3.20.30 \(\int \frac {9 x^2-6 x^3+x^4+e^{\frac {e^{\frac {-3 e^x+e^3 (9-3 x)-9 x+3 x^2}{-3+x}}}{x}+\frac {-3 e^x+e^3 (9-3 x)-9 x+3 x^2}{-3+x}} (-27+99 x-57 x^2+9 x^3+e^x (36 x-9 x^2))}{9 x^3-6 x^4+x^5+e^{\frac {e^{\frac {-3 e^x+e^3 (9-3 x)-9 x+3 x^2}{-3+x}}}{x}} (27 x^2-18 x^3+3 x^4)} \, dx\)

Optimal. Leaf size=33 \[ \log \left (3 e^{\frac {e^{3 \left (-e^3+\frac {e^x}{3-x}+x\right )}}{x}}+x\right ) \]

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Rubi [F]  time = 95.64, 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 {9 x^2-6 x^3+x^4+\exp \left (\frac {\exp \left (\frac {-3 e^x+e^3 (9-3 x)-9 x+3 x^2}{-3+x}\right )}{x}+\frac {-3 e^x+e^3 (9-3 x)-9 x+3 x^2}{-3+x}\right ) \left (-27+99 x-57 x^2+9 x^3+e^x \left (36 x-9 x^2\right )\right )}{9 x^3-6 x^4+x^5+\exp \left (\frac {\exp \left (\frac {-3 e^x+e^3 (9-3 x)-9 x+3 x^2}{-3+x}\right )}{x}\right ) \left (27 x^2-18 x^3+3 x^4\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(9*x^2 - 6*x^3 + x^4 + E^(E^((-3*E^x + E^3*(9 - 3*x) - 9*x + 3*x^2)/(-3 + x))/x + (-3*E^x + E^3*(9 - 3*x)
- 9*x + 3*x^2)/(-3 + x))*(-27 + 99*x - 57*x^2 + 9*x^3 + E^x*(36*x - 9*x^2)))/(9*x^3 - 6*x^4 + x^5 + E^(E^((-3*
E^x + E^3*(9 - 3*x) - 9*x + 3*x^2)/(-3 + x))/x)*(27*x^2 - 18*x^3 + 3*x^4)),x]

[Out]

