3.83.46 \(\int \frac {(486 x-324 x^2-108 x^3+144 x^4-42 x^5+4 x^6+e^x (-162 x+216 x^2-108 x^3+24 x^4-2 x^5)+(324-108 x-216 x^2+168 x^3-44 x^4+4 x^5) \log (x)) \log (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x))+(-270 x^2+54 x^3+180 x^4-116 x^5+26 x^6-2 x^7+e^x (270 x-324 x^2+144 x^3-28 x^4+2 x^5)+(270 x-324 x^2+144 x^3-28 x^4+2 x^5) \log (5)+(-540 x^2+648 x^3-288 x^4+56 x^5-4 x^6) \log (x)+(-270 x+324 x^2-144 x^3+28 x^4-2 x^5) \log ^2(x)) \log ^2(e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x))}{-e^{3 x} x+e^{2 x} (x^2+x^3-x \log (5))+2 e^{2 x} x^2 \log (x)+e^{2 x} x \log ^2(x)} \, dx\)
Optimal. Leaf size=33 \[ e^{-2 x} (3-x)^4 \log ^2\left (e^x-x+\log (5)-(x+\log (x))^2\right ) \]
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Rubi [F] time = 130.31, 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 {\left (486 x-324 x^2-108 x^3+144 x^4-42 x^5+4 x^6+e^x \left (-162 x+216 x^2-108 x^3+24 x^4-2 x^5\right )+\left (324-108 x-216 x^2+168 x^3-44 x^4+4 x^5\right ) \log (x)\right ) \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )+\left (-270 x^2+54 x^3+180 x^4-116 x^5+26 x^6-2 x^7+e^x \left (270 x-324 x^2+144 x^3-28 x^4+2 x^5\right )+\left (270 x-324 x^2+144 x^3-28 x^4+2 x^5\right ) \log (5)+\left (-540 x^2+648 x^3-288 x^4+56 x^5-4 x^6\right ) \log (x)+\left (-270 x+324 x^2-144 x^3+28 x^4-2 x^5\right ) \log ^2(x)\right ) \log ^2\left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )}{-e^{3 x} x+e^{2 x} \left (x^2+x^3-x \log (5)\right )+2 e^{2 x} x^2 \log (x)+e^{2 x} x \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[((486*x - 324*x^2 - 108*x^3 + 144*x^4 - 42*x^5 + 4*x^6 + E^x*(-162*x + 216*x^2 - 108*x^3 + 24*x^4 - 2*x^5)
+ (324 - 108*x - 216*x^2 + 168*x^3 - 44*x^4 + 4*x^5)*Log[x])*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]
^2] + (-270*x^2 + 54*x^3 + 180*x^4 - 116*x^5 + 26*x^6 - 2*x^7 + E^x*(270*x - 324*x^2 + 144*x^3 - 28*x^4 + 2*x^
5) + (270*x - 324*x^2 + 144*x^3 - 28*x^4 + 2*x^5)*Log[5] + (-540*x^2 + 648*x^3 - 288*x^4 + 56*x^5 - 4*x^6)*Log
[x] + (-270*x + 324*x^2 - 144*x^3 + 28*x^4 - 2*x^5)*Log[x]^2)*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]
^2]^2)/(-(E^(3*x)*x) + E^(2*x)*(x^2 + x^3 - x*Log[5]) + 2*E^(2*x)*x^2*Log[x] + E^(2*x)*x*Log[x]^2),x]
[Out]
162*Defer[Int][Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2]/E^(2*x), x] - 216*Defer[Int][(x*Log[E^x - x
- x^2 + Log[5] - 2*x*Log[x] - Log[x]^2])/E^(2*x), x] + 108*Defer[Int][(x^2*Log[E^x - x - x^2 + Log[5] - 2*x*L
og[x] - Log[x]^2])/E^(2*x), x] - 24*Defer[Int][(x^3*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2])/E^(2*
x), x] + 2*Defer[Int][(x^4*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2])/E^(2*x), x] - 162*(3 + Log[5])
*Defer[Int][Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2]/(E^(2*x)*(E^x - x - x^2 + Log[5] - 2*x*Log[x]
- Log[x]^2)), x] + 162*Defer[Int][(x*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2])/(E^(2*x)*(-E^x + x +
