3.96.70 \(\int \frac {-x+e^{-3-e^x+x} (2 x-x^2+e^x x^2) \log (2 x \log (4))+2 x \log (2 x \log (4)) \log (\log (2 x \log (4)))}{e^{-6-2 e^x+2 x} \log (2 x \log (4))+2 e^{-3-e^x+x} \log (2 x \log (4)) \log (\log (2 x \log (4)))+\log (2 x \log (4)) \log ^2(\log (2 x \log (4)))} \, dx\)
Optimal. Leaf size=26 \[ 1+\frac {x^2}{e^{-3-e^x+x}+\log (\log (2 x \log (4)))} \]
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Rubi [F] time = 7.55, 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 {-x+e^{-3-e^x+x} \left (2 x-x^2+e^x x^2\right ) \log (2 x \log (4))+2 x \log (2 x \log (4)) \log (\log (2 x \log (4)))}{e^{-6-2 e^x+2 x} \log (2 x \log (4))+2 e^{-3-e^x+x} \log (2 x \log (4)) \log (\log (2 x \log (4)))+\log (2 x \log (4)) \log ^2(\log (2 x \log (4)))} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(-x + E^(-3 - E^x + x)*(2*x - x^2 + E^x*x^2)*Log[2*x*Log[4]] + 2*x*Log[2*x*Log[4]]*Log[Log[2*x*Log[4]]])/(
E^(-6 - 2*E^x + 2*x)*Log[2*x*Log[4]] + 2*E^(-3 - E^x + x)*Log[2*x*Log[4]]*Log[Log[2*x*Log[4]]] + Log[2*x*Log[4
]]*Log[Log[2*x*Log[4]]]^2),x]
[Out]
Defer[Int][E^(3 + E^x)*x^2, x] - Defer[Int][(E^(2*(3 + E^x))*x)/(Log[x*Log[16]]*(E^x + E^(3 + E^x)*Log[Log[x*L
og[16]]])^2), x] + Defer[Int][(E^(2*(3 + E^x))*x^2*Log[Log[x*Log[16]]])/(E^x + E^(3 + E^x)*Log[Log[x*Log[16]]]
)^2, x] + Defer[Int][(E^(3*(3 + E^x))*x^2*Log[Log[x*Log[16]]]^2)/(E^x + E^(3 + E^x)*Log[Log[x*Log[16]]])^2, x]
+ 2*Defer[Int][(E^(3 + E^x)*x)/(E^x + E^(3 + E^x)*Log[Log[x*Log[16]]]), x] - Defer[Int][(E^(3 + E^x)*x^2)/(E^
x + E^(3 + E^x)*Log[Log[x*Log[16]]]), x] - 2*Defer[Int][(E^(2*(3 + E^x))*x^2*Log[Log[x*Log[16]]])/(E^x + E^(3
+ E^x)*Log[Log[x*Log[16]]]), x]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{3+e^x} x \left (-e^{3+e^x}+\log (x \log (16)) \left (e^x \left (2+\left (-1+e^x\right ) x\right )+2 e^{3+e^x} \log (\log (x \log (16)))\right )\right )}{\log (x \log (16)) \left (e^x+e^{3+e^x} \log (\log (x \log (16)))\right )^2} \, dx\\ &=\int \left (e^{3+e^x} x^2-\frac {e^{3+e^x} x \left (-2+x+2 e^{3+e^x} x \log (\log (x \log (16)))\right )}{e^x+e^{3+e^x} \log (\log (x \log (16)))}+\frac {e^{6+2 e^x} x \left (-1+x \log (x \log (16)) \log (\log (x \log (16)))+e^{3+e^x} x \log (x \log (16)) \log ^2(\log (x \log (16)))\right )}{\log (x \log (16)) \left (e^x+e^{3+e^x} \log (\log (x \log (16)))\right )^2}\right ) \, dx\\ &=\int e^{3+e^x} x^2 \, dx-\int \frac {e^{3+e^x} x \left (-2+x+2 e^{3+e^x} x \log (\log (x \log (16)))\right )}{e^x+e^{3+e^x} \log (\log (x \log (16)))} \, dx+\int \frac {e^{6+2 e^x} x \left (-1+x \log (x \log (16)) \log (\log (x \log (16)))+e^{3+e^x} x \log (x \log (16)) \log ^2(\log (x \log (16)))\right )}{\log (x \log (16)) \left (e^x+e^{3+e^x} \log (\log (x \log (16)))\right )^2} \, dx\\ &=\int e^{3+e^x} x^2 \, dx+\int \frac {e^{2 \left (3+e^x\right )} x \left (-1+x \log (x \log (16)) \log (\log (x \log (16)))+e^{3+e^x} x \log (x \log (16)) \log ^2(\log (x \log (16)))\right )}{\log (x \log (16)) \left (e^x+e^{3+e^x} \log (\log (x \log (16)))\right )^2} \, dx-\int \left (-\frac {2 e^{3+e^x} x}{e^x+e^{3+e^x} \log (\log (x \log (16)))}+\frac {e^{3+e^x} x^2}{e^x+e^{3+e^x} \log (\log (x \log (16)))}+\frac {2 e^{6+2 e^x} x^2 \log (\log (x \log (16)))}{e^x+e^{3+e^x} \log (\log (x \log (16)))}\right ) \, dx\\ &=2 \int \frac {e^{3+e^x} x}{e^x+e^{3+e^x} \log (\log (x \log (16)))} \, dx-2 \int \frac {e^{6+2 e^x} x^2 \log (\log (x \log (16)))}{e^x+e^{3+e^x} \log (\log (x \log (16)))} \, dx+\int e^{3+e^x} x^2 \, dx-\int \frac {e^{3+e^x} x^2}{e^x+e^{3+e^x} \log (\log (x \log (16)))} \, dx+\int \left (-\frac {e^{2 \left (3+e^x\right )} x}{\log (x \log (16)) \left (e^x+e^{3+e^x} \log (\log (x \log (16)))\right )^2}+\frac {e^{2 \left (3+e^x\right )} x^2 \log (\log (x \log (16)))}{\left (e^x+e^{3+e^x} \log (\log (x \log (16)))\right )^2}+\frac {e^{3+e^x+2 \left (3+e^x\right )} x^2 \log ^2(\log (x \log (16)))}{\left (e^x+e^{3+e^x} \log (\log (x \log (16)))\right )^2}\right ) \, dx\\ &=2 \int \frac {e^{3+e^x} x}{e^x+e^{3+e^x} \log (\log (x \log (16)))} \, dx-2 \int \frac {e^{2 \left (3+e^x\right )} x^2 \log (\log (x \log (16)))}{e^x+e^{3+e^x} \log (\log (x \log (16)))} \, dx+\int e^{3+e^x} x^2 \, dx-\int \frac {e^{2 \left (3+e^x\right )} x}{\log (x \log (16)) \left (e^x+e^{3+e^x} \log (\log (x \log (16)))\right )^2} \, dx+\int \frac {e^{2 \left (3+e^x\right )} x^2 \log (\log (x \log (16)))}{\left (e^x+e^{3+e^x} \log (\log (x \log (16)))\right )^2} \, dx+\int \frac {e^{3+e^x+2 \left (3+e^x\right )} x^2 \log ^2(\log (x \log (16)))}{\left (e^x+e^{3+e^x} \log (\log (x \log (16)))\right )^2} \, dx-\int \frac {e^{3+e^x} x^2}{e^x+e^{3+e^x} \log (\log (x \log (16)))} \, dx\\ &=2 \int \frac {e^{3+e^x} x}{e^x+e^{3+e^x} \log (\log (x \log (16)))} \, dx-2 \int \frac {e^{2 \left (3+e^x\right )} x^2 \log (\log (x \log (16)))}{e^x+e^{3+e^x} \log (\log (x \log (16)))} \, dx+\int e^{3+e^x} x^2 \, dx-\int \frac {e^{2 \left (3+e^x\right )} x}{\log (x \log (16)) \left (e^x+e^{3+e^x} \log (\log (x \log (16)))\right )^2} \, dx+\int \frac {e^{2 \left (3+e^x\right )} x^2 \log (\log (x \log (16)))}{\left (e^x+e^{3+e^x} \log (\log (x \log (16)))\right )^2} \, dx+\int \frac {e^{3 \left (3+e^x\right )} x^2 \log ^2(\log (x \log (16)))}{\left (e^x+e^{3+e^x} \log (\log (x \log (16)))\right )^2} \, dx-\int \frac {e^{3+e^x} x^2}{e^x+e^{3+e^x} \log (\log (x \log (16)))} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.16, size = 31, normalized size = 1.19 \begin {gather*} \frac {e^{3+e^x} x^2}{e^x+e^{3+e^x} \log (\log (x \log (16)))} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-x + E^(-3 - E^x + x)*(2*x - x^2 + E^x*x^2)*Log[2*x*Log[4]] + 2*x*Log[2*x*Log[4]]*Log[Log[2*x*Log[4
]]])/(E^(-6 - 2*E^x + 2*x)*Log[2*x*Log[4]] + 2*E^(-3 - E^x + x)*Log[2*x*Log[4]]*Log[Log[2*x*Log[4]]] + Log[2*x
*Log[4]]*Log[Log[2*x*Log[4]]]^2),x]
[Out]
(E^(3 + E^x)*x^2)/(E^x + E^(3 + E^x)*Log[Log[x*Log[16]]])
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fricas [A] time = 0.48, size = 22, normalized size = 0.85 \begin {gather*} \frac {x^{2}}{e^{\left (x - e^{x} - 3\right )} + \log \left (\log \left (4 \, x \log \relax (2)\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((2*x*log(4*x*log(2))*log(log(4*x*log(2)))+(exp(x)*x^2-x^2+2*x)*log(4*x*log(2))*exp(-exp(x)+x-3)-x)/(
log(4*x*log(2))*log(log(4*x*log(2)))^2+2*log(4*x*log(2))*exp(-exp(x)+x-3)*log(log(4*x*log(2)))+log(4*x*log(2))
*exp(-exp(x)+x-3)^2),x, algorithm="fricas")
[Out]
x^2/(e^(x - e^x - 3) + log(log(4*x*log(2))))
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giac [B] time = 1.36, size = 3138, normalized size = 120.69 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((2*x*log(4*x*log(2))*log(log(4*x*log(2)))+(exp(x)*x^2-x^2+2*x)*log(4*x*log(2))*exp(-exp(x)+x-3)-x)/(
log(4*x*log(2))*log(log(4*x*log(2)))^2+2*log(4*x*log(2))*exp(-exp(x)+x-3)*log(log(4*x*log(2)))+log(4*x*log(2))
*exp(-exp(x)+x-3)^2),x, algorithm="giac")
[Out]
(4*x^4*e^(6*x - 2*e^x + 6)*log(2)^2*log(2*log(2) + log(x) + log(log(2))) - 8*x^4*e^(5*x - 2*e^x + 6)*log(2)^2*
log(2*log(2) + log(x) + log(log(2))) + 4*x^4*e^(4*x - 2*e^x + 6)*log(2)^2*log(2*log(2) + log(x) + log(log(2)))
+ 4*x^4*e^(6*x - 2*e^x + 6)*log(2)*log(x)*log(2*log(2) + log(x) + log(log(2))) - 8*x^4*e^(5*x - 2*e^x + 6)*lo
g(2)*log(x)*log(2*log(2) + log(x) + log(log(2))) + 4*x^4*e^(4*x - 2*e^x + 6)*log(2)*log(x)*log(2*log(2) + log(
x) + log(log(2))) + x^4*e^(6*x - 2*e^x + 6)*log(x)^2*log(2*log(2) + log(x) + log(log(2))) - 2*x^4*e^(5*x - 2*e
^x + 6)*log(x)^2*log(2*log(2) + log(x) + log(log(2))) + x^4*e^(4*x - 2*e^x + 6)*log(x)^2*log(2*log(2) + log(x)
+ log(log(2))) + 4*x^4*e^(6*x - 2*e^x + 6)*log(2)*log(2*log(2) + log(x) + log(log(2)))*log(log(2)) - 8*x^4*e^