-Defer[Int][1/(E^(3*(E^3 + E^x/(-3 + x) - x))*x^2), x] + 3*Defer[Int][1/(E^(3*(E^3 + E^x/(-3 + x) - x))*x), x]
+ (4*Defer[Int][E^(-3*E^3 - (3*E^x)/(-3 + x) + 4*x)/x, x])/3 + Defer[Int][(3*E^(E^(-3*E^3 - (3*E^x)/(-3 + x)
+ 3*x)/x) + x)^(-1), x] - 3*Defer[Int][1/(E^(3*(E^3 + E^x/(-3 + x) - x))*(3*E^(E^(-3*E^3 - (3*E^x)/(-3 + x) +
3*x)/x) + x)), x] - (4*Defer[Int][E^(-3*E^3 - (3*E^x)/(-3 + x) + 4*x)/(3*E^(E^(-3*E^3 - (3*E^x)/(-3 + x) + 3*x
)/x) + x), x])/3 + 3*Defer[Int][E^(-3*E^3 - (3*E^x)/(-3 + x) + E^(-3*E^3 - (3*E^x)/(-3 + x) + 3*x)/x + 4*x)/((
-3 + x)^2*(3*E^(E^(-3*E^3 - (3*E^x)/(-3 + x) + 3*x)/x) + x)), x] - 4*Defer[Int][E^(-3*E^3 - (3*E^x)/(-3 + x) +
E^(-3*E^3 - (3*E^x)/(-3 + x) + 3*x)/x + 4*x)/((-3 + x)*(3*E^(E^(-3*E^3 - (3*E^x)/(-3 + x) + 3*x)/x) + x)), x]
+ Defer[Int][1/(E^(3*(E^3 + E^x/(-3 + x) - x))*x*(3*E^(E^(-3*E^3 - (3*E^x)/(-3 + x) + 3*x)/x) + x)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {9 x^2-6 x^3+x^4+\exp \left (-3 e^3-\frac {3 e^x}{-3+x}+\frac {e^{-3 \left (e^3+\frac {e^x}{-3+x}-x\right )}}{x}+3 x\right ) \left (-27+9 \left (11+4 e^x\right ) x-3 \left (19+3 e^x\right ) x^2+9 x^3\right )}{(3-x)^2 x^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx\\ &=\int \left (\frac {9}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )}-\frac {9 \exp \left (-3 e^3-\frac {3 e^x}{-3+x}+\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}+4 x\right ) (-4+x)}{(-3+x)^2 x \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )}-\frac {6 x}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )}+\frac {x^2}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )}+\frac {3 \exp \left (-3 e^3-\frac {3 e^x}{-3+x}+\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}+3 x\right ) (-1+3 x)}{x^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )}\right ) \, dx\\ &=3 \int \frac {\exp \left (-3 e^3-\frac {3 e^x}{-3+x}+\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}+3 x\right ) (-1+3 x)}{x^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx-6 \int \frac {x}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx+9 \int \frac {1}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx-9 \int \frac {\exp \left (-3 e^3-\frac {3 e^x}{-3+x}+\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}+4 x\right ) (-4+x)}{(-3+x)^2 x \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx+\int \frac {x^2}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx\\ &=3 \int \frac {e^{-3 \left (e^3+\frac {e^x}{-3+x}-x\right )} (-1+3 x)}{x^2 \left (3+e^{-\frac {e^{-3 \left (e^3+\frac {e^x}{-3+x}-x\right )}}{x}} x\right )} \, dx-6 \int \left (\frac {3}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )}+\frac {1}{(-3+x) \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )}\right ) \, dx+9 \int \frac {1}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx-9 \int \left (-\frac {\exp \left (-3 e^3-\frac {3 e^x}{-3+x}+\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}+4 x\right )}{3 (-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )}+\frac {4 \exp \left (-3 e^3-\frac {3 e^x}{-3+x}+\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}+4 x\right )}{9 (-3+x) \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )}-\frac {4 \exp \left (-3 e^3-\frac {3 e^x}{-3+x}+\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}+4 x\right )}{9 x \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )}\right ) \, dx+\int \left (\frac {1}{3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x}+\frac {9}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )}+\frac {6}{(-3+x) \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )}\right ) \, dx\\ &=3 \int \frac {\exp \left (-3 e^3-\frac {3 e^x}{-3+x}+\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}+4 x\right )}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx+3 \int \left (\frac {e^{-3 \left (e^3+\frac {e^x}{-3+x}-x\right )} (-1+3 x)}{3 x^2}-\frac {e^{-3 \left (e^3+\frac {e^x}{-3+x}-x\right )} (-1+3 x)}{3 x \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )}\right ) \, dx-4 \int \frac {\exp \left (-3 e^3-\frac {3 e^x}{-3+x}+\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}+4 x\right )}{(-3+x) \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx+4 \int \frac {\exp \left (-3 e^3-\frac {3 e^x}{-3+x}+\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}+4 x\right )}{x \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx+2 \left (9 \int \frac {1}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx\right )-18 \int \frac {1}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx+\int \frac {1}{3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x} \, dx\\ &=3 \int \frac {\exp \left (-3 e^3-\frac {3 e^x}{-3+x}+\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}+4 x\right )}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx-4 \int \frac {\exp \left (-3 e^3-\frac {3 e^x}{-3+x}+\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}+4 x\right )}{(-3+x) \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx+4 \int \frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+4 x}}{x \left (3+e^{-\frac {e^{-3 \left (e^3+\frac {e^x}{-3+x}-x\right )}}{x}} x\right )} \, dx+2 \left (9 \int \frac {1}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx\right )-18 \int \frac {1}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx+\int \frac {1}{3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x} \, dx+\int \frac {e^{-3 \left (e^3+\frac {e^x}{-3+x}-x\right )} (-1+3 x)}{x^2} \, dx-\int \frac {e^{-3 \left (e^3+\frac {e^x}{-3+x}-x\right )} (-1+3 x)}{x \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx\\ &=3 \int \frac {\exp \left (-3 e^3-\frac {3 e^x}{-3+x}+\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}+4 x\right )}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx-4 \int \frac {\exp \left (-3 e^3-\frac {3 e^x}{-3+x}+\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}+4 x\right )}{(-3+x) \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx+4 \int \left (\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+4 x}}{3 x}-\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+4 x}}{3 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )}\right ) \, dx+2 \left (9 \int \frac {1}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx\right )-18 \int \frac {1}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx+\int \left (-\frac {e^{-3 \left (e^3+\frac {e^x}{-3+x}-x\right )}}{x^2}+\frac {3 e^{-3 \left (e^3+\frac {e^x}{-3+x}-x\right )}}{x}\right ) \, dx+\int \frac {1}{3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x} \, dx-\int \left (\frac {3 e^{-3 \left (e^3+\frac {e^x}{-3+x}-x\right )}}{3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x}-\frac {e^{-3 \left (e^3+\frac {e^x}{-3+x}-x\right )}}{x \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )}\right ) \, dx\\ &=\frac {4}{3} \int \frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+4 x}}{x} \, dx-\frac {4}{3} \int \frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+4 x}}{3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x} \, dx+3 \int \frac {e^{-3 \left (e^3+\frac {e^x}{-3+x}-x\right )}}{x} \, dx-3 \int \frac {e^{-3 \left (e^3+\frac {e^x}{-3+x}-x\right )}}{3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x} \, dx+3 \int \frac {\exp \left (-3 e^3-\frac {3 e^x}{-3+x}+\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}+4 x\right )}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx-4 \int \frac {\exp \left (-3 e^3-\frac {3 e^x}{-3+x}+\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}+4 x\right )}{(-3+x) \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx+2 \left (9 \int \frac {1}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx\right )-18 \int \frac {1}{(-3+x)^2 \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx-\int \frac {e^{-3 \left (e^3+\frac {e^x}{-3+x}-x\right )}}{x^2} \, dx+\int \frac {1}{3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x} \, dx+\int \frac {e^{-3 \left (e^3+\frac {e^x}{-3+x}-x\right )}}{x \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.31, size = 32, normalized size = 0.97 \begin {gather*} \log \left (3 e^{\frac {e^{-3 e^3-\frac {3 e^x}{-3+x}+3 x}}{x}}+x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(9*x^2 - 6*x^3 + x^4 + E^(E^((-3*E^x + E^3*(9 - 3*x) - 9*x + 3*x^2)/(-3 + x))/x + (-3*E^x + E^3*(9 -
3*x) - 9*x + 3*x^2)/(-3 + x))*(-27 + 99*x - 57*x^2 + 9*x^3 + E^x*(36*x - 9*x^2)))/(9*x^3 - 6*x^4 + x^5 + E^(E
^((-3*E^x + E^3*(9 - 3*x) - 9*x + 3*x^2)/(-3 + x))/x)*(27*x^2 - 18*x^3 + 3*x^4)),x]

