3.48.75 \(\int \frac {-6 x^3+28 x^5-22 x^7+16 x \log (3)+(2 x^3-4 x^5+2 x^7+16 x \log (3)) \log (\frac {1}{64} (x^4-4 x^6+6 x^8-4 x^{10}+x^{12}+(16 x^2-32 x^4+16 x^6) \log (3)+64 \log ^2(3)))}{x^2-2 x^4+x^6+8 \log (3)+(3 x^2-6 x^4+3 x^6+24 \log (3)) \log (\frac {1}{64} (x^4-4 x^6+6 x^8-4 x^{10}+x^{12}+(16 x^2-32 x^4+16 x^6) \log (3)+64 \log ^2(3)))+(3 x^2-6 x^4+3 x^6+24 \log (3)) \log ^2(\frac {1}{64} (x^4-4 x^6+6 x^8-4 x^{10}+x^{12}+(16 x^2-32 x^4+16 x^6) \log (3)+64 \log ^2(3)))+(x^2-2 x^4+x^6+8 \log (3)) \log ^3(\frac {1}{64} (x^4-4 x^6+6 x^8-4 x^{10}+x^{12}+(16 x^2-32 x^4+16 x^6) \log (3)+64 \log ^2(3)))} \, dx\)

Optimal. Leaf size=27 \[ \frac {x^2}{\left (1+\log \left (\left (\frac {1}{8} \left (x-x^3\right )^2+\log (3)\right )^2\right )\right )^2} \]

________________________________________________________________________________________

Rubi [F]  time = 1.80, 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 {-6 x^3+28 x^5-22 x^7+16 x \log (3)+\left (2 x^3-4 x^5+2 x^7+16 x \log (3)\right ) \log \left (\frac {1}{64} \left (x^4-4 x^6+6 x^8-4 x^{10}+x^{12}+\left (16 x^2-32 x^4+16 x^6\right ) \log (3)+64 \log ^2(3)\right )\right )}{x^2-2 x^4+x^6+8 \log (3)+\left (3 x^2-6 x^4+3 x^6+24 \log (3)\right ) \log \left (\frac {1}{64} \left (x^4-4 x^6+6 x^8-4 x^{10}+x^{12}+\left (16 x^2-32 x^4+16 x^6\right ) \log (3)+64 \log ^2(3)\right )\right )+\left (3 x^2-6 x^4+3 x^6+24 \log (3)\right ) \log ^2\left (\frac {1}{64} \left (x^4-4 x^6+6 x^8-4 x^{10}+x^{12}+\left (16 x^2-32 x^4+16 x^6\right ) \log (3)+64 \log ^2(3)\right )\right )+\left (x^2-2 x^4+x^6+8 \log (3)\right ) \log ^3\left (\frac {1}{64} \left (x^4-4 x^6+6 x^8-4 x^{10}+x^{12}+\left (16 x^2-32 x^4+16 x^6\right ) \log (3)+64 \log ^2(3)\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-6*x^3 + 28*x^5 - 22*x^7 + 16*x*Log[3] + (2*x^3 - 4*x^5 + 2*x^7 + 16*x*Log[3])*Log[(x^4 - 4*x^6 + 6*x^8 -
4*x^10 + x^12 + (16*x^2 - 32*x^4 + 16*x^6)*Log[3] + 64*Log[3]^2)/64])/(x^2 - 2*x^4 + x^6 + 8*Log[3] + (3*x^2
- 6*x^4 + 3*x^6 + 24*Log[3])*Log[(x^4 - 4*x^6 + 6*x^8 - 4*x^10 + x^12 + (16*x^2 - 32*x^4 + 16*x^6)*Log[3] + 64
*Log[3]^2)/64] + (3*x^2 - 6*x^4 + 3*x^6 + 24*Log[3])*Log[(x^4 - 4*x^6 + 6*x^8 - 4*x^10 + x^12 + (16*x^2 - 32*x
^4 + 16*x^6)*Log[3] + 64*Log[3]^2)/64]^2 + (x^2 - 2*x^4 + x^6 + 8*Log[3])*Log[(x^4 - 4*x^6 + 6*x^8 - 4*x^10 +
x^12 + (16*x^2 - 32*x^4 + 16*x^6)*Log[3] + 64*Log[3]^2)/64]^3),x]