x^2 - Log[5] + 2*x*Log[x] + Log[x]^2)), x] - 216*(3 + Log[5])*Defer[Int][(x*Log[E^x - x - x^2 + Log[5] - 2*x*
Log[x] - Log[x]^2])/(E^(2*x)*(-E^x + x + x^2 - Log[5] + 2*x*Log[x] + Log[x]^2)), x] - 378*Defer[Int][(x^2*Log[
E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2])/(E^(2*x)*(-E^x + x + x^2 - Log[5] + 2*x*Log[x] + Log[x]^2)),
x] + 108*(3 + Log[5])*Defer[Int][(x^2*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2])/(E^(2*x)*(-E^x + x
+ x^2 - Log[5] + 2*x*Log[x] + Log[x]^2)), x] + 324*Defer[Int][(x^3*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - L
og[x]^2])/(E^(2*x)*(-E^x + x + x^2 - Log[5] + 2*x*Log[x] + Log[x]^2)), x] - 24*(3 + Log[5])*Defer[Int][(x^3*Lo
g[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2])/(E^(2*x)*(-E^x + x + x^2 - Log[5] + 2*x*Log[x] + Log[x]^2))
, x] - 132*Defer[Int][(x^4*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2])/(E^(2*x)*(-E^x + x + x^2 - Log
[5] + 2*x*Log[x] + Log[x]^2)), x] + 2*(3 + Log[5])*Defer[Int][(x^4*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - L
og[x]^2])/(E^(2*x)*(-E^x + x + x^2 - Log[5] + 2*x*Log[x] + Log[x]^2)), x] + 26*Defer[Int][(x^5*Log[E^x - x - x
^2 + Log[5] - 2*x*Log[x] - Log[x]^2])/(E^(2*x)*(-E^x + x + x^2 - Log[5] + 2*x*Log[x] + Log[x]^2)), x] - 2*Defe
r[Int][(x^6*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2])/(E^(2*x)*(-E^x + x + x^2 - Log[5] + 2*x*Log[x
] + Log[x]^2)), x] - 108*Defer[Int][(Log[x]*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2])/(E^(2*x)*(-E^
x + x + x^2 - Log[5] + 2*x*Log[x] + Log[x]^2)), x] + 324*Defer[Int][(Log[x]*Log[E^x - x - x^2 + Log[5] - 2*x*L
og[x] - Log[x]^2])/(E^(2*x)*x*(-E^x + x + x^2 - Log[5] + 2*x*Log[x] + Log[x]^2)), x] - 540*Defer[Int][(x*Log[x
]*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2])/(E^(2*x)*(-E^x + x + x^2 - Log[5] + 2*x*Log[x] + Log[x]
^2)), x] + 600*Defer[Int][(x^2*Log[x]*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2])/(E^(2*x)*(-E^x + x
+ x^2 - Log[5] + 2*x*Log[x] + Log[x]^2)), x] - 260*Defer[Int][(x^3*Log[x]*Log[E^x - x - x^2 + Log[5] - 2*x*Log
[x] - Log[x]^2])/(E^(2*x)*(-E^x + x + x^2 - Log[5] + 2*x*Log[x] + Log[x]^2)), x] + 52*Defer[Int][(x^4*Log[x]*L
og[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2])/(E^(2*x)*(-E^x + x + x^2 - Log[5] + 2*x*Log[x] + Log[x]^2)
), x] - 4*Defer[Int][(x^5*Log[x]*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2])/(E^(2*x)*(-E^x + x + x^2
- Log[5] + 2*x*Log[x] + Log[x]^2)), x] - 162*Defer[Int][(Log[x]^2*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - L
og[x]^2])/(E^(2*x)*(-E^x + x + x^2 - Log[5] + 2*x*Log[x] + Log[x]^2)), x] + 216*Defer[Int][(x*Log[x]^2*Log[E^x
- x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2])/(E^(2*x)*(-E^x + x + x^2 - Log[5] + 2*x*Log[x] + Log[x]^2)), x]
- 108*Defer[Int][(x^2*Log[x]^2*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2])/(E^(2*x)*(-E^x + x + x^2 -