[Out]

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

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fricas [A]  time = 0.89, size = 36, normalized size = 1.09 \begin {gather*} \log \left (x + 3 \, e^{\left (\frac {e^{\left (\frac {3 \, {\left (x^{2} - {\left (x - 3\right )} e^{3} - 3 \, x - e^{x}\right )}}{x - 3}\right )}}{x}\right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-9*x^2+36*x)*exp(x)+9*x^3-57*x^2+99*x-27)*exp((-3*exp(x)+(-3*x+9)*exp(3)+3*x^2-9*x)/(x-3))*exp(ex
p((-3*exp(x)+(-3*x+9)*exp(3)+3*x^2-9*x)/(x-3))/x)+x^4-6*x^3+9*x^2)/((3*x^4-18*x^3+27*x^2)*exp(exp((-3*exp(x)+(
-3*x+9)*exp(3)+3*x^2-9*x)/(x-3))/x)+x^5-6*x^4+9*x^3),x, algorithm="fricas")

[Out]

log(x + 3*e^(e^(3*(x^2 - (x - 3)*e^3 - 3*x - e^x)/(x - 3))/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((((-9*x^2+36*x)*exp(x)+9*x^3-57*x^2+99*x-27)*exp((-3*exp(x)+(-3*x+9)*exp(3)+3*x^2-9*x)/(x-3))*exp(ex
p((-3*exp(x)+(-3*x+9)*exp(3)+3*x^2-9*x)/(x-3))/x)+x^4-6*x^3+9*x^2)/((3*x^4-18*x^3+27*x^2)*exp(exp((-3*exp(x)+(
-3*x+9)*exp(3)+3*x^2-9*x)/(x-3))/x)+x^5-6*x^4+9*x^3),x, algorithm="giac")

[Out]

