3.51.44 \(\int \frac {3 x^3-x^4+(3 x+x^2) \log (\frac {16}{5})+(2 x^4-2 x^2 \log (\frac {16}{5})+(-6 x^3+6 x \log (\frac {16}{5})) \log (\frac {x^2-\log (\frac {16}{5})}{x})) \log (\frac {1}{3} (x-3 \log (\frac {x^2-\log (\frac {16}{5})}{x})))}{(x^3-x \log (\frac {16}{5})+(-3 x^2+3 \log (\frac {16}{5})) \log (\frac {x^2-\log (\frac {16}{5})}{x})) \log ^2(\frac {1}{3} (x-3 \log (\frac {x^2-\log (\frac {16}{5})}{x})))} \, dx\)

Optimal. Leaf size=27 \[ \frac {x^2}{\log \left (\frac {x}{3}-\log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )} \]

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Rubi [F]  time = 3.32, 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 {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(3*x^3 - x^4 + (3*x + x^2)*Log[16/5] + (2*x^4 - 2*x^2*Log[16/5] + (-6*x^3 + 6*x*Log[16/5])*Log[(x^2 - Log[
16/5])/x])*Log[(x - 3*Log[(x^2 - Log[16/5])/x])/3])/((x^3 - x*Log[16/5] + (-3*x^2 + 3*Log[16/5])*Log[(x^2 - Lo
g[16/5])/x])*Log[(x - 3*Log[(x^2 - Log[16/5])/x])/3]^2),x]

[Out]

3*Defer[Int][x/((x - 3*Log[x - Log[16/5]/x])*Log[(x - 3*Log[x - Log[16/5]/x])/3]^2), x] - Defer[Int][x^2/((x -
3*Log[x - Log[16/5]/x])*Log[(x - 3*Log[x - Log[16/5]/x])/3]^2), x] - 3*Log[16/5]*Defer[Int][1/((-x + Sqrt[Log
[16/5]])*(x - 3*Log[x - Log[16/5]/x])*Log[(x - 3*Log[x - Log[16/5]/x])/3]^2), x] + 3*Log[16/5]*Defer[Int][1/((
x + Sqrt[Log[16/5]])*(x - 3*Log[x - Log[16/5]/x])*Log[(x - 3*Log[x - Log[16/5]/x])/3]^2), x] + 2*Defer[Int][x/
Log[(x - 3*Log[x - Log[16/5]/x])/3], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^2-\log \left (\frac {16}{5}\right )\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx\\ &=\int \left (-\frac {x \left (-3 x^2+x^3-3 \log \left (\frac {16}{5}\right )-x \log \left (\frac {16}{5}\right )\right )}{\left (x^2-\log \left (\frac {16}{5}\right )\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}+\frac {2 x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}\right ) \, dx\\ &=2 \int \frac {x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx-\int \frac {x \left (-3 x^2+x^3-3 \log \left (\frac {16}{5}\right )-x \log \left (\frac {16}{5}\right )\right )}{\left (x^2-\log \left (\frac {16}{5}\right )\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx\\ &=2 \int \frac {x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx-\int \left (-\frac {3 x}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}+\frac {x^2}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}-\frac {6 x \log \left (\frac {16}{5}\right )}{\left (x^2-\log \left (\frac {16}{5}\right )\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}\right ) \, dx\\ &=2 \int \frac {x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx+3 \int \frac {x}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx+\left (6 \log \left (\frac {16}{5}\right )\right ) \int \frac {x}{\left (x^2-\log \left (\frac {16}{5}\right )\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx-\int \frac {x^2}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx\\ &=2 \int \frac {x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx+3 \int \frac {x}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx+\left (6 \log \left (\frac {16}{5}\right )\right ) \int \left (-\frac {1}{2 \left (-x+\sqrt {\log \left (\frac {16}{5}\right )}\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}+\frac {1}{2 \left (x+\sqrt {\log \left (\frac {16}{5}\right )}\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}\right ) \, dx-\int \frac {x^2}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx\\ &=2 \int \frac {x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx+3 \int \frac {x}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx-\left (3 \log \left (\frac {16}{5}\right )\right ) \int \frac {1}{\left (-x+\sqrt {\log \left (\frac {16}{5}\right )}\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx+\left (3 \log \left (\frac {16}{5}\right )\right ) \int \frac {1}{\left (x+\sqrt {\log \left (\frac {16}{5}\right )}\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx-\int \frac {x^2}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.07, size = 27, normalized size = 1.00 \begin {gather*} \frac {x^2}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3*x^3 - x^4 + (3*x + x^2)*Log[16/5] + (2*x^4 - 2*x^2*Log[16/5] + (-6*x^3 + 6*x*Log[16/5])*Log[(x^2
- Log[16/5])/x])*Log[(x - 3*Log[(x^2 - Log[16/5])/x])/3])/((x^3 - x*Log[16/5] + (-3*x^2 + 3*Log[16/5])*Log[(x^
2 - Log[16/5])/x])*Log[(x - 3*Log[(x^2 - Log[16/5])/x])/3]^2),x]

