3.40.20 \(\int \frac {-3072+4608 x-1152 x^2+48 x^3-16 x^4+x^5+(-192 x^2+48 x^3+x^5) \log (3)+(1536-96 x-96 x^2-26 x^3+2 x^4+(-96 x+6 x^3+2 x^4) \log (3)) \log (\frac {256-32 x+x^2+(-32 x+2 x^2) \log (3)+x^2 \log ^2(3)}{x^2})+(-16 x^2+x^3+x^3 \log (3)) \log ^2(\frac {256-32 x+x^2+(-32 x+2 x^2) \log (3)+x^2 \log ^2(3)}{x^2})}{-16 x^4+x^5+x^5 \log (3)+(-32 x^3+2 x^4+2 x^4 \log (3)) \log (\frac {256-32 x+x^2+(-32 x+2 x^2) \log (3)+x^2 \log ^2(3)}{x^2})+(-16 x^2+x^3+x^3 \log (3)) \log ^2(\frac {256-32 x+x^2+(-32 x+2 x^2) \log (3)+x^2 \log ^2(3)}{x^2})} \, dx\)
Optimal. Leaf size=30 \[ x+\frac {6 (4-x)^2}{x \left (x+\log \left (\left (1-\frac {16}{x}+\log (3)\right )^2\right )\right )} \]
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Rubi [F] time = 3.13, antiderivative size = 0, normalized size of antiderivative = 0.00,
number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used =
{} \begin {gather*} \int \frac {-3072+4608 x-1152 x^2+48 x^3-16 x^4+x^5+\left (-192 x^2+48 x^3+x^5\right ) \log (3)+\left (1536-96 x-96 x^2-26 x^3+2 x^4+\left (-96 x+6 x^3+2 x^4\right ) \log (3)\right ) \log \left (\frac {256-32 x+x^2+\left (-32 x+2 x^2\right ) \log (3)+x^2 \log ^2(3)}{x^2}\right )+\left (-16 x^2+x^3+x^3 \log (3)\right ) \log ^2\left (\frac {256-32 x+x^2+\left (-32 x+2 x^2\right ) \log (3)+x^2 \log ^2(3)}{x^2}\right )}{-16 x^4+x^5+x^5 \log (3)+\left (-32 x^3+2 x^4+2 x^4 \log (3)\right ) \log \left (\frac {256-32 x+x^2+\left (-32 x+2 x^2\right ) \log (3)+x^2 \log ^2(3)}{x^2}\right )+\left (-16 x^2+x^3+x^3 \log (3)\right ) \log ^2\left (\frac {256-32 x+x^2+\left (-32 x+2 x^2\right ) \log (3)+x^2 \log ^2(3)}{x^2}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(-3072 + 4608*x - 1152*x^2 + 48*x^3 - 16*x^4 + x^5 + (-192*x^2 + 48*x^3 + x^5)*Log[3] + (1536 - 96*x - 96*
x^2 - 26*x^3 + 2*x^4 + (-96*x + 6*x^3 + 2*x^4)*Log[3])*Log[(256 - 32*x + x^2 + (-32*x + 2*x^2)*Log[3] + x^2*Lo
g[3]^2)/x^2] + (-16*x^2 + x^3 + x^3*Log[3])*Log[(256 - 32*x + x^2 + (-32*x + 2*x^2)*Log[3] + x^2*Log[3]^2)/x^2
]^2)/(-16*x^4 + x^5 + x^5*Log[3] + (-32*x^3 + 2*x^4 + 2*x^4*Log[3])*Log[(256 - 32*x + x^2 + (-32*x + 2*x^2)*Lo
g[3] + x^2*Log[3]^2)/x^2] + (-16*x^2 + x^3 + x^3*Log[3])*Log[(256 - 32*x + x^2 + (-32*x + 2*x^2)*Log[3] + x^2*
Log[3]^2)/x^2]^2),x]
[Out]
x + 48*Defer[Int][(x + Log[(-16 + x + x*Log[3])^2/x^2])^(-2), x] + 192*Defer[Int][1/(x^2*(x + Log[(-16 + x + x
*Log[3])^2/x^2])^2), x] - 6*(30 - Log[9])*Defer[Int][1/(x*(x + Log[(-16 + x + x*Log[3])^2/x^2])^2), x] - 6*Def
er[Int][x/(x + Log[(-16 + x + x*Log[3])^2/x^2])^2, x] + 12*(3 - Log[3])^2*Defer[Int][1/((16 - x*(1 + Log[3]))*
(x + Log[(-16 + x + x*Log[3])^2/x^2])^2), x] + 6*Defer[Int][(x + Log[(-16 + x + x*Log[3])^2/x^2])^(-1), x] - 9
