3.71.8 \(\int \frac {3+e^{25}-x+e^{1+x} (9+e^{50} (1-x)-15 x+7 x^2-x^3+e^{25} (6-8 x+2 x^2))+(-3-e^{25}+2 x) \log (x)+(9 x+e^{50} x-6 x^2+x^3+e^{25} (6 x-2 x^2)+e^{1+x} (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x))+(3+e^{25}-x) \log (x)) \log (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} (-3-e^{25}+x)+\log (x)}) \log (\log (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} (-3-e^{25}+x)+\log (x)}))}{(9 x+e^{50} x-6 x^2+x^3+e^{25} (6 x-2 x^2)+e^{1+x} (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x))+(3+e^{25}-x) \log (x)) \log (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} (-3-e^{25}+x)+\log (x)}) \log ^2(\log (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} (-3-e^{25}+x)+\log (x)}))} \, dx\)

Optimal. Leaf size=32 \[ \frac {x}{\log \left (\log \left (\frac {x}{-e^{1+x}+x+\frac {\log (x)}{3+e^{25}-x}}\right )\right )} \]

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Rubi [F]  time = 58.31, 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 {3+e^{25}-x+e^{1+x} \left (9+e^{50} (1-x)-15 x+7 x^2-x^3+e^{25} \left (6-8 x+2 x^2\right )\right )+\left (-3-e^{25}+2 x\right ) \log (x)+\left (9 x+e^{50} x-6 x^2+x^3+e^{25} \left (6 x-2 x^2\right )+e^{1+x} \left (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x)\right )+\left (3+e^{25}-x\right ) \log (x)\right ) \log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right ) \log \left (\log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right )\right )}{\left (9 x+e^{50} x-6 x^2+x^3+e^{25} \left (6 x-2 x^2\right )+e^{1+x} \left (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x)\right )+\left (3+e^{25}-x\right ) \log (x)\right ) \log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right ) \log ^2\left (\log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(3 + E^25 - x + E^(1 + x)*(9 + E^50*(1 - x) - 15*x + 7*x^2 - x^3 + E^25*(6 - 8*x + 2*x^2)) + (-3 - E^25 +
2*x)*Log[x] + (9*x + E^50*x - 6*x^2 + x^3 + E^25*(6*x - 2*x^2) + E^(1 + x)*(-9 - E^50 + 6*x - x^2 + E^25*(-6 +
2*x)) + (3 + E^25 - x)*Log[x])*Log[(3*x + E^25*x - x^2)/(3*x + E^25*x - x^2 + E^(1 + x)*(-3 - E^25 + x) + Log
[x])]*Log[Log[(3*x + E^25*x - x^2)/(3*x + E^25*x - x^2 + E^(1 + x)*(-3 - E^25 + x) + Log[x])]])/((9*x + E^50*x
- 6*x^2 + x^3 + E^25*(6*x - 2*x^2) + E^(1 + x)*(-9 - E^50 + 6*x - x^2 + E^25*(-6 + 2*x)) + (3 + E^25 - x)*Log
[x])*Log[(3*x + E^25*x - x^2)/(3*x + E^25*x - x^2 + E^(1 + x)*(-3 - E^25 + x) + Log[x])]*Log[Log[(3*x + E^25*x
- x^2)/(3*x + E^25*x - x^2 + E^(1 + x)*(-3 - E^25 + x) + Log[x])]]^2),x]

[Out]