[Out]

x^2/Log[(x - 3*Log[x - Log[16/5]/x])/3]

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fricas [A]  time = 0.81, size = 26, normalized size = 0.96 \begin {gather*} \frac {x^{2}}{\log \left (\frac {1}{3} \, x - \log \left (\frac {x^{2} - \log \left (\frac {16}{5}\right )}{x}\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((6*x*log(16/5)-6*x^3)*log((-log(16/5)+x^2)/x)-2*x^2*log(16/5)+2*x^4)*log(-log((-log(16/5)+x^2)/x)+
1/3*x)+(x^2+3*x)*log(16/5)-x^4+3*x^3)/((3*log(16/5)-3*x^2)*log((-log(16/5)+x^2)/x)-x*log(16/5)+x^3)/log(-log((
-log(16/5)+x^2)/x)+1/3*x)^2,x, algorithm="fricas")

[Out]

x^2/log(1/3*x - log((x^2 - log(16/5))/x))

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giac [B]  time = 2.15, size = 1559, normalized size = 57.74 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((6*x*log(16/5)-6*x^3)*log((-log(16/5)+x^2)/x)-2*x^2*log(16/5)+2*x^4)*log(-log((-log(16/5)+x^2)/x)+
1/3*x)+(x^2+3*x)*log(16/5)-x^4+3*x^3)/((3*log(16/5)-3*x^2)*log((-log(16/5)+x^2)/x)-x*log(16/5)+x^3)/log(-log((
-log(16/5)+x^2)/x)+1/3*x)^2,x, algorithm="giac")

[Out]