6*Defer[Int][1/(x^2*(x + Log[(-16 + x + x*Log[3])^2/x^2])), x]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-3072+4608 x-1152 x^2+48 x^3-16 x^4+x^5+\left (-192 x^2+48 x^3+x^5\right ) \log (3)+\left (1536-96 x-96 x^2-26 x^3+2 x^4+\left (-96 x+6 x^3+2 x^4\right ) \log (3)\right ) \log \left (\frac {256-32 x+x^2+\left (-32 x+2 x^2\right ) \log (3)+x^2 \log ^2(3)}{x^2}\right )+\left (-16 x^2+x^3+x^3 \log (3)\right ) \log ^2\left (\frac {256-32 x+x^2+\left (-32 x+2 x^2\right ) \log (3)+x^2 \log ^2(3)}{x^2}\right )}{-16 x^4+x^5 (1+\log (3))+\left (-32 x^3+2 x^4+2 x^4 \log (3)\right ) \log \left (\frac {256-32 x+x^2+\left (-32 x+2 x^2\right ) \log (3)+x^2 \log ^2(3)}{x^2}\right )+\left (-16 x^2+x^3+x^3 \log (3)\right ) \log ^2\left (\frac {256-32 x+x^2+\left (-32 x+2 x^2\right ) \log (3)+x^2 \log ^2(3)}{x^2}\right )} \, dx\\ &=\int \frac {3072-4608 x+16 x^4-48 x^3 (1+\log (3))-x^5 (1+\log (3))+192 x^2 (6+\log (3))-2 \left (-48+3 x^2+x^3\right ) (-16+x+x \log (3)) \log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )-x^2 (-16+x+x \log (3)) \log ^2\left (\frac {(-16+x+x \log (3))^2}{x^2}\right )}{x^2 (16-x (1+\log (3))) \left (x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )\right )^2} \, dx\\ &=\int \left (1+\frac {6 (4-x)^2 \left (32-16 x+x^2 (1+\log (3))\right )}{x^2 (16-x (1+\log (3))) \left (x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )\right )^2}+\frac {6 \left (-16+x^2\right )}{x^2 \left (x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )\right )}\right ) \, dx\\ &=x+6 \int \frac {(4-x)^2 \left (32-16 x+x^2 (1+\log (3))\right )}{x^2 (16-x (1+\log (3))) \left (x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )\right )^2} \, dx+6 \int \frac {-16+x^2}{x^2 \left (x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )\right )} \, dx\\ &=x+6 \int \left (\frac {8}{\left (x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )\right )^2}+\frac {32}{x^2 \left (x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )\right )^2}-\frac {x}{\left (x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )\right )^2}+\frac {32 (-1-\log (3)) \left (1-\frac {(5+\log (3))^2}{16 (1+\log (3))}\right )}{(16-x (1+\log (3))) \left (x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )\right )^2}+\frac {-30+\log (9)}{x \left (x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )\right )^2}\right ) \, dx+6 \int \left (\frac {1}{x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )}-\frac {16}{x^2 \left (x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )\right )}\right ) \, dx\\ &=x-6 \int \frac {x}{\left (x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )\right )^2} \, dx+6 \int \frac {1}{x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )} \, dx+48 \int \frac {1}{\left (x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )\right )^2} \, dx-96 \int \frac {1}{x^2 \left (x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )\right )} \, dx+192 \int \frac {1}{x^2 \left (x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )\right )^2} \, dx+\left (12 (3-\log (3))^2\right ) \int \frac {1}{(16-x (1+\log (3))) \left (x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )\right )^2} \, dx-(6 (30-\log (9))) \int \frac {1}{x \left (x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.09, size = 30, normalized size = 1.00 \begin {gather*} x+\frac {6 (-4+x)^2}{x \left (x+\log \left (\frac {(-16+x+x \log (3))^2}{x^2}\right )\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-3072 + 4608*x - 1152*x^2 + 48*x^3 - 16*x^4 + x^5 + (-192*x^2 + 48*x^3 + x^5)*Log[3] + (1536 - 96*x