(5*x - 2*e^x + 6)*log(2)*log(2*log(2) + log(x) + log(log(2)))*log(log(2)) + 4*x^4*e^(4*x - 2*e^x + 6)*log(2)*l
og(2*log(2) + log(x) + log(log(2)))*log(log(2)) + 2*x^4*e^(6*x - 2*e^x + 6)*log(x)*log(2*log(2) + log(x) + log
(log(2)))*log(log(2)) - 4*x^4*e^(5*x - 2*e^x + 6)*log(x)*log(2*log(2) + log(x) + log(log(2)))*log(log(2)) + 2*
x^4*e^(4*x - 2*e^x + 6)*log(x)*log(2*log(2) + log(x) + log(log(2)))*log(log(2)) + x^4*e^(6*x - 2*e^x + 6)*log(
2*log(2) + log(x) + log(log(2)))*log(log(2))^2 - 2*x^4*e^(5*x - 2*e^x + 6)*log(2*log(2) + log(x) + log(log(2))
)*log(log(2))^2 + x^4*e^(4*x - 2*e^x + 6)*log(2*log(2) + log(x) + log(log(2)))*log(log(2))^2 + 4*x^4*e^(7*x -
3*e^x + 3)*log(2)^2 - 8*x^4*e^(6*x - 3*e^x + 3)*log(2)^2 + 4*x^4*e^(5*x - 3*e^x + 3)*log(2)^2 + 4*x^4*e^(7*x -
3*e^x + 3)*log(2)*log(x) - 8*x^4*e^(6*x - 3*e^x + 3)*log(2)*log(x) + 4*x^4*e^(5*x - 3*e^x + 3)*log(2)*log(x)
+ x^4*e^(7*x - 3*e^x + 3)*log(x)^2 - 2*x^4*e^(6*x - 3*e^x + 3)*log(x)^2 + x^4*e^(5*x - 3*e^x + 3)*log(x)^2 + 4
*x^4*e^(7*x - 3*e^x + 3)*log(2)*log(log(2)) - 8*x^4*e^(6*x - 3*e^x + 3)*log(2)*log(log(2)) + 4*x^4*e^(5*x - 3*
e^x + 3)*log(2)*log(log(2)) + 2*x^4*e^(7*x - 3*e^x + 3)*log(x)*log(log(2)) - 4*x^4*e^(6*x - 3*e^x + 3)*log(x)*
log(log(2)) + 2*x^4*e^(5*x - 3*e^x + 3)*log(x)*log(log(2)) + x^4*e^(7*x - 3*e^x + 3)*log(log(2))^2 - 2*x^4*e^(
6*x - 3*e^x + 3)*log(log(2))^2 + x^4*e^(5*x - 3*e^x + 3)*log(log(2))^2 - 4*x^3*e^(4*x - e^x + 9)*log(2)*log(2*
log(2) + log(x) + log(log(2))) + 4*x^3*e^(3*x - e^x + 9)*log(2)*log(2*log(2) + log(x) + log(log(2))) - 2*x^3*e
^(4*x - e^x + 9)*log(x)*log(2*log(2) + log(x) + log(log(2))) + 2*x^3*e^(3*x - e^x + 9)*log(x)*log(2*log(2) + l
og(x) + log(log(2))) - 2*x^3*e^(4*x - e^x + 9)*log(2*log(2) + log(x) + log(log(2)))*log(log(2)) + 2*x^3*e^(3*x
- e^x + 9)*log(2*log(2) + log(x) + log(log(2)))*log(log(2)) - 4*x^3*e^(5*x - 2*e^x + 6)*log(2) + 4*x^3*e^(4*x
- 2*e^x + 6)*log(2) - 2*x^3*e^(5*x - 2*e^x + 6)*log(x) + 2*x^3*e^(4*x - 2*e^x + 6)*log(x) - 2*x^3*e^(5*x - 2*
e^x + 6)*log(log(2)) + 2*x^3*e^(4*x - 2*e^x + 6)*log(log(2)) + x^2*e^(2*x + 12)*log(2*log(2) + log(x) + log(lo
g(2))) + x^2*e^(3*x - e^x + 9))/(4*x^2*e^(6*x - 2*e^x + 6)*log(2)^2*log(2*log(2) + log(x) + log(log(2)))^2 - 8
*x^2*e^(5*x - 2*e^x + 6)*log(2)^2*log(2*log(2) + log(x) + log(log(2)))^2 + 4*x^2*e^(4*x - 2*e^x + 6)*log(2)^2*
log(2*log(2) + log(x) + log(log(2)))^2 + 4*x^2*e^(6*x - 2*e^x + 6)*log(2)*log(x)*log(2*log(2) + log(x) + log(l
og(2)))^2 - 8*x^2*e^(5*x - 2*e^x + 6)*log(2)*log(x)*log(2*log(2) + log(x) + log(log(2)))^2 + 4*x^2*e^(4*x - 2*