-Defer[Int][1/(Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/
((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]]^2), x] + Defer[Int][x/(Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^
(1 + x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]]^2), x] - (3 +
E^25)^3*Defer[Int][1/(((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])*Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1
+ x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]]^2), x] + (3 + E^2
5)^2*(7 + 2*E^25)*Defer[Int][1/(((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])*Log[(x*(-3 - E^25 + x))/((3 + E^25 -
x)*(E^(1 + x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]]^2), x]
+ (8 + 6*E^25 + E^50)*Defer[Int][1/(((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])*Log[(x*(-3 - E^25 + x))/((3 + E^
25 - x)*(E^(1 + x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]]^2),
x] + (3 + E^25)^4*Defer[Int][1/((3 + E^25 - x)*((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])*Log[(x*(-3 - E^25 +
x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - L
og[x])]]^2), x] + (3 + E^25)^3*(5 + E^25)*Defer[Int][1/((3 + E^25 - x)*((3 + E^25 - x)*(E^(1 + x) - x) - Log[x
])*Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3 + E^25 -
x)*(E^(1 + x) - x) - Log[x])]]^2), x] - (3 + E^25)^3*(7 + 2*E^25)*Defer[Int][1/((3 + E^25 - x)*((3 + E^25 - x
)*(E^(1 + x) - x) - Log[x])*Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]*Log[Log[(x*(-3
- E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]]^2), x] - (3 + E^25)*(8 + 6*E^25 + E^50)*Defer[Int][1/
((3 + E^25 - x)*((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])*Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) -
x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]]^2), x] + (3 + E^25)*(7
+ 2*E^25)*Defer[Int][x/(((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])*Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(
1 + x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]]^2), x] - (3 + E
^25)*Defer[Int][x^2/(((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])*Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 +
x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]]^2), x] + (7 + 2*E^
25)*Defer[Int][x^2/(((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])*Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 +
x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]]^2), x] + (3 + E^25)
*Defer[Int][1/((-3 - E^25 + x)*((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])*Log[(x*(-3 - E^25 + x))/((3 + E^25 -
x)*(E^(1 + x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]]^2), x] +
(3 + E^25)*Defer[Int][Log[x]/(((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])*Log[(x*(-3 - E^25 + x))/((3 + E^25 -
x)*(E^(1 + x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]]^2), x] +
(2 + E^25)*(3 + E^25)*Defer[Int][Log[x]/((3 + E^25 - x)*((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])*Log[(x*(-3
- E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x)
- x) - Log[x])]]^2), x] + Defer[Int][(x*Log[x])/(((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])*Log[(x*(-3 - E^25
+ x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) -
Log[x])]]^2), x] + (3 + E^25)^2*Defer[Int][Log[x]/((-3 - E^25 + x)*((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])*
Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)
*(E^(1 + x) - x) - Log[x])]]^2), x] + (3 + E^25)^2*(5 + E^25)*Defer[Int][1/((-((3 + E^25 - x)*(E^(1 + x) - x))
+ Log[x])*Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3
+ E^25 - x)*(E^(1 + x) - x) - Log[x])]]^2), x] + (3 + E^25)^2*Defer[Int][x/((-((3 + E^25 - x)*(E^(1 + x) - x))
+ Log[x])*Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3
+ E^25 - x)*(E^(1 + x) - x) - Log[x])]]^2), x] + (15 + 8*E^25 + E^50)*Defer[Int][x/((-((3 + E^25 - x)*(E^(1 +
x) - x)) + Log[x])*Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 +
x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]]^2), x] + Defer[Int][x^3/((-((3 + E^25 - x)*(E^(1 + x) - x)) +
Log[x])*Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3 + E
^25 - x)*(E^(1 + x) - x) - Log[x])]]^2), x] + (2 + E^25)*Defer[Int][Log[x]/((-((3 + E^25 - x)*(E^(1 + x) - x))
+ Log[x])*Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]*Log[Log[(x*(-3 - E^25 + x))/((3
+ E^25 - x)*(E^(1 + x) - x) - Log[x])]]^2), x] + Defer[Int][Log[Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1