Log[5] + 2*x*Log[x] + Log[x]^2)), x] + 24*Defer[Int][(x^3*Log[x]^2*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] -
Log[x]^2])/(E^(2*x)*(-E^x + x + x^2 - Log[5] + 2*x*Log[x] + Log[x]^2)), x] - 2*Defer[Int][(x^4*Log[x]^2*Log[E^
x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2])/(E^(2*x)*(-E^x + x + x^2 - Log[5] + 2*x*Log[x] + Log[x]^2)), x]
- 270*Defer[Int][Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2]^2/E^(2*x), x] + 324*Defer[Int][(x*Log[E^
x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2]^2)/E^(2*x), x] - 144*Defer[Int][(x^2*Log[E^x - x - x^2 + Log[5]
- 2*x*Log[x] - Log[x]^2]^2)/E^(2*x), x] + 28*Defer[Int][(x^3*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^
2]^2)/E^(2*x), x] - 2*Defer[Int][(x^4*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2]^2)/E^(2*x), x]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-2 x} \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right ) \left (-486 x+2 e^x (-3+x)^4 x+324 x^2+108 x^3-144 x^4+42 x^5-4 x^6-4 (-3+x)^4 (1+x) \log (x)+2 (-5+x) (-3+x)^3 x \left (-e^x+x+x^2-\log (5)+2 x \log (x)+\log ^2(x)\right ) \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )\right )}{x \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )} \, dx\\ &=\int \left (\frac {2 e^{-2 x} (3-x)^4 \left (-x^2+x^3-3 x \left (1+\frac {\log (5)}{3}\right )-2 \log (x)-2 x \log (x)+2 x^2 \log (x)+x \log ^2(x)\right ) \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )}{x \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )}-2 e^{-2 x} (-3+x)^3 \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right ) \left (3-x-5 \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )+x \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )\right )\right ) \, dx\\ &=2 \int \frac {e^{-2 x} (3-x)^4 \left (-x^2+x^3-3 x \left (1+\frac {\log (5)}{3}\right )-2 \log (x)-2 x \log (x)+2 x^2 \log (x)+x \log ^2(x)\right ) \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )}{x \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )} \, dx-2 \int e^{-2 x} (-3+x)^3 \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right ) \left (3-x-5 \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )+x \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )\right ) \, dx\\ &=-\left (2 \int e^{-2 x} (3-x)^3 \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right ) \left (-3+x-(-5+x) \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )\right ) \, dx\right )+2 \int \left (\frac {108 e^{-2 x} \left (x^2-x^3+3 x \left (1+\frac {\log (5)}{3}\right )+2 \log (x)+2 x \log (x)-2 x^2 \log (x)-x \log ^2(x)\right ) \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )}{e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)}+\frac {12 e^{-2 x} x^2 \left (x^2-x^3+3 x \left (1+\frac {\log (5)}{3}\right )+2 \log (x)+2 x \log (x)-2 x^2 \log (x)-x \log ^2(x)\right ) \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )}{e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)}+\frac {81 e^{-2 x} \left (-x^2+x^3-3 x \left (1+\frac {\log (5)}{3}\right )-2 \log (x)-2 x \log (x)+2 x^2 \log (x)+x \log ^2(x)\right ) \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )}{x \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )}+\frac {54 e^{-2 x} x \left (-x^2+x^3-3 x \left (1+\frac {\log (5)}{3}\right )-2 \log (x)-2 x \log (x)+2 x^2 \log (x)+x \log ^2(x)\right ) \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )}{e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)}+\frac {e^{-2 x} x^3 \left (-x^2+x^3-3 x \left (1+\frac {\log (5)}{3}\right )-2 \log (x)-2 x \log (x)+2 x^2 \log (x)+x \log ^2(x)\right ) \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )}{e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)}\right ) \, dx\\ &=2 \int \frac {e^{-2 x} x^3 \left (-x^2+x^3-3 x \left (1+\frac {\log (5)}{3}\right )-2 \log (x)-2 x \log (x)+2 x^2 \log (x)+x \log ^2(x)\right ) \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )}{e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)} \, dx-2 \int \left (-e^{-2 x} (-3+x)^4 \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )+e^{-2 x} (-5+x) (-3+x)^3 \log ^2\left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )\right ) \, dx+24 \int \frac {e^{-2 x} x^2 \left (x^2-x^3+3 x \left (1+\frac {\log (5)}{3}\right )+2 \log (x)+2 x \log (x)-2 x^2 \log (x)-x \log ^2(x)\right ) \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )}{e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)} \, dx+108 \int \frac {e^{-2 x} x \left (-x^2+x^3-3 x \left (1+\frac {\log (5)}{3}\right )-2 \log (x)-2 x \log (x)+2 x^2 \log (x)+x \log ^2(x)\right ) \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )}{e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)} \, dx+162 \int \frac {e^{-2 x} \left (-x^2+x^3-3 x \left (1+\frac {\log (5)}{3}\right )-2 \log (x)-2 x \log (x)+2 x^2 \log (x)+x \log ^2(x)\right ) \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )}{x \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )} \, dx+216 \int \frac {e^{-2 x} \left (x^2-x^3+3 x \left (1+\frac {\log (5)}{3}\right )+2 \log (x)+2 x \log (x)-2 x^2 \log (x)-x \log ^2(x)\right ) \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )}{e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.37, size = 39, normalized size = 1.18 \begin {gather*} e^{-2 x} (-3+x)^4 \log ^2\left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[((486*x - 324*x^2 - 108*x^3 + 144*x^4 - 42*x^5 + 4*x^6 + E^x*(-162*x + 216*x^2 - 108*x^3 + 24*x^4 -
2*x^5) + (324 - 108*x - 216*x^2 + 168*x^3 - 44*x^4 + 4*x^5)*Log[x])*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] -
Log[x]^2] + (-270*x^2 + 54*x^3 + 180*x^4 - 116*x^5 + 26*x^6 - 2*x^7 + E^x*(270*x - 324*x^2 + 144*x^3 - 28*x^4
+ 2*x^5) + (270*x - 324*x^2 + 144*x^3 - 28*x^4 + 2*x^5)*Log[5] + (-540*x^2 + 648*x^3 - 288*x^4 + 56*x^5 - 4*x^