e^x + 6)*log(2)*log(x)*log(2*log(2) + log(x) + log(log(2)))^2 + x^2*e^(6*x - 2*e^x + 6)*log(x)^2*log(2*log(2)
+ log(x) + log(log(2)))^2 - 2*x^2*e^(5*x - 2*e^x + 6)*log(x)^2*log(2*log(2) + log(x) + log(log(2)))^2 + x^2*e^
(4*x - 2*e^x + 6)*log(x)^2*log(2*log(2) + log(x) + log(log(2)))^2 + 4*x^2*e^(6*x - 2*e^x + 6)*log(2)*log(2*log
(2) + log(x) + log(log(2)))^2*log(log(2)) - 8*x^2*e^(5*x - 2*e^x + 6)*log(2)*log(2*log(2) + log(x) + log(log(2
)))^2*log(log(2)) + 4*x^2*e^(4*x - 2*e^x + 6)*log(2)*log(2*log(2) + log(x) + log(log(2)))^2*log(log(2)) + 2*x^
2*e^(6*x - 2*e^x + 6)*log(x)*log(2*log(2) + log(x) + log(log(2)))^2*log(log(2)) - 4*x^2*e^(5*x - 2*e^x + 6)*lo
g(x)*log(2*log(2) + log(x) + log(log(2)))^2*log(log(2)) + 2*x^2*e^(4*x - 2*e^x + 6)*log(x)*log(2*log(2) + log(
x) + log(log(2)))^2*log(log(2)) + x^2*e^(6*x - 2*e^x + 6)*log(2*log(2) + log(x) + log(log(2)))^2*log(log(2))^2
- 2*x^2*e^(5*x - 2*e^x + 6)*log(2*log(2) + log(x) + log(log(2)))^2*log(log(2))^2 + x^2*e^(4*x - 2*e^x + 6)*lo
g(2*log(2) + log(x) + log(log(2)))^2*log(log(2))^2 + 8*x^2*e^(7*x - 3*e^x + 3)*log(2)^2*log(2*log(2) + log(x)
+ log(log(2))) - 16*x^2*e^(6*x - 3*e^x + 3)*log(2)^2*log(2*log(2) + log(x) + log(log(2))) + 8*x^2*e^(5*x - 3*e
^x + 3)*log(2)^2*log(2*log(2) + log(x) + log(log(2))) + 8*x^2*e^(7*x - 3*e^x + 3)*log(2)*log(x)*log(2*log(2) +
log(x) + log(log(2))) - 16*x^2*e^(6*x - 3*e^x + 3)*log(2)*log(x)*log(2*log(2) + log(x) + log(log(2))) + 8*x^2
*e^(5*x - 3*e^x + 3)*log(2)*log(x)*log(2*log(2) + log(x) + log(log(2))) + 2*x^2*e^(7*x - 3*e^x + 3)*log(x)^2*l
og(2*log(2) + log(x) + log(log(2))) - 4*x^2*e^(6*x - 3*e^x + 3)*log(x)^2*log(2*log(2) + log(x) + log(log(2)))
+ 2*x^2*e^(5*x - 3*e^x + 3)*log(x)^2*log(2*log(2) + log(x) + log(log(2))) + 8*x^2*e^(7*x - 3*e^x + 3)*log(2)*l
og(2*log(2) + log(x) + log(log(2)))*log(log(2)) - 16*x^2*e^(6*x - 3*e^x + 3)*log(2)*log(2*log(2) + log(x) + lo
g(log(2)))*log(log(2)) + 8*x^2*e^(5*x - 3*e^x + 3)*log(2)*log(2*log(2) + log(x) + log(log(2)))*log(log(2)) + 4
*x^2*e^(7*x - 3*e^x + 3)*log(x)*log(2*log(2) + log(x) + log(log(2)))*log(log(2)) - 8*x^2*e^(6*x - 3*e^x + 3)*l
og(x)*log(2*log(2) + log(x) + log(log(2)))*log(log(2)) + 4*x^2*e^(5*x - 3*e^x + 3)*log(x)*log(2*log(2) + log(x
) + log(log(2)))*log(log(2)) + 2*x^2*e^(7*x - 3*e^x + 3)*log(2*log(2) + log(x) + log(log(2)))*log(log(2))^2 -
4*x^2*e^(6*x - 3*e^x + 3)*log(2*log(2) + log(x) + log(log(2)))*log(log(2))^2 + 2*x^2*e^(5*x - 3*e^x + 3)*log(2