[Out]

-12*Defer[Subst][Defer[Int][(1 + Log[(x - 2*x^2 + x^3 + 8*Log[3])^2/64])^(-3), x], x, x^2] + 96*Log[3]*Defer[S
ubst][Defer[Int][1/((x - 2*x^2 + x^3 + 8*Log[3])*(1 + Log[(x - 2*x^2 + x^3 + 8*Log[3])^2/64])^3), x], x, x^2]
+ 8*Defer[Subst][Defer[Int][x/((x - 2*x^2 + x^3 + 8*Log[3])*(1 + Log[(x - 2*x^2 + x^3 + 8*Log[3])^2/64])^3), x
], x, x^2] - 8*Defer[Subst][Defer[Int][x^2/((x - 2*x^2 + x^3 + 8*Log[3])*(1 + Log[(x - 2*x^2 + x^3 + 8*Log[3])
^2/64])^3), x], x, x^2] + Defer[Subst][Defer[Int][(1 + Log[(x - 2*x^2 + x^3 + 8*Log[3])^2/64])^(-2), x], x, x^
2]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 x \left (-3 x^2+14 x^4-11 x^6+8 \log (3)+\left (x^2-2 x^4+x^6+8 \log (3)\right ) \log \left (\frac {1}{64} \left (x^2-2 x^4+x^6+8 \log (3)\right )^2\right )\right )}{\left (x^2-2 x^4+x^6+8 \log (3)\right ) \left (1+\log \left (\frac {1}{64} \left (x^2-2 x^4+x^6+8 \log (3)\right )^2\right )\right )^3} \, dx\\ &=2 \int \frac {x \left (-3 x^2+14 x^4-11 x^6+8 \log (3)+\left (x^2-2 x^4+x^6+8 \log (3)\right ) \log \left (\frac {1}{64} \left (x^2-2 x^4+x^6+8 \log (3)\right )^2\right )\right )}{\left (x^2-2 x^4+x^6+8 \log (3)\right ) \left (1+\log \left (\frac {1}{64} \left (x^2-2 x^4+x^6+8 \log (3)\right )^2\right )\right )^3} \, dx\\ &=\operatorname {Subst}\left (\int \frac {-3 x+14 x^2-11 x^3+8 \log (3)+\left (x-2 x^2+x^3+8 \log (3)\right ) \log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )}{\left (x-2 x^2+x^3+8 \log (3)\right ) \left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^3} \, dx,x,x^2\right )\\ &=\operatorname {Subst}\left (\int \left (-\frac {4 x \left (1-4 x+3 x^2\right )}{\left (x-2 x^2+x^3+8 \log (3)\right ) \left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^3}+\frac {1}{\left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^2}\right ) \, dx,x,x^2\right )\\ &=-\left (4 \operatorname {Subst}\left (\int \frac {x \left (1-4 x+3 x^2\right )}{\left (x-2 x^2+x^3+8 \log (3)\right ) \left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^3} \, dx,x,x^2\right )\right )+\operatorname {Subst}\left (\int \frac {1}{\left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^2} \, dx,x,x^2\right )\\ &=-\left (4 \operatorname {Subst}\left (\int \left (\frac {3}{\left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^3}+\frac {2 \left (-x+x^2-12 \log (3)\right )}{\left (x-2 x^2+x^3+8 \log (3)\right ) \left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^3}\right ) \, dx,x,x^2\right )\right )+\operatorname {Subst}\left (\int \frac {1}{\left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^2} \, dx,x,x^2\right )\\ &=-\left (8 \operatorname {Subst}\left (\int \frac {-x+x^2-12 \log (3)}{\left (x-2 x^2+x^3+8 \log (3)\right ) \left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^3} \, dx,x,x^2\right )\right )-12 \operatorname {Subst}\left (\int \frac {1}{\left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^3} \, dx,x,x^2\right )+\operatorname {Subst}\left (\int \frac {1}{\left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^2} \, dx,x,x^2\right )\\ &=-\left (8 \operatorname {Subst}\left (\int \left (-\frac {x}{\left (x-2 x^2+x^3+8 \log (3)\right ) \left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^3}+\frac {x^2}{\left (x-2 x^2+x^3+8 \log (3)\right ) \left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^3}-\frac {12 \log (3)}{\left (x-2 x^2+x^3+8 \log (3)\right ) \left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^3}\right ) \, dx,x,x^2\right )\right )-12 \operatorname {Subst}\left (\int \frac {1}{\left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^3} \, dx,x,x^2\right )+\operatorname {Subst}\left (\int \frac {1}{\left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^2} \, dx,x,x^2\right )\\ &=8 \operatorname {Subst}\left (\int \frac {x}{\left (x-2 x^2+x^3+8 \log (3)\right ) \left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^3} \, dx,x,x^2\right )-8 \operatorname {Subst}\left (\int \frac {x^2}{\left (x-2 x^2+x^3+8 \log (3)\right ) \left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^3} \, dx,x,x^2\right )-12 \operatorname {Subst}\left (\int \frac {1}{\left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^3} \, dx,x,x^2\right )+(96 \log (3)) \operatorname {Subst}\left (\int \frac {1}{\left (x-2 x^2+x^3+8 \log (3)\right ) \left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^3} \, dx,x,x^2\right )+\operatorname {Subst}\left (\int \frac {1}{\left (1+\log \left (\frac {1}{64} \left (x-2 x^2+x^3+8 \log (3)\right )^2\right )\right )^2} \, dx,x,x^2\right )\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.06, size = 31, normalized size = 1.15 \begin {gather*} \frac {x^2}{\left (1+\log \left (\frac {1}{64} \left (x^2-2 x^4+x^6+8 \log (3)\right )^2\right )\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-6*x^3 + 28*x^5 - 22*x^7 + 16*x*Log[3] + (2*x^3 - 4*x^5 + 2*x^7 + 16*x*Log[3])*Log[(x^4 - 4*x^6 + 6
*x^8 - 4*x^10 + x^12 + (16*x^2 - 32*x^4 + 16*x^6)*Log[3] + 64*Log[3]^2)/64])/(x^2 - 2*x^4 + x^6 + 8*Log[3] + (
3*x^2 - 6*x^4 + 3*x^6 + 24*Log[3])*Log[(x^4 - 4*x^6 + 6*x^8 - 4*x^10 + x^12 + (16*x^2 - 32*x^4 + 16*x^6)*Log[3
] + 64*Log[3]^2)/64] + (3*x^2 - 6*x^4 + 3*x^6 + 24*Log[3])*Log[(x^4 - 4*x^6 + 6*x^8 - 4*x^10 + x^12 + (16*x^2
- 32*x^4 + 16*x^6)*Log[3] + 64*Log[3]^2)/64]^2 + (x^2 - 2*x^4 + x^6 + 8*Log[3])*Log[(x^4 - 4*x^6 + 6*x^8 - 4*x
^10 + x^12 + (16*x^2 - 32*x^4 + 16*x^6)*Log[3] + 64*Log[3]^2)/64]^3),x]