- 96*x^2 - 26*x^3 + 2*x^4 + (-96*x + 6*x^3 + 2*x^4)*Log[3])*Log[(256 - 32*x + x^2 + (-32*x + 2*x^2)*Log[3] +
x^2*Log[3]^2)/x^2] + (-16*x^2 + x^3 + x^3*Log[3])*Log[(256 - 32*x + x^2 + (-32*x + 2*x^2)*Log[3] + x^2*Log[3]^
2)/x^2]^2)/(-16*x^4 + x^5 + x^5*Log[3] + (-32*x^3 + 2*x^4 + 2*x^4*Log[3])*Log[(256 - 32*x + x^2 + (-32*x + 2*x
^2)*Log[3] + x^2*Log[3]^2)/x^2] + (-16*x^2 + x^3 + x^3*Log[3])*Log[(256 - 32*x + x^2 + (-32*x + 2*x^2)*Log[3]
+ x^2*Log[3]^2)/x^2]^2),x]
[Out]
x + (6*(-4 + x)^2)/(x*(x + Log[(-16 + x + x*Log[3])^2/x^2]))
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fricas [B] time = 1.13, size = 90, normalized size = 3.00 \begin {gather*} \frac {x^{3} + x^{2} \log \left (\frac {x^{2} \log \relax (3)^{2} + x^{2} + 2 \, {\left (x^{2} - 16 \, x\right )} \log \relax (3) - 32 \, x + 256}{x^{2}}\right ) + 6 \, x^{2} - 48 \, x + 96}{x^{2} + x \log \left (\frac {x^{2} \log \relax (3)^{2} + x^{2} + 2 \, {\left (x^{2} - 16 \, x\right )} \log \relax (3) - 32 \, x + 256}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((x^3*log(3)+x^3-16*x^2)*log((x^2*log(3)^2+(2*x^2-32*x)*log(3)+x^2-32*x+256)/x^2)^2+((2*x^4+6*x^3-96
*x)*log(3)+2*x^4-26*x^3-96*x^2-96*x+1536)*log((x^2*log(3)^2+(2*x^2-32*x)*log(3)+x^2-32*x+256)/x^2)+(x^5+48*x^3
-192*x^2)*log(3)+x^5-16*x^4+48*x^3-1152*x^2+4608*x-3072)/((x^3*log(3)+x^3-16*x^2)*log((x^2*log(3)^2+(2*x^2-32*
x)*log(3)+x^2-32*x+256)/x^2)^2+(2*x^4*log(3)+2*x^4-32*x^3)*log((x^2*log(3)^2+(2*x^2-32*x)*log(3)+x^2-32*x+256)
/x^2)+x^5*log(3)+x^5-16*x^4),x, algorithm="fricas")
[Out]
(x^3 + x^2*log((x^2*log(3)^2 + x^2 + 2*(x^2 - 16*x)*log(3) - 32*x + 256)/x^2) + 6*x^2 - 48*x + 96)/(x^2 + x*lo
g((x^2*log(3)^2 + x^2 + 2*(x^2 - 16*x)*log(3) - 32*x + 256)/x^2))
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giac [A] time = 1.23, size = 56, normalized size = 1.87 \begin {gather*} x + \frac {6 \, {\left (x^{2} - 8 \, x + 16\right )}}{x^{2} + x \log \left (x^{2} \log \relax (3)^{2} + 2 \, x^{2} \log \relax (3) + x^{2} - 32 \, x \log \relax (3) - 32 \, x + 256\right ) - x \log \left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((x^3*log(3)+x^3-16*x^2)*log((x^2*log(3)^2+(2*x^2-32*x)*log(3)+x^2-32*x+256)/x^2)^2+((2*x^4+6*x^3-96
*x)*log(3)+2*x^4-26*x^3-96*x^2-96*x+1536)*log((x^2*log(3)^2+(2*x^2-32*x)*log(3)+x^2-32*x+256)/x^2)+(x^5+48*x^3
-192*x^2)*log(3)+x^5-16*x^4+48*x^3-1152*x^2+4608*x-3072)/((x^3*log(3)+x^3-16*x^2)*log((x^2*log(3)^2+(2*x^2-32*
x)*log(3)+x^2-32*x+256)/x^2)^2+(2*x^4*log(3)+2*x^4-32*x^3)*log((x^2*log(3)^2+(2*x^2-32*x)*log(3)+x^2-32*x+256)
/x^2)+x^5*log(3)+x^5-16*x^4),x, algorithm="giac")
[Out]
x + 6*(x^2 - 8*x + 16)/(x^2 + x*log(x^2*log(3)^2 + 2*x^2*log(3) + x^2 - 32*x*log(3) - 32*x + 256) - x*log(x^2)
)
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maple [A] time = 0.33, size = 53, normalized size = 1.77
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| method |
result |
size |
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| risch |
\(x +\frac {6 x^{2}-48 x +96}{x \left (x +\ln \left (\frac {x^{2} \ln \relax (3)^{2}+\left (2 x^{2}-32 x \right ) \ln \relax (3)+x^{2}-32 x +256}{x^{2}}\right )\right )}\) |
\(53\) |
| norman |