*log(2) + log(x) + log(log(2)))*log(log(2))^2 + 4*x^2*e^(8*x - 4*e^x)*log(2)^2 - 8*x^2*e^(7*x - 4*e^x)*log(2)^
2 + 4*x^2*e^(6*x - 4*e^x)*log(2)^2 + 4*x^2*e^(8*x - 4*e^x)*log(2)*log(x) - 8*x^2*e^(7*x - 4*e^x)*log(2)*log(x)
+ 4*x^2*e^(6*x - 4*e^x)*log(2)*log(x) + x^2*e^(8*x - 4*e^x)*log(x)^2 - 2*x^2*e^(7*x - 4*e^x)*log(x)^2 + x^2*e
^(6*x - 4*e^x)*log(x)^2 - 4*x*e^(4*x - e^x + 9)*log(2)*log(2*log(2) + log(x) + log(log(2)))^2 + 4*x*e^(3*x - e
^x + 9)*log(2)*log(2*log(2) + log(x) + log(log(2)))^2 - 2*x*e^(4*x - e^x + 9)*log(x)*log(2*log(2) + log(x) + l
og(log(2)))^2 + 2*x*e^(3*x - e^x + 9)*log(x)*log(2*log(2) + log(x) + log(log(2)))^2 + 4*x^2*e^(8*x - 4*e^x)*lo
g(2)*log(log(2)) - 8*x^2*e^(7*x - 4*e^x)*log(2)*log(log(2)) + 4*x^2*e^(6*x - 4*e^x)*log(2)*log(log(2)) + 2*x^2
*e^(8*x - 4*e^x)*log(x)*log(log(2)) - 4*x^2*e^(7*x - 4*e^x)*log(x)*log(log(2)) + 2*x^2*e^(6*x - 4*e^x)*log(x)*
log(log(2)) - 2*x*e^(4*x - e^x + 9)*log(2*log(2) + log(x) + log(log(2)))^2*log(log(2)) + 2*x*e^(3*x - e^x + 9)
*log(2*log(2) + log(x) + log(log(2)))^2*log(log(2)) + x^2*e^(8*x - 4*e^x)*log(log(2))^2 - 2*x^2*e^(7*x - 4*e^x
)*log(log(2))^2 + x^2*e^(6*x - 4*e^x)*log(log(2))^2 - 8*x*e^(5*x - 2*e^x + 6)*log(2)*log(2*log(2) + log(x) + l
og(log(2))) + 8*x*e^(4*x - 2*e^x + 6)*log(2)*log(2*log(2) + log(x) + log(log(2))) - 4*x*e^(5*x - 2*e^x + 6)*lo
g(x)*log(2*log(2) + log(x) + log(log(2))) + 4*x*e^(4*x - 2*e^x + 6)*log(x)*log(2*log(2) + log(x) + log(log(2))
) - 4*x*e^(5*x - 2*e^x + 6)*log(2*log(2) + log(x) + log(log(2)))*log(log(2)) + 4*x*e^(4*x - 2*e^x + 6)*log(2*l
og(2) + log(x) + log(log(2)))*log(log(2)) - 4*x*e^(6*x - 3*e^x + 3)*log(2) + 4*x*e^(5*x - 3*e^x + 3)*log(2) -
2*x*e^(6*x - 3*e^x + 3)*log(x) + 2*x*e^(5*x - 3*e^x + 3)*log(x) + e^(2*x + 12)*log(2*log(2) + log(x) + log(log
(2)))^2 - 2*x*e^(6*x - 3*e^x + 3)*log(log(2)) + 2*x*e^(5*x - 3*e^x + 3)*log(log(2)) + 2*e^(3*x - e^x + 9)*log(
2*log(2) + log(x) + log(log(2))) + e^(4*x - 2*e^x + 6))
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maple [A] time = 0.12, size = 23, normalized size = 0.88
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result |
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\(\frac {x^{2}}{{\mathrm e}^{-{\mathrm e}^{x}+x -3}+\ln \left (\ln \left (4 x \ln \relax (2)\right )\right )}\) |
\(23\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int((2*x*ln(4*x*ln(2))*ln(ln(4*x*ln(2)))+(exp(x)*x^2-x^2+2*x)*ln(4*x*ln(2))*exp(-exp(x)+x-3)-x)/(ln(4*x*ln(2))
*ln(ln(4*x*ln(2)))^2+2*ln(4*x*ln(2))*exp(-exp(x)+x-3)*ln(ln(4*x*ln(2)))+ln(4*x*ln(2))*exp(-exp(x)+x-3)^2),x,me
thod=_RETURNVERBOSE)