+ x) - x) - Log[x])]]^(-1), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3+e^{25}-x+e^{1+x} \left (9+e^{50} (1-x)-15 x+7 x^2-x^3+e^{25} \left (6-8 x+2 x^2\right )\right )+\left (-3-e^{25}+2 x\right ) \log (x)+\left (9 x+e^{50} x-6 x^2+x^3+e^{25} \left (6 x-2 x^2\right )+e^{1+x} \left (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x)\right )+\left (3+e^{25}-x\right ) \log (x)\right ) \log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right ) \log \left (\log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right )\right )}{\left (\left (9+e^{50}\right ) x-6 x^2+x^3+e^{25} \left (6 x-2 x^2\right )+e^{1+x} \left (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x)\right )+\left (3+e^{25}-x\right ) \log (x)\right ) \log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right ) \log ^2\left (\log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right )\right )} \, dx\\ &=\int \frac {-3 \left (1+\frac {e^{25}}{3}\right )+e^{1+x} \left (3+e^{25}-x\right )^2 (-1+x)+x+\left (3+e^{25}-2 x\right ) \log (x)-\left (-3-e^{25}+x\right ) \left (\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)\right ) \log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right ) \log \left (\log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right )\right )}{\left (3+e^{25}-x\right ) \left (\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)\right ) \log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right ) \log ^2\left (\log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right )\right )} \, dx\\ &=\int \left (\frac {-3 \left (1+\frac {e^{25}}{3}\right )-8 \left (1+\frac {1}{8} e^{25} \left (6+e^{25}\right )\right ) x+15 \left (1+\frac {1}{15} e^{25} \left (8+e^{25}\right )\right ) x^2-7 \left (1+\frac {2 e^{25}}{7}\right ) x^3+x^4+2 \left (1+\frac {e^{25}}{2}\right ) x \log (x)-x^2 \log (x)}{\left (3+e^{25}-x\right ) \left (3 e^{1+x} \left (1+\frac {e^{25}}{3}\right )-e^{1+x} x-3 \left (1+\frac {e^{25}}{3}\right ) x+x^2-\log (x)\right ) \log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right ) \log ^2\left (\log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right )\right )}+\frac {-1+x+\log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right ) \log \left (\log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right )\right )}{\log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right ) \log ^2\left (\log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right )\right )}\right ) \, dx\\ &=\int \frac {-3 \left (1+\frac {e^{25}}{3}\right )-8 \left (1+\frac {1}{8} e^{25} \left (6+e^{25}\right )\right ) x+15 \left (1+\frac {1}{15} e^{25} \left (8+e^{25}\right )\right ) x^2-7 \left (1+\frac {2 e^{25}}{7}\right ) x^3+x^4+2 \left (1+\frac {e^{25}}{2}\right ) x \log (x)-x^2 \log (x)}{\left (3+e^{25}-x\right ) \left (3 e^{1+x} \left (1+\frac {e^{25}}{3}\right )-e^{1+x} x-3 \left (1+\frac {e^{25}}{3}\right ) x+x^2-\log (x)\right ) \log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right ) \log ^2\left (\log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right )\right )} \, dx+\int \frac {-1+x+\log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right ) \log \left (\log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right )\right )}{\log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right ) \log ^2\left (\log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right )\right )} \, dx\\ &=\int \left (\frac {-1+x}{\log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right ) \log ^2\left (\log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right )\right )}+\frac {1}{\log \left (\log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right )\right )}\right ) \, dx+\int \frac {-3-8 x+e^{50} (-1+x) x+15 x^2-7 x^3+x^4-e^{25} \left (1+6 x-8 x^2+2 x^3\right )+\left (2+e^{25}-x\right ) x \log (x)}{\left (3+e^{25}-x\right ) \left (\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)\right ) \log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right ) \log ^2\left (\log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right )\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.35, size = 41, normalized size = 1.28 \begin {gather*} \frac {x}{\log \left (\log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3 + E^25 - x + E^(1 + x)*(9 + E^50*(1 - x) - 15*x + 7*x^2 - x^3 + E^25*(6 - 8*x + 2*x^2)) + (-3 - E
^25 + 2*x)*Log[x] + (9*x + E^50*x - 6*x^2 + x^3 + E^25*(6*x - 2*x^2) + E^(1 + x)*(-9 - E^50 + 6*x - x^2 + E^25
*(-6 + 2*x)) + (3 + E^25 - x)*Log[x])*Log[(3*x + E^25*x - x^2)/(3*x + E^25*x - x^2 + E^(1 + x)*(-3 - E^25 + x)
+ Log[x])]*Log[Log[(3*x + E^25*x - x^2)/(3*x + E^25*x - x^2 + E^(1 + x)*(-3 - E^25 + x) + Log[x])]])/((9*x +
E^50*x - 6*x^2 + x^3 + E^25*(6*x - 2*x^2) + E^(1 + x)*(-9 - E^50 + 6*x - x^2 + E^25*(-6 + 2*x)) + (3 + E^25 -
x)*Log[x])*Log[(3*x + E^25*x - x^2)/(3*x + E^25*x - x^2 + E^(1 + x)*(-3 - E^25 + x) + Log[x])]*Log[Log[(3*x +
E^25*x - x^2)/(3*x + E^25*x - x^2 + E^(1 + x)*(-3 - E^25 + x) + Log[x])]]^2),x]