[Out]

x^2/(1 + Log[(x^2 - 2*x^4 + x^6 + 8*Log[3])^2/64])^2

________________________________________________________________________________________

fricas [B]  time = 0.65, size = 106, normalized size = 3.93 \begin {gather*} \frac {x^{2}}{\log \left (\frac {1}{64} \, x^{12} - \frac {1}{16} \, x^{10} + \frac {3}{32} \, x^{8} - \frac {1}{16} \, x^{6} + \frac {1}{64} \, x^{4} + \frac {1}{4} \, {\left (x^{6} - 2 \, x^{4} + x^{2}\right )} \log \relax (3) + \log \relax (3)^{2}\right )^{2} + 2 \, \log \left (\frac {1}{64} \, x^{12} - \frac {1}{16} \, x^{10} + \frac {3}{32} \, x^{8} - \frac {1}{16} \, x^{6} + \frac {1}{64} \, x^{4} + \frac {1}{4} \, {\left (x^{6} - 2 \, x^{4} + x^{2}\right )} \log \relax (3) + \log \relax (3)^{2}\right ) + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((16*x*log(3)+2*x^7-4*x^5+2*x^3)*log(log(3)^2+1/64*(16*x^6-32*x^4+16*x^2)*log(3)+1/64*x^12-1/16*x^10
+3/32*x^8-1/16*x^6+1/64*x^4)+16*x*log(3)-22*x^7+28*x^5-6*x^3)/((8*log(3)+x^6-2*x^4+x^2)*log(log(3)^2+1/64*(16*
x^6-32*x^4+16*x^2)*log(3)+1/64*x^12-1/16*x^10+3/32*x^8-1/16*x^6+1/64*x^4)^3+(24*log(3)+3*x^6-6*x^4+3*x^2)*log(
log(3)^2+1/64*(16*x^6-32*x^4+16*x^2)*log(3)+1/64*x^12-1/16*x^10+3/32*x^8-1/16*x^6+1/64*x^4)^2+(24*log(3)+3*x^6
-6*x^4+3*x^2)*log(log(3)^2+1/64*(16*x^6-32*x^4+16*x^2)*log(3)+1/64*x^12-1/16*x^10+3/32*x^8-1/16*x^6+1/64*x^4)+
8*log(3)+x^6-2*x^4+x^2),x, algorithm="fricas")