-(x^8 - 3*x^7*log(x^2 - log(16/5)) + 3*x^7*log(x) - 3*x^7 + x^6*log(5) - x^6*log(16/5) - 4*x^6*log(2) + 9*x^6*
log(x^2 - log(16/5)) - 3*x^5*log(5)*log(x^2 - log(16/5)) + 3*x^5*log(16/5)*log(x^2 - log(16/5)) + 12*x^5*log(2
)*log(x^2 - log(16/5)) - 9*x^6*log(x) + 3*x^5*log(5)*log(x) - 3*x^5*log(16/5)*log(x) - 12*x^5*log(2)*log(x) +
3*x^5*log(5) + 3*x^5*log(16/5) - x^4*log(5)*log(16/5) - 12*x^5*log(2) + 4*x^4*log(16/5)*log(2) - 9*x^4*log(5)*
log(x^2 - log(16/5)) - 9*x^4*log(16/5)*log(x^2 - log(16/5)) + 3*x^3*log(5)*log(16/5)*log(x^2 - log(16/5)) + 36
*x^4*log(2)*log(x^2 - log(16/5)) - 12*x^3*log(16/5)*log(2)*log(x^2 - log(16/5)) + 9*x^4*log(5)*log(x) + 9*x^4*
log(16/5)*log(x) - 3*x^3*log(5)*log(16/5)*log(x) - 36*x^4*log(2)*log(x) + 12*x^3*log(16/5)*log(2)*log(x) - 3*x
^3*log(5)*log(16/5) + 12*x^3*log(16/5)*log(2) + 9*x^2*log(5)*log(16/5)*log(x^2 - log(16/5)) - 36*x^2*log(16/5)
*log(2)*log(x^2 - log(16/5)) - 9*x^2*log(5)*log(16/5)*log(x) + 36*x^2*log(16/5)*log(2)*log(x))/(x^6*log(3) - x
^6*log(x - 3*log(x^2 - log(16/5)) + 3*log(x)) - 3*x^5*log(3)*log((x^2 + log(5) - 4*log(2))/x) + 3*x^5*log(x -
3*log(x^2 - log(16/5)) + 3*log(x))*log((x^2 + log(5) - 4*log(2))/x) - 3*x^5*log(3) + x^4*log(5)*log(3) - x^4*l
og(16/5)*log(3) - 4*x^4*log(3)*log(2) + 3*x^5*log(x - 3*log(x^2 - log(16/5)) + 3*log(x)) - x^4*log(5)*log(x -
3*log(x^2 - log(16/5)) + 3*log(x)) + x^4*log(16/5)*log(x - 3*log(x^2 - log(16/5)) + 3*log(x)) + 4*x^4*log(2)*l
og(x - 3*log(x^2 - log(16/5)) + 3*log(x)) + 9*x^4*log(3)*log((x^2 + log(5) - 4*log(2))/x) - 3*x^3*log(5)*log(3
)*log((x^2 + log(5) - 4*log(2))/x) + 3*x^3*log(16/5)*log(3)*log((x^2 + log(5) - 4*log(2))/x) + 12*x^3*log(3)*l
og(2)*log((x^2 + log(5) - 4*log(2))/x) - 9*x^4*log(x - 3*log(x^2 - log(16/5)) + 3*log(x))*log((x^2 + log(5) -
4*log(2))/x) + 3*x^3*log(5)*log(x - 3*log(x^2 - log(16/5)) + 3*log(x))*log((x^2 + log(5) - 4*log(2))/x) - 3*x^
3*log(16/5)*log(x - 3*log(x^2 - log(16/5)) + 3*log(x))*log((x^2 + log(5) - 4*log(2))/x) - 12*x^3*log(2)*log(x
- 3*log(x^2 - log(16/5)) + 3*log(x))*log((x^2 + log(5) - 4*log(2))/x) - 3*x^3*log(5)*log(3) - 3*x^3*log(16/5)*
log(3) - x^2*log(5)*log(16/5)*log(3) + 12*x^3*log(3)*log(2) + 4*x^2*log(16/5)*log(3)*log(2) + 3*x^3*log(5)*log
(x - 3*log(x^2 - log(16/5)) + 3*log(x)) + 3*x^3*log(16/5)*log(x - 3*log(x^2 - log(16/5)) + 3*log(x)) + x^2*log
(5)*log(16/5)*log(x - 3*log(x^2 - log(16/5)) + 3*log(x)) - 12*x^3*log(2)*log(x - 3*log(x^2 - log(16/5)) + 3*lo
g(x)) - 4*x^2*log(16/5)*log(2)*log(x - 3*log(x^2 - log(16/5)) + 3*log(x)) + 9*x^2*log(5)*log(3)*log((x^2 + log
(5) - 4*log(2))/x) + 9*x^2*log(16/5)*log(3)*log((x^2 + log(5) - 4*log(2))/x) + 3*x*log(5)*log(16/5)*log(3)*log
((x^2 + log(5) - 4*log(2))/x) - 36*x^2*log(3)*log(2)*log((x^2 + log(5) - 4*log(2))/x) - 12*x*log(16/5)*log(3)*
log(2)*log((x^2 + log(5) - 4*log(2))/x) - 9*x^2*log(5)*log(x - 3*log(x^2 - log(16/5)) + 3*log(x))*log((x^2 + l
og(5) - 4*log(2))/x) - 9*x^2*log(16/5)*log(x - 3*log(x^2 - log(16/5)) + 3*log(x))*log((x^2 + log(5) - 4*log(2)
)/x) - 3*x*log(5)*log(16/5)*log(x - 3*log(x^2 - log(16/5)) + 3*log(x))*log((x^2 + log(5) - 4*log(2))/x) + 36*x
^2*log(2)*log(x - 3*log(x^2 - log(16/5)) + 3*log(x))*log((x^2 + log(5) - 4*log(2))/x) + 12*x*log(16/5)*log(2)*
log(x - 3*log(x^2 - log(16/5)) + 3*log(x))*log((x^2 + log(5) - 4*log(2))/x) - 3*x*log(5)*log(16/5)*log(3) + 12
*x*log(16/5)*log(3)*log(2) + 3*x*log(5)*log(16/5)*log(x - 3*log(x^2 - log(16/5)) + 3*log(x)) - 12*x*log(16/5)*
log(2)*log(x - 3*log(x^2 - log(16/5)) + 3*log(x)) + 9*log(5)*log(16/5)*log(3)*log((x^2 + log(5) - 4*log(2))/x)
- 36*log(16/5)*log(3)*log(2)*log((x^2 + log(5) - 4*log(2))/x) - 9*log(5)*log(16/5)*log(x - 3*log(x^2 - log(16
/5)) + 3*log(x))*log((x^2 + log(5) - 4*log(2))/x) + 36*log(16/5)*log(2)*log(x - 3*log(x^2 - log(16/5)) + 3*log
(x))*log((x^2 + log(5) - 4*log(2))/x))