[Out]

x/Log[Log[(x*(-3 - E^25 + x))/((3 + E^25 - x)*(E^(1 + x) - x) - Log[x])]]

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fricas [A]  time = 1.05, size = 50, normalized size = 1.56 \begin {gather*} \frac {x}{\log \left (\log \left (\frac {x^{2} - x e^{25} - 3 \, x}{x^{2} - x e^{25} - {\left (x - e^{25} - 3\right )} e^{\left (x + 1\right )} - 3 \, x - \log \relax (x)}\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((exp(25)+3-x)*log(x)+(-exp(25)^2+(2*x-6)*exp(25)-x^2+6*x-9)*exp(x+1)+x*exp(25)^2+(-2*x^2+6*x)*exp(
25)+x^3-6*x^2+9*x)*log((x*exp(25)-x^2+3*x)/(log(x)+(-exp(25)+x-3)*exp(x+1)+x*exp(25)-x^2+3*x))*log(log((x*exp(
25)-x^2+3*x)/(log(x)+(-exp(25)+x-3)*exp(x+1)+x*exp(25)-x^2+3*x)))+(-exp(25)+2*x-3)*log(x)+((-x+1)*exp(25)^2+(2
*x^2-8*x+6)*exp(25)-x^3+7*x^2-15*x+9)*exp(x+1)+exp(25)+3-x)/((exp(25)+3-x)*log(x)+(-exp(25)^2+(2*x-6)*exp(25)-
x^2+6*x-9)*exp(x+1)+x*exp(25)^2+(-2*x^2+6*x)*exp(25)+x^3-6*x^2+9*x)/log((x*exp(25)-x^2+3*x)/(log(x)+(-exp(25)+
x-3)*exp(x+1)+x*exp(25)-x^2+3*x))/log(log((x*exp(25)-x^2+3*x)/(log(x)+(-exp(25)+x-3)*exp(x+1)+x*exp(25)-x^2+3*
x)))^2,x, algorithm="fricas")

[Out]

x/log(log((x^2 - x*e^25 - 3*x)/(x^2 - x*e^25 - (x - e^25 - 3)*e^(x + 1) - 3*x - log(x))))

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((exp(25)+3-x)*log(x)+(-exp(25)^2+(2*x-6)*exp(25)-x^2+6*x-9)*exp(x+1)+x*exp(25)^2+(-2*x^2+6*x)*exp(
25)+x^3-6*x^2+9*x)*log((x*exp(25)-x^2+3*x)/(log(x)+(-exp(25)+x-3)*exp(x+1)+x*exp(25)-x^2+3*x))*log(log((x*exp(
25)-x^2+3*x)/(log(x)+(-exp(25)+x-3)*exp(x+1)+x*exp(25)-x^2+3*x)))+(-exp(25)+2*x-3)*log(x)+((-x+1)*exp(25)^2+(2
*x^2-8*x+6)*exp(25)-x^3+7*x^2-15*x+9)*exp(x+1)+exp(25)+3-x)/((exp(25)+3-x)*log(x)+(-exp(25)^2+(2*x-6)*exp(25)-
x^2+6*x-9)*exp(x+1)+x*exp(25)^2+(-2*x^2+6*x)*exp(25)+x^3-6*x^2+9*x)/log((x*exp(25)-x^2+3*x)/(log(x)+(-exp(25)+
x-3)*exp(x+1)+x*exp(25)-x^2+3*x))/log(log((x*exp(25)-x^2+3*x)/(log(x)+(-exp(25)+x-3)*exp(x+1)+x*exp(25)-x^2+3*
x)))^2,x, algorithm="giac")