\(\frac {96+x^{3}-6 x \ln \left (\frac {x^{2} \ln \relax (3)^{2}+\left (2 x^{2}-32 x \right ) \ln \relax (3)+x^{2}-32 x +256}{x^{2}}\right )+x^{2} \ln \left (\frac {x^{2} \ln \relax (3)^{2}+\left (2 x^{2}-32 x \right ) \ln \relax (3)+x^{2}-32 x +256}{x^{2}}\right )-48 x}{x \left (x +\ln \left (\frac {x^{2} \ln \relax (3)^{2}+\left (2 x^{2}-32 x \right ) \ln \relax (3)+x^{2}-32 x +256}{x^{2}}\right )\right )}\) |
\(123\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((x^3*ln(3)+x^3-16*x^2)*ln((x^2*ln(3)^2+(2*x^2-32*x)*ln(3)+x^2-32*x+256)/x^2)^2+((2*x^4+6*x^3-96*x)*ln(3)+
2*x^4-26*x^3-96*x^2-96*x+1536)*ln((x^2*ln(3)^2+(2*x^2-32*x)*ln(3)+x^2-32*x+256)/x^2)+(x^5+48*x^3-192*x^2)*ln(3
)+x^5-16*x^4+48*x^3-1152*x^2+4608*x-3072)/((x^3*ln(3)+x^3-16*x^2)*ln((x^2*ln(3)^2+(2*x^2-32*x)*ln(3)+x^2-32*x+
256)/x^2)^2+(2*x^4*ln(3)+2*x^4-32*x^3)*ln((x^2*ln(3)^2+(2*x^2-32*x)*ln(3)+x^2-32*x+256)/x^2)+x^5*ln(3)+x^5-16*
x^4),x,method=_RETURNVERBOSE)
[Out]
x+6*(x^2-8*x+16)/x/(x+ln((x^2*ln(3)^2+(2*x^2-32*x)*ln(3)+x^2-32*x+256)/x^2))
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maxima [A] time = 0.48, size = 58, normalized size = 1.93 \begin {gather*} \frac {x^{3} + 2 \, x^{2} \log \left (x {\left (\log \relax (3) + 1\right )} - 16\right ) - 2 \, x^{2} \log \relax (x) + 6 \, x^{2} - 48 \, x + 96}{x^{2} + 2 \, x \log \left (x {\left (\log \relax (3) + 1\right )} - 16\right ) - 2 \, x \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((x^3*log(3)+x^3-16*x^2)*log((x^2*log(3)^2+(2*x^2-32*x)*log(3)+x^2-32*x+256)/x^2)^2+((2*x^4+6*x^3-96
*x)*log(3)+2*x^4-26*x^3-96*x^2-96*x+1536)*log((x^2*log(3)^2+(2*x^2-32*x)*log(3)+x^2-32*x+256)/x^2)+(x^5+48*x^3
-192*x^2)*log(3)+x^5-16*x^4+48*x^3-1152*x^2+4608*x-3072)/((x^3*log(3)+x^3-16*x^2)*log((x^2*log(3)^2+(2*x^2-32*
x)*log(3)+x^2-32*x+256)/x^2)^2+(2*x^4*log(3)+2*x^4-32*x^3)*log((x^2*log(3)^2+(2*x^2-32*x)*log(3)+x^2-32*x+256)
/x^2)+x^5*log(3)+x^5-16*x^4),x, algorithm="maxima")
[Out]
(x^3 + 2*x^2*log(x*(log(3) + 1) - 16) - 2*x^2*log(x) + 6*x^2 - 48*x + 96)/(x^2 + 2*x*log(x*(log(3) + 1) - 16)
- 2*x*log(x))
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mupad [B] time = 5.42, size = 5211, normalized size = 173.70 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((4608*x + log(3)*(48*x^3 - 192*x^2 + x^5) - log((x^2*log(3)^2 - 32*x - log(3)*(32*x - 2*x^2) + x^2 + 256)/
x^2)*(96*x - log(3)*(6*x^3 - 96*x + 2*x^4) + 96*x^2 + 26*x^3 - 2*x^4 - 1536) + log((x^2*log(3)^2 - 32*x - log(
3)*(32*x - 2*x^2) + x^2 + 256)/x^2)^2*(x^3*log(3) - 16*x^2 + x^3) - 1152*x^2 + 48*x^3 - 16*x^4 + x^5 - 3072)/(
x^5*log(3) + log((x^2*log(3)^2 - 32*x - log(3)*(32*x - 2*x^2) + x^2 + 256)/x^2)*(2*x^4*log(3) - 32*x^3 + 2*x^4
) + log((x^2*log(3)^2 - 32*x - log(3)*(32*x - 2*x^2) + x^2 + 256)/x^2)^2*(x^3*log(3) - 16*x^2 + x^3) - 16*x^4
+ x^5),x)
[Out]
x + 3072/(32*x*log(1/x^2) + 32*x*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) - 16*x^2*lo
g(1/x^2) + x^3*log(1/x^2) - 16*x^2*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^3*log
(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^4*log(3) + 32*x^2 - 16*x^3 + x^4 + x^3*log(
x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256)*log(3) + x^3*log(1/x^2)*log(3)) + (1152*x^2)/(32