[Out]

x^2/(log(1/64*x^12 - 1/16*x^10 + 3/32*x^8 - 1/16*x^6 + 1/64*x^4 + 1/4*(x^6 - 2*x^4 + x^2)*log(3) + log(3)^2)^2
+ 2*log(1/64*x^12 - 1/16*x^10 + 3/32*x^8 - 1/16*x^6 + 1/64*x^4 + 1/4*(x^6 - 2*x^4 + x^2)*log(3) + log(3)^2) +
1)

________________________________________________________________________________________

giac [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((16*x*log(3)+2*x^7-4*x^5+2*x^3)*log(log(3)^2+1/64*(16*x^6-32*x^4+16*x^2)*log(3)+1/64*x^12-1/16*x^10
+3/32*x^8-1/16*x^6+1/64*x^4)+16*x*log(3)-22*x^7+28*x^5-6*x^3)/((8*log(3)+x^6-2*x^4+x^2)*log(log(3)^2+1/64*(16*
x^6-32*x^4+16*x^2)*log(3)+1/64*x^12-1/16*x^10+3/32*x^8-1/16*x^6+1/64*x^4)^3+(24*log(3)+3*x^6-6*x^4+3*x^2)*log(
log(3)^2+1/64*(16*x^6-32*x^4+16*x^2)*log(3)+1/64*x^12-1/16*x^10+3/32*x^8-1/16*x^6+1/64*x^4)^2+(24*log(3)+3*x^6
-6*x^4+3*x^2)*log(log(3)^2+1/64*(16*x^6-32*x^4+16*x^2)*log(3)+1/64*x^12-1/16*x^10+3/32*x^8-1/16*x^6+1/64*x^4)+
8*log(3)+x^6-2*x^4+x^2),x, algorithm="giac")

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:Simplification assuming t_nostep near 0Simplification assuming t_nostep near 0Simplification assuming t_nos
tep near 0S

________________________________________________________________________________________

maple [B]  time = 0.05, size = 60, normalized size = 2.22

method	result	size
risch	\(\frac {x^{2}}{\left (\ln \left (\ln \relax (3)^{2}+\frac {\left (16 x^{6}-32 x^{4}+16 x^{2}\right ) \ln \relax (3)}{64}+\frac {x^{12}}{64}-\frac {x^{10}}{16}+\frac {3 x^{8}}{32}-\frac {x^{6}}{16}+\frac {x^{4}}{64}\right )+1\right )^{2}}\)	\(60\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((16*x*ln(3)+2*x^7-4*x^5+2*x^3)*ln(ln(3)^2+1/64*(16*x^6-32*x^4+16*x^2)*ln(3)+1/64*x^12-1/16*x^10+3/32*x^8-
1/16*x^6+1/64*x^4)+16*x*ln(3)-22*x^7+28*x^5-6*x^3)/((8*ln(3)+x^6-2*x^4+x^2)*ln(ln(3)^2+1/64*(16*x^6-32*x^4+16*
x^2)*ln(3)+1/64*x^12-1/16*x^10+3/32*x^8-1/16*x^6+1/64*x^4)^3+(24*ln(3)+3*x^6-6*x^4+3*x^2)*ln(ln(3)^2+1/64*(16*
x^6-32*x^4+16*x^2)*ln(3)+1/64*x^12-1/16*x^10+3/32*x^8-1/16*x^6+1/64*x^4)^2+(24*ln(3)+3*x^6-6*x^4+3*x^2)*ln(ln(
3)^2+1/64*(16*x^6-32*x^4+16*x^2)*ln(3)+1/64*x^12-1/16*x^10+3/32*x^8-1/16*x^6+1/64*x^4)+8*ln(3)+x^6-2*x^4+x^2),
x,method=_RETURNVERBOSE)