[Out]
x^2/(exp(-exp(x)+x-3)+ln(ln(4*x*ln(2))))
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maxima [A] time = 0.55, size = 31, normalized size = 1.19 \begin {gather*} \frac {x^{2} e^{\left (e^{x} + 3\right )}}{e^{\left (e^{x} + 3\right )} \log \left (2 \, \log \relax (2) + \log \relax (x) + \log \left (\log \relax (2)\right )\right ) + e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((2*x*log(4*x*log(2))*log(log(4*x*log(2)))+(exp(x)*x^2-x^2+2*x)*log(4*x*log(2))*exp(-exp(x)+x-3)-x)/(
log(4*x*log(2))*log(log(4*x*log(2)))^2+2*log(4*x*log(2))*exp(-exp(x)+x-3)*log(log(4*x*log(2)))+log(4*x*log(2))
*exp(-exp(x)+x-3)^2),x, algorithm="maxima")
[Out]
x^2*e^(e^x + 3)/(e^(e^x + 3)*log(2*log(2) + log(x) + log(log(2))) + e^x)
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\mathrm {e}}^{x-{\mathrm {e}}^x-3}\,\ln \left (4\,x\,\ln \relax (2)\right )\,\left (2\,x+x^2\,{\mathrm {e}}^x-x^2\right )-x+2\,x\,\ln \left (\ln \left (4\,x\,\ln \relax (2)\right )\right )\,\ln \left (4\,x\,\ln \relax (2)\right )}{\ln \left (4\,x\,\ln \relax (2)\right )\,{\ln \left (\ln \left (4\,x\,\ln \relax (2)\right )\right )}^2+2\,{\mathrm {e}}^{x-{\mathrm {e}}^x-3}\,\ln \left (4\,x\,\ln \relax (2)\right )\,\ln \left (\ln \left (4\,x\,\ln \relax (2)\right )\right )+{\mathrm {e}}^{2\,x-2\,{\mathrm {e}}^x-6}\,\ln \left (4\,x\,\ln \relax (2)\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((exp(x - exp(x) - 3)*log(4*x*log(2))*(2*x + x^2*exp(x) - x^2) - x + 2*x*log(log(4*x*log(2)))*log(4*x*log(2
)))/(log(log(4*x*log(2)))^2*log(4*x*log(2)) + exp(2*x - 2*exp(x) - 6)*log(4*x*log(2)) + 2*log(log(4*x*log(2)))
*exp(x - exp(x) - 3)*log(4*x*log(2))),x)
[Out]
int((exp(x - exp(x) - 3)*log(4*x*log(2))*(2*x + x^2*exp(x) - x^2) - x + 2*x*log(log(4*x*log(2)))*log(4*x*log(2
)))/(log(log(4*x*log(2)))^2*log(4*x*log(2)) + exp(2*x - 2*exp(x) - 6)*log(4*x*log(2)) + 2*log(log(4*x*log(2)))
*exp(x - exp(x) - 3)*log(4*x*log(2))), x)
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sympy [A] time = 0.54, size = 20, normalized size = 0.77 \begin {gather*} \frac {x^{2}}{e^{x - e^{x} - 3} + \log {\left (\log {\left (4 x \log {\relax (2 )} \right )} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((2*x*ln(4*x*ln(2))*ln(ln(4*x*ln(2)))+(exp(x)*x**2-x**2+2*x)*ln(4*x*ln(2))*exp(-exp(x)+x-3)-x)/(ln(4*
x*ln(2))*ln(ln(4*x*ln(2)))**2+2*ln(4*x*ln(2))*exp(-exp(x)+x-3)*ln(ln(4*x*ln(2)))+ln(4*x*ln(2))*exp(-exp(x)+x-3
)**2),x)
[Out]
x**2/(exp(x - exp(x) - 3) + log(log(4*x*log(2))))
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