6)*Log[x] + (-270*x + 324*x^2 - 144*x^3 + 28*x^4 - 2*x^5)*Log[x]^2)*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] -
Log[x]^2]^2)/(-(E^(3*x)*x) + E^(2*x)*(x^2 + x^3 - x*Log[5]) + 2*E^(2*x)*x^2*Log[x] + E^(2*x)*x*Log[x]^2),x]
[Out]
((-3 + x)^4*Log[E^x - x - x^2 + Log[5] - 2*x*Log[x] - Log[x]^2]^2)/E^(2*x)
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fricas [A] time = 0.92, size = 50, normalized size = 1.52 \begin {gather*} {\left (x^{4} - 12 \, x^{3} + 54 \, x^{2} - 108 \, x + 81\right )} e^{\left (-2 \, x\right )} \log \left (-x^{2} - 2 \, x \log \relax (x) - \log \relax (x)^{2} - x + e^{x} + \log \relax (5)\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((-2*x^5+28*x^4-144*x^3+324*x^2-270*x)*log(x)^2+(-4*x^6+56*x^5-288*x^4+648*x^3-540*x^2)*log(x)+(2*x
^5-28*x^4+144*x^3-324*x^2+270*x)*exp(x)+(2*x^5-28*x^4+144*x^3-324*x^2+270*x)*log(5)-2*x^7+26*x^6-116*x^5+180*x
^4+54*x^3-270*x^2)*log(-log(x)^2-2*x*log(x)+exp(x)+log(5)-x^2-x)^2+((4*x^5-44*x^4+168*x^3-216*x^2-108*x+324)*l
og(x)+(-2*x^5+24*x^4-108*x^3+216*x^2-162*x)*exp(x)+4*x^6-42*x^5+144*x^4-108*x^3-324*x^2+486*x)*log(-log(x)^2-2
*x*log(x)+exp(x)+log(5)-x^2-x))/(x*exp(x)^2*log(x)^2+2*x^2*exp(x)^2*log(x)-x*exp(x)^3+(-x*log(5)+x^3+x^2)*exp(
x)^2),x, algorithm="fricas")
[Out]
(x^4 - 12*x^3 + 54*x^2 - 108*x + 81)*e^(-2*x)*log(-x^2 - 2*x*log(x) - log(x)^2 - x + e^x + log(5))^2
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giac [B] time = 0.34, size = 160, normalized size = 4.85 \begin {gather*} {\left (x^{4} \log \left (-x^{2} - 2 \, x \log \relax (x) - \log \relax (x)^{2} - x + e^{x} + \log \relax (5)\right )^{2} - 12 \, x^{3} \log \left (-x^{2} - 2 \, x \log \relax (x) - \log \relax (x)^{2} - x + e^{x} + \log \relax (5)\right )^{2} + 54 \, x^{2} \log \left (-x^{2} - 2 \, x \log \relax (x) - \log \relax (x)^{2} - x + e^{x} + \log \relax (5)\right )^{2} - 108 \, x \log \left (-x^{2} - 2 \, x \log \relax (x) - \log \relax (x)^{2} - x + e^{x} + \log \relax (5)\right )^{2} + 81 \, \log \left (-x^{2} - 2 \, x \log \relax (x) - \log \relax (x)^{2} - x + e^{x} + \log \relax (5)\right )^{2}\right )} e^{\left (-2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((-2*x^5+28*x^4-144*x^3+324*x^2-270*x)*log(x)^2+(-4*x^6+56*x^5-288*x^4+648*x^3-540*x^2)*log(x)+(2*x
^5-28*x^4+144*x^3-324*x^2+270*x)*exp(x)+(2*x^5-28*x^4+144*x^3-324*x^2+270*x)*log(5)-2*x^7+26*x^6-116*x^5+180*x
^4+54*x^3-270*x^2)*log(-log(x)^2-2*x*log(x)+exp(x)+log(5)-x^2-x)^2+((4*x^5-44*x^4+168*x^3-216*x^2-108*x+324)*l
og(x)+(-2*x^5+24*x^4-108*x^3+216*x^2-162*x)*exp(x)+4*x^6-42*x^5+144*x^4-108*x^3-324*x^2+486*x)*log(-log(x)^2-2
*x*log(x)+exp(x)+log(5)-x^2-x))/(x*exp(x)^2*log(x)^2+2*x^2*exp(x)^2*log(x)-x*exp(x)^3+(-x*log(5)+x^3+x^2)*exp(
x)^2),x, algorithm="giac")
[Out]
(x^4*log(-x^2 - 2*x*log(x) - log(x)^2 - x + e^x + log(5))^2 - 12*x^3*log(-x^2 - 2*x*log(x) - log(x)^2 - x + e^