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maple [F]  time = 0.02, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (6 x \ln \left (\frac {16}{5}\right )-6 x^{3}\right ) \ln \left (\frac {-\ln \left (\frac {16}{5}\right )+x^{2}}{x}\right )-2 x^{2} \ln \left (\frac {16}{5}\right )+2 x^{4}\right ) \ln \left (-\ln \left (\frac {-\ln \left (\frac {16}{5}\right )+x^{2}}{x}\right )+\frac {x}{3}\right )+\left (x^{2}+3 x \right ) \ln \left (\frac {16}{5}\right )-x^{4}+3 x^{3}}{\left (\left (3 \ln \left (\frac {16}{5}\right )-3 x^{2}\right ) \ln \left (\frac {-\ln \left (\frac {16}{5}\right )+x^{2}}{x}\right )-x \ln \left (\frac {16}{5}\right )+x^{3}\right ) \ln \left (-\ln \left (\frac {-\ln \left (\frac {16}{5}\right )+x^{2}}{x}\right )+\frac {x}{3}\right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((6*x*ln(16/5)-6*x^3)*ln((-ln(16/5)+x^2)/x)-2*x^2*ln(16/5)+2*x^4)*ln(-ln((-ln(16/5)+x^2)/x)+1/3*x)+(x^2+3
*x)*ln(16/5)-x^4+3*x^3)/((3*ln(16/5)-3*x^2)*ln((-ln(16/5)+x^2)/x)-x*ln(16/5)+x^3)/ln(-ln((-ln(16/5)+x^2)/x)+1/
3*x)^2,x)

[Out]

int((((6*x*ln(16/5)-6*x^3)*ln((-ln(16/5)+x^2)/x)-2*x^2*ln(16/5)+2*x^4)*ln(-ln((-ln(16/5)+x^2)/x)+1/3*x)+(x^2+3
*x)*ln(16/5)-x^4+3*x^3)/((3*ln(16/5)-3*x^2)*ln((-ln(16/5)+x^2)/x)-x*ln(16/5)+x^3)/ln(-ln((-ln(16/5)+x^2)/x)+1/
3*x)^2,x)