[Out]

x^2/(ln(ln(3)^2+1/64*(16*x^6-32*x^4+16*x^2)*ln(3)+1/64*x^12-1/16*x^10+3/32*x^8-1/16*x^6+1/64*x^4)+1)^2

________________________________________________________________________________________

maxima [B]  time = 0.54, size = 64, normalized size = 2.37 \begin {gather*} \frac {x^{2}}{36 \, \log \relax (2)^{2} - 4 \, {\left (6 \, \log \relax (2) - 1\right )} \log \left (x^{6} - 2 \, x^{4} + x^{2} + 8 \, \log \relax (3)\right ) + 4 \, \log \left (x^{6} - 2 \, x^{4} + x^{2} + 8 \, \log \relax (3)\right )^{2} - 12 \, \log \relax (2) + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((16*x*log(3)+2*x^7-4*x^5+2*x^3)*log(log(3)^2+1/64*(16*x^6-32*x^4+16*x^2)*log(3)+1/64*x^12-1/16*x^10
+3/32*x^8-1/16*x^6+1/64*x^4)+16*x*log(3)-22*x^7+28*x^5-6*x^3)/((8*log(3)+x^6-2*x^4+x^2)*log(log(3)^2+1/64*(16*
x^6-32*x^4+16*x^2)*log(3)+1/64*x^12-1/16*x^10+3/32*x^8-1/16*x^6+1/64*x^4)^3+(24*log(3)+3*x^6-6*x^4+3*x^2)*log(
log(3)^2+1/64*(16*x^6-32*x^4+16*x^2)*log(3)+1/64*x^12-1/16*x^10+3/32*x^8-1/16*x^6+1/64*x^4)^2+(24*log(3)+3*x^6
-6*x^4+3*x^2)*log(log(3)^2+1/64*(16*x^6-32*x^4+16*x^2)*log(3)+1/64*x^12-1/16*x^10+3/32*x^8-1/16*x^6+1/64*x^4)+
8*log(3)+x^6-2*x^4+x^2),x, algorithm="maxima")

[Out]

x^2/(36*log(2)^2 - 4*(6*log(2) - 1)*log(x^6 - 2*x^4 + x^2 + 8*log(3)) + 4*log(x^6 - 2*x^4 + x^2 + 8*log(3))^2
- 12*log(2) + 1)

