 24*
x**3*log(x**2) - 240*x**3 - 480*x**2)*log(x/3 + 1/3))/(5*x**4*log(x**2) + 40*x**3*log(x**2) + 80*x**2*log(x**2
) + (-10*x**4*log(x**2) - 120*x**3*log(x**2) - 480*x**2*log(x**2) - 640*x*log(x**2))*log(x/3 + 1/3) + (5*x**4*
log(x**2) + 80*x**3*log(x**2) + 480*x**2*log(x**2) + 1280*x*log(x**2) + 1280*log(x**2))*log(x/3 + 1/3)**2) + (
-6*x*log(x**2) + 15*x + 60)/((x + 4)*log(x**2)**2)

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