*x*log(1/x^2) + 32*x*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) - 16*x^2*log(1/x^2) + x
^3*log(1/x^2) - 16*x^2*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^3*log(x^2*log(3)^
2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^4*log(3) + 32*x^2 - 16*x^3 + x^4 + x^3*log(x^2*log(3)^2
- 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256)*log(3) + x^3*log(1/x^2)*log(3)) - (48*x^3)/(32*x*log(1/x^2)
+ 32*x*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) - 16*x^2*log(1/x^2) + x^3*log(1/x^2)
- 16*x^2*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^3*log(x^2*log(3)^2 - 32*x - 32*
x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^4*log(3) + 32*x^2 - 16*x^3 + x^4 + x^3*log(x^2*log(3)^2 - 32*x - 32*x
*log(3) + 2*x^2*log(3) + x^2 + 256)*log(3) + x^3*log(1/x^2)*log(3)) - (1536*log(1/x^2))/(32*x*log(1/x^2) + 32*
x*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) - 16*x^2*log(1/x^2) + x^3*log(1/x^2) - 16*
x^2*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log
(3) + 2*x^2*log(3) + x^2 + 256) + x^4*log(3) + 32*x^2 - 16*x^3 + x^4 + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(
3) + 2*x^2*log(3) + x^2 + 256)*log(3) + x^3*log(1/x^2)*log(3)) + symsum(log(490733568*root(1134*log(3) + 23490
*log(3)^4 - 15795*log(3)^2 - 15390*log(3)^6 + 6804*log(3)^5 - 4536*log(3)^7 - 4536*log(3)^3 + 3645*log(3)^8 +
1134*log(3)^9 + 81*log(3)^10 + 3969, z, k) + 49545216*x - 3284140032*log(3) + 1283457024*root(1134*log(3) + 23
490*log(3)^4 - 15795*log(3)^2 - 15390*log(3)^6 + 6804*log(3)^5 - 4536*log(3)^7 - 4536*log(3)^3 + 3645*log(3)^8
+ 1134*log(3)^9 + 81*log(3)^10 + 3969, z, k)*log(3) - 42467328*root(1134*log(3) + 23490*log(3)^4 - 15795*log(
3)^2 - 15390*log(3)^6 + 6804*log(3)^5 - 4536*log(3)^7 - 4536*log(3)^3 + 3645*log(3)^8 + 1134*log(3)^9 + 81*log
(3)^10 + 3969, z, k)*x + 254803968*x*log(3) - 75497472*root(1134*log(3) + 23490*log(3)^4 - 15795*log(3)^2 - 15
390*log(3)^6 + 6804*log(3)^5 - 4536*log(3)^7 - 4536*log(3)^3 + 3645*log(3)^8 + 1134*log(3)^9 + 81*log(3)^10 +
3969, z, k)*log(3)^2 - 2642411520*root(1134*log(3) + 23490*log(3)^4 - 15795*log(3)^2 - 15390*log(3)^6 + 6804*l
og(3)^5 - 4536*log(3)^7 - 4536*log(3)^3 + 3645*log(3)^8 + 1134*log(3)^9 + 81*log(3)^10 + 3969, z, k)*log(3)^3
- 1509949440*root(1134*log(3) + 23490*log(3)^4 - 15795*log(3)^2 - 15390*log(3)^6 + 6804*log(3)^5 - 4536*log(3)
^7 - 4536*log(3)^3 + 3645*log(3)^8 + 1134*log(3)^9 + 81*log(3)^10 + 3969, z, k)*log(3)^4 + 1434451968*root(113
4*log(3) + 23490*log(3)^4 - 15795*log(3)^2 - 15390*log(3)^6 + 6804*log(3)^5 - 4536*log(3)^7 - 4536*log(3)^3 +
3645*log(3)^8 + 1134*log(3)^9 + 81*log(3)^10 + 3969, z, k)*log(3)^5 + 1283457024*root(1134*log(3) + 23490*log(
3)^4 - 15795*log(3)^2 - 15390*log(3)^6 + 6804*log(3)^5 - 4536*log(3)^7 - 4536*log(3)^3 + 3645*log(3)^8 + 1134*
log(3)^9 + 81*log(3)^10 + 3969, z, k)*log(3)^6 - 75497472*root(1134*log(3) + 23490*log(3)^4 - 15795*log(3)^2 -
15390*log(3)^6 + 6804*log(3)^5 - 4536*log(3)^7 - 4536*log(3)^3 + 3645*log(3)^8 + 1134*log(3)^9 + 81*log(3)^10
+ 3969, z, k)*log(3)^7 - 188743680*root(1134*log(3) + 23490*log(3)^4 - 15795*log(3)^2 - 15390*log(3)^6 + 6804
*log(3)^5 - 4536*log(3)^7 - 4536*log(3)^3 + 3645*log(3)^8 + 1134*log(3)^9 + 81*log(3)^10 + 3969, z, k)*log(3)^