________________________________________________________________________________________

mupad [B]  time = 4.00, size = 562, normalized size = 20.81 \begin {gather*} \frac {x^2}{72}-\frac {\frac {-11\,x^6+14\,x^4-3\,x^2+8\,\ln \relax (3)}{4\,\left (3\,x^4-4\,x^2+1\right )}+\frac {\ln \left ({\ln \relax (3)}^2+\frac {\ln \relax (3)\,\left (16\,x^6-32\,x^4+16\,x^2\right )}{64}+\frac {x^4}{64}-\frac {x^6}{16}+\frac {3\,x^8}{32}-\frac {x^{10}}{16}+\frac {x^{12}}{64}\right )\,\left (x^6-2\,x^4+x^2+8\,\ln \relax (3)\right )}{4\,\left (3\,x^4-4\,x^2+1\right )}}{{\ln \left ({\ln \relax (3)}^2+\frac {\ln \relax (3)\,\left (16\,x^6-32\,x^4+16\,x^2\right )}{64}+\frac {x^4}{64}-\frac {x^6}{16}+\frac {3\,x^8}{32}-\frac {x^{10}}{16}+\frac {x^{12}}{64}\right )}^2+2\,\ln \left ({\ln \relax (3)}^2+\frac {\ln \relax (3)\,\left (16\,x^6-32\,x^4+16\,x^2\right )}{64}+\frac {x^4}{64}-\frac {x^6}{16}+\frac {3\,x^8}{32}-\frac {x^{10}}{16}+\frac {x^{12}}{64}\right )+1}+\frac {\left (-27\,\ln \relax (3)-\frac {1}{4}\right )\,x^8+\left (72\,\ln \relax (3)+\frac {2}{3}\right )\,x^6+\left (-54\,\ln \relax (3)-\frac {1}{2}\right )\,x^4-432\,{\ln \relax (3)}^2\,x^2+9\,\ln \relax (3)+288\,{\ln \relax (3)}^2+\frac {1}{12}}{243\,x^{12}-972\,x^{10}+1539\,x^8-1224\,x^6+513\,x^4-108\,x^2+9}+\frac {\frac {\left (x^6-2\,x^4+x^2+8\,\ln \relax (3)\right )\,\left (48\,x^2\,\ln \relax (3)-32\,\ln \relax (3)-12\,x^2+36\,x^4-40\,x^6+15\,x^8+1\right )}{8\,{\left (3\,x^4-4\,x^2+1\right )}^3}-\frac {\ln \left ({\ln \relax (3)}^2+\frac {\ln \relax (3)\,\left (16\,x^6-32\,x^4+16\,x^2\right )}{64}+\frac {x^4}{64}-\frac {x^6}{16}+\frac {3\,x^8}{32}-\frac {x^{10}}{16}+\frac {x^{12}}{64}\right )\,\left (x^6-2\,x^4+x^2+8\,\ln \relax (3)\right )\,\left (32\,\ln \relax (3)-48\,x^2\,\ln \relax (3)-4\,x^2+8\,x^4-8\,x^6+3\,x^8+1\right )}{8\,{\left (3\,x^4-4\,x^2+1\right )}^3}}{\ln \left ({\ln \relax (3)}^2+\frac {\ln \relax (3)\,\left (16\,x^6-32\,x^4+16\,x^2\right )}{64}+\frac {x^4}{64}-\frac {x^6}{16}+\frac {3\,x^8}{32}-\frac {x^{10}}{16}+\frac {x^{12}}{64}\right )+1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(log(3)^2 + (log(3)*(16*x^2 - 32*x^4 + 16*x^6))/64 + x^4/64 - x^6/16 + (3*x^8)/32 - x^10/16 + x^12/64)
*(16*x*log(3) + 2*x^3 - 4*x^5 + 2*x^7) + 16*x*log(3) - 6*x^3 + 28*x^5 - 22*x^7)/(8*log(3) + log(log(3)^2 + (lo
g(3)*(16*x^2 - 32*x^4 + 16*x^6))/64 + x^4/64 - x^6/16 + (3*x^8)/32 - x^10/16 + x^12/64)^2*(24*log(3) + 3*x^2 -
6*x^4 + 3*x^6) + log(log(3)^2 + (log(3)*(16*x^2 - 32*x^4 + 16*x^6))/64 + x^4/64 - x^6/16 + (3*x^8)/32 - x^10/
16 + x^12/64)^3*(8*log(3) + x^2 - 2*x^4 + x^6) + log(log(3)^2 + (log(3)*(16*x^2 - 32*x^4 + 16*x^6))/64 + x^4/6
4 - x^6/16 + (3*x^8)/32 - x^10/16 + x^12/64)*(24*log(3) + 3*x^2 - 6*x^4 + 3*x^6) + x^2 - 2*x^4 + x^6),x)

[Out]