[Out]

Timed out

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maple [C]  time = 0.33, size = 453, normalized size = 14.16

method	result	size
risch	\(\frac {x}{\ln \left (\ln \relax (x )+\ln \left ({\mathrm e}^{25}+3-x \right )-\ln \left (\left (x -{\mathrm e}^{x +1}\right ) {\mathrm e}^{25}-x^{2}+\left ({\mathrm e}^{x +1}+3\right ) x -3 \,{\mathrm e}^{x +1}+\ln \relax (x )\right )-\frac {i \pi \,\mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{25}+3-x \right )}{\left (x -{\mathrm e}^{x +1}\right ) {\mathrm e}^{25}-x^{2}+\left ({\mathrm e}^{x +1}+3\right ) x -3 \,{\mathrm e}^{x +1}+\ln \relax (x )}\right ) \left (-\mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{25}+3-x \right )}{\left (x -{\mathrm e}^{x +1}\right ) {\mathrm e}^{25}-x^{2}+\left ({\mathrm e}^{x +1}+3\right ) x -3 \,{\mathrm e}^{x +1}+\ln \relax (x )}\right )+\mathrm {csgn}\left (i \left ({\mathrm e}^{25}+3-x \right )\right )\right ) \left (-\mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{25}+3-x \right )}{\left (x -{\mathrm e}^{x +1}\right ) {\mathrm e}^{25}-x^{2}+\left ({\mathrm e}^{x +1}+3\right ) x -3 \,{\mathrm e}^{x +1}+\ln \relax (x )}\right )+\mathrm {csgn}\left (\frac {i}{\left (x -{\mathrm e}^{x +1}\right ) {\mathrm e}^{25}-x^{2}+\left ({\mathrm e}^{x +1}+3\right ) x -3 \,{\mathrm e}^{x +1}+\ln \relax (x )}\right )\right )}{2}-\frac {i \pi \,\mathrm {csgn}\left (\frac {i x \left ({\mathrm e}^{25}+3-x \right )}{\left (x -{\mathrm e}^{x +1}\right ) {\mathrm e}^{25}-x^{2}+\left ({\mathrm e}^{x +1}+3\right ) x -3 \,{\mathrm e}^{x +1}+\ln \relax (x )}\right ) \left (-\mathrm {csgn}\left (\frac {i x \left ({\mathrm e}^{25}+3-x \right )}{\left (x -{\mathrm e}^{x +1}\right ) {\mathrm e}^{25}-x^{2}+\left ({\mathrm e}^{x +1}+3\right ) x -3 \,{\mathrm e}^{x +1}+\ln \relax (x )}\right )+\mathrm {csgn}\left (i x \right )\right ) \left (-\mathrm {csgn}\left (\frac {i x \left ({\mathrm e}^{25}+3-x \right )}{\left (x -{\mathrm e}^{x +1}\right ) {\mathrm e}^{25}-x^{2}+\left ({\mathrm e}^{x +1}+3\right ) x -3 \,{\mathrm e}^{x +1}+\ln \relax (x )}\right )+\mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{25}+3-x \right )}{\left (x -{\mathrm e}^{x +1}\right ) {\mathrm e}^{25}-x^{2}+\left ({\mathrm e}^{x +1}+3\right ) x -3 \,{\mathrm e}^{x +1}+\ln \relax (x )}\right )\right )}{2}\right )}\)	\(453\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((exp(25)+3-x)*ln(x)+(-exp(25)^2+(2*x-6)*exp(25)-x^2+6*x-9)*exp(x+1)+x*exp(25)^2+(-2*x^2+6*x)*exp(25)+x^3
-6*x^2+9*x)*ln((x*exp(25)-x^2+3*x)/(ln(x)+(-exp(25)+x-3)*exp(x+1)+x*exp(25)-x^2+3*x))*ln(ln((x*exp(25)-x^2+3*x
)/(ln(x)+(-exp(25)+x-3)*exp(x+1)+x*exp(25)-x^2+3*x)))+(-exp(25)+2*x-3)*ln(x)+((1-x)*exp(25)^2+(2*x^2-8*x+6)*ex
p(25)-x^3+7*x^2-15*x+9)*exp(x+1)+exp(25)+3-x)/((exp(25)+3-x)*ln(x)+(-exp(25)^2+(2*x-6)*exp(25)-x^2+6*x-9)*exp(
x+1)+x*exp(25)^2+(-2*x^2+6*x)*exp(25)+x^3-6*x^2+9*x)/ln((x*exp(25)-x^2+3*x)/(ln(x)+(-exp(25)+x-3)*exp(x+1)+x*e
xp(25)-x^2+3*x))/ln(ln((x*exp(25)-x^2+3*x)/(ln(x)+(-exp(25)+x-3)*exp(x+1)+x*exp(25)-x^2+3*x)))^2,x,method=_RET
URNVERBOSE)