8 + 431751168*x*log(3)^2 + 56623104*x*log(3)^3 - 693633024*x*log(3)^4 - 792723456*x*log(3)^5 - 99090432*x*log(
3)^6 + 396361728*x*log(3)^7 + 304349184*x*log(3)^8 + 84934656*x*log(3)^9 + 7077888*x*log(3)^10 - 3623878656*lo
g(3)^2 + 2717908992*log(3)^3 + 8380219392*log(3)^4 + 4303355904*log(3)^5 - 2717908992*log(3)^6 - 3623878656*lo
g(3)^7 - 1245708288*log(3)^8 - 113246208*log(3)^9 - 165150720*root(1134*log(3) + 23490*log(3)^4 - 15795*log(3)
^2 - 15390*log(3)^6 + 6804*log(3)^5 - 4536*log(3)^7 - 4536*log(3)^3 + 3645*log(3)^8 + 1134*log(3)^9 + 81*log(3
)^10 + 3969, z, k)*x*log(3) - 150994944*root(1134*log(3) + 23490*log(3)^4 - 15795*log(3)^2 - 15390*log(3)^6 +
6804*log(3)^5 - 4536*log(3)^7 - 4536*log(3)^3 + 3645*log(3)^8 + 1134*log(3)^9 + 81*log(3)^10 + 3969, z, k)*x*l
og(3)^2 + 188743680*root(1134*log(3) + 23490*log(3)^4 - 15795*log(3)^2 - 15390*log(3)^6 + 6804*log(3)^5 - 4536
*log(3)^7 - 4536*log(3)^3 + 3645*log(3)^8 + 1134*log(3)^9 + 81*log(3)^10 + 3969, z, k)*x*log(3)^3 + 405798912*
root(1134*log(3) + 23490*log(3)^4 - 15795*log(3)^2 - 15390*log(3)^6 + 6804*log(3)^5 - 4536*log(3)^7 - 4536*log
(3)^3 + 3645*log(3)^8 + 1134*log(3)^9 + 81*log(3)^10 + 3969, z, k)*x*log(3)^4 + 122683392*root(1134*log(3) + 2
3490*log(3)^4 - 15795*log(3)^2 - 15390*log(3)^6 + 6804*log(3)^5 - 4536*log(3)^7 - 4536*log(3)^3 + 3645*log(3)^
8 + 1134*log(3)^9 + 81*log(3)^10 + 3969, z, k)*x*log(3)^5 - 188743680*root(1134*log(3) + 23490*log(3)^4 - 1579
5*log(3)^2 - 15390*log(3)^6 + 6804*log(3)^5 - 4536*log(3)^7 - 4536*log(3)^3 + 3645*log(3)^8 + 1134*log(3)^9 +
81*log(3)^10 + 3969, z, k)*x*log(3)^6 - 150994944*root(1134*log(3) + 23490*log(3)^4 - 15795*log(3)^2 - 15390*l
og(3)^6 + 6804*log(3)^5 - 4536*log(3)^7 - 4536*log(3)^3 + 3645*log(3)^8 + 1134*log(3)^9 + 81*log(3)^10 + 3969,
z, k)*x*log(3)^7 - 23592960*root(1134*log(3) + 23490*log(3)^4 - 15795*log(3)^2 - 15390*log(3)^6 + 6804*log(3)
^5 - 4536*log(3)^7 - 4536*log(3)^3 + 3645*log(3)^8 + 1134*log(3)^9 + 81*log(3)^10 + 3969, z, k)*x*log(3)^8 + 4
718592*root(1134*log(3) + 23490*log(3)^4 - 15795*log(3)^2 - 15390*log(3)^6 + 6804*log(3)^5 - 4536*log(3)^7 - 4
536*log(3)^3 + 3645*log(3)^8 + 1134*log(3)^9 + 81*log(3)^10 + 3969, z, k)*x*log(3)^9 - 792723456)*root(1134*lo
g(3) + 23490*log(3)^4 - 15795*log(3)^2 - 15390*log(3)^6 + 6804*log(3)^5 - 4536*log(3)^7 - 4536*log(3)^3 + 3645
*log(3)^8 + 1134*log(3)^9 + 81*log(3)^10 + 3969, z, k), k, 1, 4) + 48/x - (1536*log(x^2*log(3)^2 - 32*x - 32*x
*log(3) + 2*x^2*log(3) + x^2 + 256))/(32*x*log(1/x^2) + 32*x*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log
(3) + x^2 + 256) - 16*x^2*log(1/x^2) + x^3*log(1/x^2) - 16*x^2*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*l
og(3) + x^2 + 256) + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^4*log(3) + 32*x
^2 - 16*x^3 + x^4 + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256)*log(3) + x^3*log(1/x
^2)*log(3)) - (4608*x)/(32*x*log(1/x^2) + 32*x*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 25
6) - 16*x^2*log(1/x^2) + x^3*log(1/x^2) - 16*x^2*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 +
256) + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^4*log(3) + 32*x^2 - 16*x^3 +
x^4 + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256)*log(3) + x^3*log(1/x^2)*log(3)) +
(96*x*log(1/x^2))/(32*x*log(1/x^2) + 32*x*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) -
16*x^2*log(1/x^2) + x^3*log(1/x^2) - 16*x^2*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256)
+ x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^4*log(3) + 32*x^2 - 16*x^3 + x^4 +
x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256)*log(3) + x^3*log(1/x^2)*log(3)) + (96*x
*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256))/(32*x*log(1/x^2) + 32*x*log(x^2*log(3)^2 -
32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) - 16*x^2*log(1/x^2) + x^3*log(1/x^2) - 16*x^2*log(x^2*log(3)^2
- 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) +
x^2 + 256) + x^4*log(3) + 32*x^2 - 16*x^3 + x^4 + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) +
x^2 + 256)*log(3) + x^3*log(1/x^2)*log(3)) + (96*x^2*log(1/x^2))/(32*x*log(1/x^2) + 32*x*log(x^2*log(3)^2 - 32
*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) - 16*x^2*log(1/x^2) + x^3*log(1/x^2) - 16*x^2*log(x^2*log(3)^2 -
32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^
2 + 256) + x^4*log(3) + 32*x^2 - 16*x^3 + x^4 + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2
+ 256)*log(3) + x^3*log(1/x^2)*log(3)) - (6*x^3*log(1/x^2))/(32*x*log(1/x^2) + 32*x*log(x^2*log(3)^2 - 32*x -
32*x*log(3) + 2*x^2*log(3) + x^2 + 256) - 16*x^2*log(1/x^2) + x^3*log(1/x^2) - 16*x^2*log(x^2*log(3)^2 - 32*x
- 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 +
256) + x^4*log(3) + 32*x^2 - 16*x^3 + x^4 + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 2
56)*log(3) + x^3*log(1/x^2)*log(3)) + (96*x^2*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256
))/(32*x*log(1/x^2) + 32*x*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) - 16*x^2*log(1/x^
2) + x^3*log(1/x^2) - 16*x^2*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^3*log(x^2*l
og(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^4*log(3) + 32*x^2 - 16*x^3 + x^4 + x^3*log(x^2*lo
g(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256)*log(3) + x^3*log(1/x^2)*log(3)) - (6*x^3*log(x^2*log(3
)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256))/(32*x*log(1/x^2) + 32*x*log(x^2*log(3)^2 - 32*x - 32*x*l
og(3) + 2*x^2*log(3) + x^2 + 256) - 16*x^2*log(1/x^2) + x^3*log(1/x^2) - 16*x^2*log(x^2*log(3)^2 - 32*x - 32*x
*log(3) + 2*x^2*log(3) + x^2 + 256) + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) +
x^4*log(3) + 32*x^2 - 16*x^3 + x^4 + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256)*log
(3) + x^3*log(1/x^2)*log(3)) + (192*x^2*log(3))/(32*x*log(1/x^2) + 32*x*log(x^2*log(3)^2 - 32*x - 32*x*log(3)
+ 2*x^2*log(3) + x^2 + 256) - 16*x^2*log(1/x^2) + x^3*log(1/x^2) - 16*x^2*log(x^2*log(3)^2 - 32*x - 32*x*log(3
) + 2*x^2*log(3) + x^2 + 256) + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^4*lo
g(3) + 32*x^2 - 16*x^3 + x^4 + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256)*log(3) +
x^3*log(1/x^2)*log(3)) - (48*x^3*log(3))/(32*x*log(1/x^2) + 32*x*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2