Timed out

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maple [A]  time = 0.18, size = 38, normalized size = 1.15

method	result	size
risch	\(\ln \left (\frac {x}{3}+{\mathrm e}^{\frac {{\mathrm e}^{-\frac {3 \left (x \,{\mathrm e}^{3}-x^{2}+{\mathrm e}^{x}-3 \,{\mathrm e}^{3}+3 x \right )}{x -3}}}{x}}\right )\)	\(38\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-9*x^2+36*x)*exp(x)+9*x^3-57*x^2+99*x-27)*exp((-3*exp(x)+(-3*x+9)*exp(3)+3*x^2-9*x)/(x-3))*exp(exp((-3*
exp(x)+(-3*x+9)*exp(3)+3*x^2-9*x)/(x-3))/x)+x^4-6*x^3+9*x^2)/((3*x^4-18*x^3+27*x^2)*exp(exp((-3*exp(x)+(-3*x+9
)*exp(3)+3*x^2-9*x)/(x-3))/x)+x^5-6*x^4+9*x^3),x,method=_RETURNVERBOSE)

[Out]

ln(1/3*x+exp(exp(-3*(x*exp(3)-x^2+exp(x)-3*exp(3)+3*x)/(x-3))/x))

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maxima [A]  time = 0.69, size = 28, normalized size = 0.85 \begin {gather*} \log \left (\frac {1}{3} \, x + e^{\left (\frac {e^{\left (3 \, x - \frac {3 \, e^{x}}{x - 3} - 3 \, e^{3}\right )}}{x}\right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-9*x^2+36*x)*exp(x)+9*x^3-57*x^2+99*x-27)*exp((-3*exp(x)+(-3*x+9)*exp(3)+3*x^2-9*x)/(x-3))*exp(ex
p((-3*exp(x)+(-3*x+9)*exp(3)+3*x^2-9*x)/(x-3))/x)+x^4-6*x^3+9*x^2)/((3*x^4-18*x^3+27*x^2)*exp(exp((-3*exp(x)+(
-3*x+9)*exp(3)+3*x^2-9*x)/(x-3))/x)+x^5-6*x^4+9*x^3),x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 1.72, size = 40, normalized size = 1.21 \begin {gather*} \ln \left (x+3\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{-\frac {9\,x-9\,{\mathrm {e}}^3+3\,{\mathrm {e}}^x+3\,x\,{\mathrm {e}}^3-3\,x^2}{x-3}}}{x}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((9*x^2 - 6*x^3 + x^4 + exp(exp(-(9*x + 3*exp(x) - 3*x^2 + exp(3)*(3*x - 9))/(x - 3))/x)*exp(-(9*x + 3*exp(
x) - 3*x^2 + exp(3)*(3*x - 9))/(x - 3))*(99*x + exp(x)*(36*x - 9*x^2) - 57*x^2 + 9*x^3 - 27))/(exp(exp(-(9*x +
3*exp(x) - 3*x^2 + exp(3)*(3*x - 9))/(x - 3))/x)*(27*x^2 - 18*x^3 + 3*x^4) + 9*x^3 - 6*x^4 + x^5),x)

[Out]

log(x + 3*exp(exp(-(9*x - 9*exp(3) + 3*exp(x) + 3*x*exp(3) - 3*x^2)/(x - 3))/x))

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sympy [A]  time = 2.01, size = 34, normalized size = 1.03 \begin {gather*} \log {\left (\frac {x}{3} + e^{\frac {e^{\frac {3 x^{2} - 9 x + \left (9 - 3 x\right ) e^{3} - 3 e^{x}}{x - 3}}}{x}} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-9*x**2+36*x)*exp(x)+9*x**3-57*x**2+99*x-27)*exp((-3*exp(x)+(-3*x+9)*exp(3)+3*x**2-9*x)/(x-3))*ex
p(exp((-3*exp(x)+(-3*x+9)*exp(3)+3*x**2-9*x)/(x-3))/x)+x**4-6*x**3+9*x**2)/((3*x**4-18*x**3+27*x**2)*exp(exp((
-3*exp(x)+(-3*x+9)*exp(3)+3*x**2-9*x)/(x-3))/x)+x**5-6*x**4+9*x**3),x)

[Out]

log(x/3 + exp(exp((3*x**2 - 9*x + (9 - 3*x)*exp(3) - 3*exp(x))/(x - 3))/x))

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