[Out]

x/ln(ln(x)+ln(exp(25)+3-x)-ln((x-exp(x+1))*exp(25)-x^2+(exp(x+1)+3)*x-3*exp(x+1)+ln(x))-1/2*I*Pi*csgn(I*(exp(2
5)+3-x)/((x-exp(x+1))*exp(25)-x^2+(exp(x+1)+3)*x-3*exp(x+1)+ln(x)))*(-csgn(I*(exp(25)+3-x)/((x-exp(x+1))*exp(2
5)-x^2+(exp(x+1)+3)*x-3*exp(x+1)+ln(x)))+csgn(I*(exp(25)+3-x)))*(-csgn(I*(exp(25)+3-x)/((x-exp(x+1))*exp(25)-x
^2+(exp(x+1)+3)*x-3*exp(x+1)+ln(x)))+csgn(I/((x-exp(x+1))*exp(25)-x^2+(exp(x+1)+3)*x-3*exp(x+1)+ln(x))))-1/2*I
*Pi*csgn(I*x/((x-exp(x+1))*exp(25)-x^2+(exp(x+1)+3)*x-3*exp(x+1)+ln(x))*(exp(25)+3-x))*(-csgn(I*x/((x-exp(x+1)
)*exp(25)-x^2+(exp(x+1)+3)*x-3*exp(x+1)+ln(x))*(exp(25)+3-x))+csgn(I*x))*(-csgn(I*x/((x-exp(x+1))*exp(25)-x^2+
(exp(x+1)+3)*x-3*exp(x+1)+ln(x))*(exp(25)+3-x))+csgn(I*(exp(25)+3-x)/((x-exp(x+1))*exp(25)-x^2+(exp(x+1)+3)*x-
3*exp(x+1)+ln(x)))))

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maxima [A]  time = 35.28, size = 51, normalized size = 1.59 \begin {gather*} \frac {x}{\log \left (-\log \left (x^{2} - x {\left (e^{25} + 3\right )} - {\left (x e - e^{26} - 3 \, e\right )} e^{x} - \log \relax (x)\right ) + \log \left (x - e^{25} - 3\right ) + \log \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((exp(25)+3-x)*log(x)+(-exp(25)^2+(2*x-6)*exp(25)-x^2+6*x-9)*exp(x+1)+x*exp(25)^2+(-2*x^2+6*x)*exp(
25)+x^3-6*x^2+9*x)*log((x*exp(25)-x^2+3*x)/(log(x)+(-exp(25)+x-3)*exp(x+1)+x*exp(25)-x^2+3*x))*log(log((x*exp(
25)-x^2+3*x)/(log(x)+(-exp(25)+x-3)*exp(x+1)+x*exp(25)-x^2+3*x)))+(-exp(25)+2*x-3)*log(x)+((-x+1)*exp(25)^2+(2
*x^2-8*x+6)*exp(25)-x^3+7*x^2-15*x+9)*exp(x+1)+exp(25)+3-x)/((exp(25)+3-x)*log(x)+(-exp(25)^2+(2*x-6)*exp(25)-
x^2+6*x-9)*exp(x+1)+x*exp(25)^2+(-2*x^2+6*x)*exp(25)+x^3-6*x^2+9*x)/log((x*exp(25)-x^2+3*x)/(log(x)+(-exp(25)+
x-3)*exp(x+1)+x*exp(25)-x^2+3*x))/log(log((x*exp(25)-x^2+3*x)/(log(x)+(-exp(25)+x-3)*exp(x+1)+x*exp(25)-x^2+3*
x)))^2,x, algorithm="maxima")