x + log(5))^2 + 54*x^2*log(-x^2 - 2*x*log(x) - log(x)^2 - x + e^x + log(5))^2 - 108*x*log(-x^2 - 2*x*log(x) -
log(x)^2 - x + e^x + log(5))^2 + 81*log(-x^2 - 2*x*log(x) - log(x)^2 - x + e^x + log(5))^2)*e^(-2*x)
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maple [A] time = 0.10, size = 51, normalized size = 1.55
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\(\left (x^{4}-12 x^{3}+54 x^{2}-108 x +81\right ) {\mathrm e}^{-2 x} \ln \left (-\ln \relax (x )^{2}-2 x \ln \relax (x )+{\mathrm e}^{x}+\ln \relax (5)-x^{2}-x \right )^{2}\) |
\(51\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int((((-2*x^5+28*x^4-144*x^3+324*x^2-270*x)*ln(x)^2+(-4*x^6+56*x^5-288*x^4+648*x^3-540*x^2)*ln(x)+(2*x^5-28*x^
4+144*x^3-324*x^2+270*x)*exp(x)+(2*x^5-28*x^4+144*x^3-324*x^2+270*x)*ln(5)-2*x^7+26*x^6-116*x^5+180*x^4+54*x^3
-270*x^2)*ln(-ln(x)^2-2*x*ln(x)+exp(x)+ln(5)-x^2-x)^2+((4*x^5-44*x^4+168*x^3-216*x^2-108*x+324)*ln(x)+(-2*x^5+
24*x^4-108*x^3+216*x^2-162*x)*exp(x)+4*x^6-42*x^5+144*x^4-108*x^3-324*x^2+486*x)*ln(-ln(x)^2-2*x*ln(x)+exp(x)+
ln(5)-x^2-x))/(x*exp(x)^2*ln(x)^2+2*x^2*exp(x)^2*ln(x)-x*exp(x)^3+(-x*ln(5)+x^3+x^2)*exp(x)^2),x,method=_RETUR
NVERBOSE)
[Out]
(x^4-12*x^3+54*x^2-108*x+81)*exp(-2*x)*ln(-ln(x)^2-2*x*ln(x)+exp(x)+ln(5)-x^2-x)^2
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maxima [A] time = 0.60, size = 50, normalized size = 1.52 \begin {gather*} {\left (x^{4} - 12 \, x^{3} + 54 \, x^{2} - 108 \, x + 81\right )} e^{\left (-2 \, x\right )} \log \left (-x^{2} - 2 \, x \log \relax (x) - \log \relax (x)^{2} - x + e^{x} + \log \relax (5)\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((-2*x^5+28*x^4-144*x^3+324*x^2-270*x)*log(x)^2+(-4*x^6+56*x^5-288*x^4+648*x^3-540*x^2)*log(x)+(2*x
^5-28*x^4+144*x^3-324*x^2+270*x)*exp(x)+(2*x^5-28*x^4+144*x^3-324*x^2+270*x)*log(5)-2*x^7+26*x^6-116*x^5+180*x
^4+54*x^3-270*x^2)*log(-log(x)^2-2*x*log(x)+exp(x)+log(5)-x^2-x)^2+((4*x^5-44*x^4+168*x^3-216*x^2-108*x+324)*l
og(x)+(-2*x^5+24*x^4-108*x^3+216*x^2-162*x)*exp(x)+4*x^6-42*x^5+144*x^4-108*x^3-324*x^2+486*x)*log(-log(x)^2-2
*x*log(x)+exp(x)+log(5)-x^2-x))/(x*exp(x)^2*log(x)^2+2*x^2*exp(x)^2*log(x)-x*exp(x)^3+(-x*log(5)+x^3+x^2)*exp(
x)^2),x, algorithm="maxima")
[Out]
(x^4 - 12*x^3 + 54*x^2 - 108*x + 81)*e^(-2*x)*log(-x^2 - 2*x*log(x) - log(x)^2 - x + e^x + log(5))^2
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\ln \left (\ln \relax (5)-x+{\mathrm {e}}^x-{\ln \relax (x)}^2-2\,x\,\ln \relax (x)-x^2\right )}^2\,\left ({\mathrm {e}}^x\,\left (2\,x^5-28\,x^4+144\,x^3-324\,x^2+270\,x\right )-{\ln \relax (x)}^2\,\left (2\,x^5-28\,x^4+144\,x^3-324\,x^2+270\,x\right )-\ln \relax (x)\,\left (4\,x^6-56\,x^5+288\,x^4-648\,x^3+540\,x^2\right )-270\,x^2+54\,x^3+180\,x^4-116\,x^5+26\,x^6-2\,x^7+\ln \relax (5)\,\left (2\,x^5-28\,x^4+144\,x^3-324\,x^2+270\,x\right )\right )-\ln \left (\ln \relax (5)-x+{\mathrm {e}}^x-{\ln \relax (x)}^2-2\,x\,\ln \relax (x)-x^2\right )\,\left ({\mathrm {e}}^x\,\left (2\,x^5-24\,x^4+108\,x^3-216\,x^2+162\,x\right )-486\,x+\ln \relax (x)\,\left (-4\,x^5+44\,x^4-168\,x^3+216\,x^2+108\,x-324\right )+324\,x^2+108\,x^3-144\,x^4+42\,x^5-4\,x^6\right )}{{\mathrm {e}}^{2\,x}\,\left (x^3+x^2-\ln \relax (5)\,x\right )-x\,{\mathrm {e}}^{3\,x}+x\,{\mathrm {e}}^{2\,x}\,{\ln \relax (x)}^2+2\,x^2\,{\mathrm {e}}^{2\,x}\,\ln \relax (x)} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((log(log(5) - x + exp(x) - log(x)^2 - 2*x*log(x) - x^2)^2*(exp(x)*(270*x - 324*x^2 + 144*x^3 - 28*x^4 + 2*
x^5) - log(x)^2*(270*x - 324*x^2 + 144*x^3 - 28*x^4 + 2*x^5) - log(x)*(540*x^2 - 648*x^3 + 288*x^4 - 56*x^5 +
4*x^6) - 270*x^2 + 54*x^3 + 180*x^4 - 116*x^5 + 26*x^6 - 2*x^7 + log(5)*(270*x - 324*x^2 + 144*x^3 - 28*x^4 +
2*x^5)) - log(log(5) - x + exp(x) - log(x)^2 - 2*x*log(x) - x^2)*(exp(x)*(162*x - 216*x^2 + 108*x^3 - 24*x^4 +
2*x^5) - 486*x + log(x)*(108*x + 216*x^2 - 168*x^3 + 44*x^4 - 4*x^5 - 324) + 324*x^2 + 108*x^3 - 144*x^4 + 42
*x^5 - 4*x^6))/(exp(2*x)*(x^2 - x*log(5) + x^3) - x*exp(3*x) + x*exp(2*x)*log(x)^2 + 2*x^2*exp(2*x)*log(x)),x)
[Out]
int((log(log(5) - x + exp(x) - log(x)^2 - 2*x*log(x) - x^2)^2*(exp(x)*(270*x - 324*x^2 + 144*x^3 - 28*x^4 + 2*
x^5) - log(x)^2*(270*x - 324*x^2 + 144*x^3 - 28*x^4 + 2*x^5) - log(x)*(540*x^2 - 648*x^3 + 288*x^4 - 56*x^5 +
4*x^6) - 270*x^2 + 54*x^3 + 180*x^4 - 116*x^5 + 26*x^6 - 2*x^7 + log(5)*(270*x - 324*x^2 + 144*x^3 - 28*x^4 +
2*x^5)) - log(log(5) - x + exp(x) - log(x)^2 - 2*x*log(x) - x^2)*(exp(x)*(162*x - 216*x^2 + 108*x^3 - 24*x^4 +
2*x^5) - 486*x + log(x)*(108*x + 216*x^2 - 168*x^3 + 44*x^4 - 4*x^5 - 324) + 324*x^2 + 108*x^3 - 144*x^4 + 42
*x^5 - 4*x^6))/(exp(2*x)*(x^2 - x*log(5) + x^3) - x*exp(3*x) + x*exp(2*x)*log(x)^2 + 2*x^2*exp(2*x)*log(x)), x
)
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sympy [A] time = 3.66, size = 49, normalized size = 1.48 \begin {gather*} \left (x^{4} - 12 x^{3} + 54 x^{2} - 108 x + 81\right ) e^{- 2 x} \log {\left (- x^{2} - 2 x \log {\relax (x )} - x + e^{x} - \log {\relax (x )}^{2} + \log {\relax (5 )} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((-2*x**5+28*x**4-144*x**3+324*x**2-270*x)*ln(x)**2+(-4*x**6+56*x**5-288*x**4+648*x**3-540*x**2)*ln
(x)+(2*x**5-28*x**4+144*x**3-324*x**2+270*x)*exp(x)+(2*x**5-28*x**4+144*x**3-324*x**2+270*x)*ln(5)-2*x**7+26*x
**6-116*x**5+180*x**4+54*x**3-270*x**2)*ln(-ln(x)**2-2*x*ln(x)+exp(x)+ln(5)-x**2-x)**2+((4*x**5-44*x**4+168*x*
*3-216*x**2-108*x+324)*ln(x)+(-2*x**5+24*x**4-108*x**3+216*x**2-162*x)*exp(x)+4*x**6-42*x**5+144*x**4-108*x**3
-324*x**2+486*x)*ln(-ln(x)**2-2*x*ln(x)+exp(x)+ln(5)-x**2-x))/(x*exp(x)**2*ln(x)**2+2*x**2*exp(x)**2*ln(x)-x*e
xp(x)**3+(-x*ln(5)+x**3+x**2)*exp(x)**2),x)
[Out]
(x**4 - 12*x**3 + 54*x**2 - 108*x + 81)*exp(-2*x)*log(-x**2 - 2*x*log(x) - x + exp(x) - log(x)**2 + log(5))**2
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