x^2/72 - ((8*log(3) - 3*x^2 + 14*x^4 - 11*x^6)/(4*(3*x^4 - 4*x^2 + 1)) + (log(log(3)^2 + (log(3)*(16*x^2 - 32*
x^4 + 16*x^6))/64 + x^4/64 - x^6/16 + (3*x^8)/32 - x^10/16 + x^12/64)*(8*log(3) + x^2 - 2*x^4 + x^6))/(4*(3*x^
4 - 4*x^2 + 1)))/(2*log(log(3)^2 + (log(3)*(16*x^2 - 32*x^4 + 16*x^6))/64 + x^4/64 - x^6/16 + (3*x^8)/32 - x^1
0/16 + x^12/64) + log(log(3)^2 + (log(3)*(16*x^2 - 32*x^4 + 16*x^6))/64 + x^4/64 - x^6/16 + (3*x^8)/32 - x^10/
16 + x^12/64)^2 + 1) + (9*log(3) - 432*x^2*log(3)^2 - x^8*(27*log(3) + 1/4) - x^4*(54*log(3) + 1/2) + x^6*(72*
log(3) + 2/3) + 288*log(3)^2 + 1/12)/(513*x^4 - 108*x^2 - 1224*x^6 + 1539*x^8 - 972*x^10 + 243*x^12 + 9) + (((
8*log(3) + x^2 - 2*x^4 + x^6)*(48*x^2*log(3) - 32*log(3) - 12*x^2 + 36*x^4 - 40*x^6 + 15*x^8 + 1))/(8*(3*x^4 -
4*x^2 + 1)^3) - (log(log(3)^2 + (log(3)*(16*x^2 - 32*x^4 + 16*x^6))/64 + x^4/64 - x^6/16 + (3*x^8)/32 - x^10/
16 + x^12/64)*(8*log(3) + x^2 - 2*x^4 + x^6)*(32*log(3) - 48*x^2*log(3) - 4*x^2 + 8*x^4 - 8*x^6 + 3*x^8 + 1))/
(8*(3*x^4 - 4*x^2 + 1)^3))/(log(log(3)^2 + (log(3)*(16*x^2 - 32*x^4 + 16*x^6))/64 + x^4/64 - x^6/16 + (3*x^8)/
32 - x^10/16 + x^12/64) + 1)

________________________________________________________________________________________

sympy [B]  time = 0.34, size = 112, normalized size = 4.15 \begin {gather*} \frac {x^{2}}{\log {\left (\frac {x^{12}}{64} - \frac {x^{10}}{16} + \frac {3 x^{8}}{32} - \frac {x^{6}}{16} + \frac {x^{4}}{64} + \left (\frac {x^{6}}{4} - \frac {x^{4}}{2} + \frac {x^{2}}{4}\right ) \log {\relax (3 )} + \log {\relax (3 )}^{2} \right )}^{2} + 2 \log {\left (\frac {x^{12}}{64} - \frac {x^{10}}{16} + \frac {3 x^{8}}{32} - \frac {x^{6}}{16} + \frac {x^{4}}{64} + \left (\frac {x^{6}}{4} - \frac {x^{4}}{2} + \frac {x^{2}}{4}\right ) \log {\relax (3 )} + \log {\relax (3 )}^{2} \right )} + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((16*x*ln(3)+2*x**7-4*x**5+2*x**3)*ln(ln(3)**2+1/64*(16*x**6-32*x**4+16*x**2)*ln(3)+1/64*x**12-1/16*
x**10+3/32*x**8-1/16*x**6+1/64*x**4)+16*x*ln(3)-22*x**7+28*x**5-6*x**3)/((8*ln(3)+x**6-2*x**4+x**2)*ln(ln(3)**
2+1/64*(16*x**6-32*x**4+16*x**2)*ln(3)+1/64*x**12-1/16*x**10+3/32*x**8-1/16*x**6+1/64*x**4)**3+(24*ln(3)+3*x**
6-6*x**4+3*x**2)*ln(ln(3)**2+1/64*(16*x**6-32*x**4+16*x**2)*ln(3)+1/64*x**12-1/16*x**10+3/32*x**8-1/16*x**6+1/
64*x**4)**2+(24*ln(3)+3*x**6-6*x**4+3*x**2)*ln(ln(3)**2+1/64*(16*x**6-32*x**4+16*x**2)*ln(3)+1/64*x**12-1/16*x
**10+3/32*x**8-1/16*x**6+1/64*x**4)+8*ln(3)+x**6-2*x**4+x**2),x)

[Out]

x**2/(log(x**12/64 - x**10/16 + 3*x**8/32 - x**6/16 + x**4/64 + (x**6/4 - x**4/2 + x**2/4)*log(3) + log(3)**2)
**2 + 2*log(x**12/64 - x**10/16 + 3*x**8/32 - x**6/16 + x**4/64 + (x**6/4 - x**4/2 + x**2/4)*log(3) + log(3)**
2) + 1)

________________________________________________________________________________________