[Out]

x/log(-log(x^2 - x*(e^25 + 3) - (x*e - e^26 - 3*e)*e^x - log(x)) + log(x - e^25 - 3) + log(x))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} -\int \frac {x-{\mathrm {e}}^{25}+{\mathrm {e}}^{x+1}\,\left (15\,x-{\mathrm {e}}^{25}\,\left (2\,x^2-8\,x+6\right )+{\mathrm {e}}^{50}\,\left (x-1\right )-7\,x^2+x^3-9\right )+\ln \relax (x)\,\left ({\mathrm {e}}^{25}-2\,x+3\right )-\ln \left (\ln \left (\frac {3\,x+x\,{\mathrm {e}}^{25}-x^2}{3\,x+\ln \relax (x)-{\mathrm {e}}^{x+1}\,\left ({\mathrm {e}}^{25}-x+3\right )+x\,{\mathrm {e}}^{25}-x^2}\right )\right )\,\ln \left (\frac {3\,x+x\,{\mathrm {e}}^{25}-x^2}{3\,x+\ln \relax (x)-{\mathrm {e}}^{x+1}\,\left ({\mathrm {e}}^{25}-x+3\right )+x\,{\mathrm {e}}^{25}-x^2}\right )\,\left (9\,x-{\mathrm {e}}^{x+1}\,\left ({\mathrm {e}}^{50}-6\,x+x^2-{\mathrm {e}}^{25}\,\left (2\,x-6\right )+9\right )+{\mathrm {e}}^{25}\,\left (6\,x-2\,x^2\right )+x\,{\mathrm {e}}^{50}-6\,x^2+x^3+\ln \relax (x)\,\left ({\mathrm {e}}^{25}-x+3\right )\right )-3}{{\ln \left (\ln \left (\frac {3\,x+x\,{\mathrm {e}}^{25}-x^2}{3\,x+\ln \relax (x)-{\mathrm {e}}^{x+1}\,\left ({\mathrm {e}}^{25}-x+3\right )+x\,{\mathrm {e}}^{25}-x^2}\right )\right )}^2\,\ln \left (\frac {3\,x+x\,{\mathrm {e}}^{25}-x^2}{3\,x+\ln \relax (x)-{\mathrm {e}}^{x+1}\,\left ({\mathrm {e}}^{25}-x+3\right )+x\,{\mathrm {e}}^{25}-x^2}\right )\,\left (9\,x-{\mathrm {e}}^{x+1}\,\left ({\mathrm {e}}^{50}-6\,x+x^2-{\mathrm {e}}^{25}\,\left (2\,x-6\right )+9\right )+{\mathrm {e}}^{25}\,\left (6\,x-2\,x^2\right )+x\,{\mathrm {e}}^{50}-6\,x^2+x^3+\ln \relax (x)\,\left ({\mathrm {e}}^{25}-x+3\right )\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(x - exp(25) + exp(x + 1)*(15*x - exp(25)*(2*x^2 - 8*x + 6) + exp(50)*(x - 1) - 7*x^2 + x^3 - 9) + log(x)
*(exp(25) - 2*x + 3) - log(log((3*x + x*exp(25) - x^2)/(3*x + log(x) - exp(x + 1)*(exp(25) - x + 3) + x*exp(25
) - x^2)))*log((3*x + x*exp(25) - x^2)/(3*x + log(x) - exp(x + 1)*(exp(25) - x + 3) + x*exp(25) - x^2))*(9*x -
exp(x + 1)*(exp(50) - 6*x + x^2 - exp(25)*(2*x - 6) + 9) + exp(25)*(6*x - 2*x^2) + x*exp(50) - 6*x^2 + x^3 +
log(x)*(exp(25) - x + 3)) - 3)/(log(log((3*x + x*exp(25) - x^2)/(3*x + log(x) - exp(x + 1)*(exp(25) - x + 3) +
x*exp(25) - x^2)))^2*log((3*x + x*exp(25) - x^2)/(3*x + log(x) - exp(x + 1)*(exp(25) - x + 3) + x*exp(25) - x
^2))*(9*x - exp(x + 1)*(exp(50) - 6*x + x^2 - exp(25)*(2*x - 6) + 9) + exp(25)*(6*x - 2*x^2) + x*exp(50) - 6*x
^2 + x^3 + log(x)*(exp(25) - x + 3))),x)