*log(3) + x^2 + 256) - 16*x^2*log(1/x^2) + x^3*log(1/x^2) - 16*x^2*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x
^2*log(3) + x^2 + 256) + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^4*log(3) +
32*x^2 - 16*x^3 + x^4 + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256)*log(3) + x^3*log
(1/x^2)*log(3)) - (6*x^3*log(1/x^2)*log(3))/(32*x*log(1/x^2) + 32*x*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*
x^2*log(3) + x^2 + 256) - 16*x^2*log(1/x^2) + x^3*log(1/x^2) - 16*x^2*log(x^2*log(3)^2 - 32*x - 32*x*log(3) +
2*x^2*log(3) + x^2 + 256) + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^4*log(3)
+ 32*x^2 - 16*x^3 + x^4 + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256)*log(3) + x^3*
log(1/x^2)*log(3)) - (6*x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256)*log(3))/(32*x*lo
g(1/x^2) + 32*x*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) - 16*x^2*log(1/x^2) + x^3*lo
g(1/x^2) - 16*x^2*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^3*log(x^2*log(3)^2 - 3
2*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^4*log(3) + 32*x^2 - 16*x^3 + x^4 + x^3*log(x^2*log(3)^2 - 32
*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256)*log(3) + x^3*log(1/x^2)*log(3)) + (96*x*log(1/x^2)*log(3))/(32*x*
log(1/x^2) + 32*x*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) - 16*x^2*log(1/x^2) + x^3*
log(1/x^2) - 16*x^2*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^3*log(x^2*log(3)^2 -
32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^4*log(3) + 32*x^2 - 16*x^3 + x^4 + x^3*log(x^2*log(3)^2 -
32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256)*log(3) + x^3*log(1/x^2)*log(3)) + (96*x*log(x^2*log(3)^2 - 32*x
- 32*x*log(3) + 2*x^2*log(3) + x^2 + 256)*log(3))/(32*x*log(1/x^2) + 32*x*log(x^2*log(3)^2 - 32*x - 32*x*log(
3) + 2*x^2*log(3) + x^2 + 256) - 16*x^2*log(1/x^2) + x^3*log(1/x^2) - 16*x^2*log(x^2*log(3)^2 - 32*x - 32*x*lo
g(3) + 2*x^2*log(3) + x^2 + 256) + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256) + x^4
*log(3) + 32*x^2 - 16*x^3 + x^4 + x^3*log(x^2*log(3)^2 - 32*x - 32*x*log(3) + 2*x^2*log(3) + x^2 + 256)*log(3)
+ x^3*log(1/x^2)*log(3))
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sympy [B] time = 0.29, size = 49, normalized size = 1.63 \begin {gather*} x + \frac {6 x^{2} - 48 x + 96}{x^{2} + x \log {\left (\frac {x^{2} + x^{2} \log {\relax (3 )}^{2} - 32 x + \left (2 x^{2} - 32 x\right ) \log {\relax (3 )} + 256}{x^{2}} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((x**3*ln(3)+x**3-16*x**2)*ln((x**2*ln(3)**2+(2*x**2-32*x)*ln(3)+x**2-32*x+256)/x**2)**2+((2*x**4+6*
x**3-96*x)*ln(3)+2*x**4-26*x**3-96*x**2-96*x+1536)*ln((x**2*ln(3)**2+(2*x**2-32*x)*ln(3)+x**2-32*x+256)/x**2)+
(x**5+48*x**3-192*x**2)*ln(3)+x**5-16*x**4+48*x**3-1152*x**2+4608*x-3072)/((x**3*ln(3)+x**3-16*x**2)*ln((x**2*
ln(3)**2+(2*x**2-32*x)*ln(3)+x**2-32*x+256)/x**2)**2+(2*x**4*ln(3)+2*x**4-32*x**3)*ln((x**2*ln(3)**2+(2*x**2-3
2*x)*ln(3)+x**2-32*x+256)/x**2)+x**5*ln(3)+x**5-16*x**4),x)
[Out]
x + (6*x**2 - 48*x + 96)/(x**2 + x*log((x**2 + x**2*log(3)**2 - 32*x + (2*x**2 - 32*x)*log(3) + 256)/x**2))
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