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maxima [A]  time = 0.50, size = 32, normalized size = 1.19 \begin {gather*} -\frac {x^{2}}{\log \relax (3) - \log \left (x - 3 \, \log \left (x^{2} + \log \relax (5) - 4 \, \log \relax (2)\right ) + 3 \, \log \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((6*x*log(16/5)-6*x^3)*log((-log(16/5)+x^2)/x)-2*x^2*log(16/5)+2*x^4)*log(-log((-log(16/5)+x^2)/x)+
1/3*x)+(x^2+3*x)*log(16/5)-x^4+3*x^3)/((3*log(16/5)-3*x^2)*log((-log(16/5)+x^2)/x)-x*log(16/5)+x^3)/log(-log((
-log(16/5)+x^2)/x)+1/3*x)^2,x, algorithm="maxima")

[Out]

-x^2/(log(3) - log(x - 3*log(x^2 + log(5) - 4*log(2)) + 3*log(x)))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {\ln \left (\frac {x}{3}-\ln \left (-\frac {\ln \left (\frac {16}{5}\right )-x^2}{x}\right )\right )\,\left (2\,x^4-2\,x^2\,\ln \left (\frac {16}{5}\right )+\ln \left (-\frac {\ln \left (\frac {16}{5}\right )-x^2}{x}\right )\,\left (6\,x\,\ln \left (\frac {16}{5}\right )-6\,x^3\right )\right )+3\,x^3-x^4+\ln \left (\frac {16}{5}\right )\,\left (x^2+3\,x\right )}{{\ln \left (\frac {x}{3}-\ln \left (-\frac {\ln \left (\frac {16}{5}\right )-x^2}{x}\right )\right )}^2\,\left (\ln \left (-\frac {\ln \left (\frac {16}{5}\right )-x^2}{x}\right )\,\left (3\,\ln \left (\frac {16}{5}\right )-3\,x^2\right )-x\,\ln \left (\frac {16}{5}\right )+x^3\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x/3 - log(-(log(16/5) - x^2)/x))*(2*x^4 - 2*x^2*log(16/5) + log(-(log(16/5) - x^2)/x)*(6*x*log(16/5)
- 6*x^3)) + 3*x^3 - x^4 + log(16/5)*(3*x + x^2))/(log(x/3 - log(-(log(16/5) - x^2)/x))^2*(log(-(log(16/5) - x^
2)/x)*(3*log(16/5) - 3*x^2) - x*log(16/5) + x^3)),x)

[Out]

int((log(x/3 - log(-(log(16/5) - x^2)/x))*(2*x^4 - 2*x^2*log(16/5) + log(-(log(16/5) - x^2)/x)*(6*x*log(16/5)
- 6*x^3)) + 3*x^3 - x^4 + log(16/5)*(3*x + x^2))/(log(x/3 - log(-(log(16/5) - x^2)/x))^2*(log(-(log(16/5) - x^
2)/x)*(3*log(16/5) - 3*x^2) - x*log(16/5) + x^3)), x)

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sympy [A]  time = 0.75, size = 19, normalized size = 0.70 \begin {gather*} \frac {x^{2}}{\log {\left (\frac {x}{3} - \log {\left (\frac {x^{2} - \log {\left (\frac {16}{5} \right )}}{x} \right )} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((6*x*ln(16/5)-6*x**3)*ln((-ln(16/5)+x**2)/x)-2*x**2*ln(16/5)+2*x**4)*ln(-ln((-ln(16/5)+x**2)/x)+1/
3*x)+(x**2+3*x)*ln(16/5)-x**4+3*x**3)/((3*ln(16/5)-3*x**2)*ln((-ln(16/5)+x**2)/x)-x*ln(16/5)+x**3)/ln(-ln((-ln
(16/5)+x**2)/x)+1/3*x)**2,x)

[Out]

x**2/log(x/3 - log((x**2 - log(16/5))/x))

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