[Out]

-int((x - exp(25) + exp(x + 1)*(15*x - exp(25)*(2*x^2 - 8*x + 6) + exp(50)*(x - 1) - 7*x^2 + x^3 - 9) + log(x)
*(exp(25) - 2*x + 3) - log(log((3*x + x*exp(25) - x^2)/(3*x + log(x) - exp(x + 1)*(exp(25) - x + 3) + x*exp(25
) - x^2)))*log((3*x + x*exp(25) - x^2)/(3*x + log(x) - exp(x + 1)*(exp(25) - x + 3) + x*exp(25) - x^2))*(9*x -
exp(x + 1)*(exp(50) - 6*x + x^2 - exp(25)*(2*x - 6) + 9) + exp(25)*(6*x - 2*x^2) + x*exp(50) - 6*x^2 + x^3 +
log(x)*(exp(25) - x + 3)) - 3)/(log(log((3*x + x*exp(25) - x^2)/(3*x + log(x) - exp(x + 1)*(exp(25) - x + 3) +
x*exp(25) - x^2)))^2*log((3*x + x*exp(25) - x^2)/(3*x + log(x) - exp(x + 1)*(exp(25) - x + 3) + x*exp(25) - x
^2))*(9*x - exp(x + 1)*(exp(50) - 6*x + x^2 - exp(25)*(2*x - 6) + 9) + exp(25)*(6*x - 2*x^2) + x*exp(50) - 6*x
^2 + x^3 + log(x)*(exp(25) - x + 3))), x)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((exp(25)+3-x)*ln(x)+(-exp(25)**2+(2*x-6)*exp(25)-x**2+6*x-9)*exp(x+1)+x*exp(25)**2+(-2*x**2+6*x)*e
xp(25)+x**3-6*x**2+9*x)*ln((x*exp(25)-x**2+3*x)/(ln(x)+(-exp(25)+x-3)*exp(x+1)+x*exp(25)-x**2+3*x))*ln(ln((x*e
xp(25)-x**2+3*x)/(ln(x)+(-exp(25)+x-3)*exp(x+1)+x*exp(25)-x**2+3*x)))+(-exp(25)+2*x-3)*ln(x)+((-x+1)*exp(25)**
2+(2*x**2-8*x+6)*exp(25)-x**3+7*x**2-15*x+9)*exp(x+1)+exp(25)+3-x)/((exp(25)+3-x)*ln(x)+(-exp(25)**2+(2*x-6)*e
xp(25)-x**2+6*x-9)*exp(x+1)+x*exp(25)**2+(-2*x**2+6*x)*exp(25)+x**3-6*x**2+9*x)/ln((x*exp(25)-x**2+3*x)/(ln(x)
+(-exp(25)+x-3)*exp(x+1)+x*exp(25)-x**2+3*x))/ln(ln((x*exp(25)-x**2+3*x)/(ln(x)+(-exp(25)+x-3)*exp(x+1)+x*exp(
25)-x**2+3*x)))**2,x)

[Out]

Timed out

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