\(\int e^{-17+e^{\frac {6 x+e^{17} (-5+4 x+x^2)}{e^{17}}}+\frac {6 x+e^{17} (-5+4 x+x^2)}{e^{17}}} (6+e^{17} (4+2 x)) \, dx\) [42]

Optimal result

Integrand size = 58, antiderivative size = 18 \[ \int e^{-17+e^{\frac {6 x+e^{17} \left (-5+4 x+x^2\right )}{e^{17}}}+\frac {6 x+e^{17} \left (-5+4 x+x^2\right )}{e^{17}}} \left (6+e^{17} (4+2 x)\right ) \, dx=5+e^{e^{-5+x \left (4+\frac {6}{e^{17}}+x\right )}} \]

[Out]

5+exp(exp((4+x+6/exp(17))*x-5))

Rubi [F]

\[ \int e^{-17+e^{\frac {6 x+e^{17} \left (-5+4 x+x^2\right )}{e^{17}}}+\frac {6 x+e^{17} \left (-5+4 x+x^2\right )}{e^{17}}} \left (6+e^{17} (4+2 x)\right ) \, dx=\int \exp \left (-17+e^{\frac {6 x+e^{17} \left (-5+4 x+x^2\right )}{e^{17}}}+\frac {6 x+e^{17} \left (-5+4 x+x^2\right )}{e^{17}}\right ) \left (6+e^{17} (4+2 x)\right ) \, dx \]

[In]

Int[E^(-17 + E^((6*x + E^17*(-5 + 4*x + x^2))/E^17) + (6*x + E^17*(-5 + 4*x + x^2))/E^17)*(6 + E^17*(4 + 2*x))
,x]

[Out]

2*(3 + 2*E^17)*Defer[Int][E^(-22 + E^(-5 + 4*x + (6*x)/E^17 + x^2) + 4*(1 + 3/(2*E^17))*x + x^2), x] + 2*Defer
[Int][E^(-5 + E^(-5 + 4*x + (6*x)/E^17 + x^2) + 4*(1 + 3/(2*E^17))*x + x^2)*x, x]

Rubi steps \begin{align*} \text {integral}& = \int \exp \left (\frac {-22 e^{17}+e^{12+4 x+\frac {6 x}{e^{17}}+x^2}+6 \left (1+\frac {2 e^{17}}{3}\right ) x+e^{17} x^2}{e^{17}}\right ) \left (2 \left (3+2 e^{17}\right )+2 e^{17} x\right ) \, dx \\ & = \int \exp \left (-22+e^{-5+4 x+\frac {6 x}{e^{17}}+x^2}+4 \left (1+\frac {3}{2 e^{17}}\right ) x+x^2\right ) \left (2 \left (3+2 e^{17}\right )+2 e^{17} x\right ) \, dx \\ & = \int \left (2 \exp \left (-22+e^{-5+4 x+\frac {6 x}{e^{17}}+x^2}+4 \left (1+\frac {3}{2 e^{17}}\right ) x+x^2\right ) \left (3+2 e^{17}\right )+2 \exp \left (-5+e^{-5+4 x+\frac {6 x}{e^{17}}+x^2}+4 \left (1+\frac {3}{2 e^{17}}\right ) x+x^2\right ) x\right ) \, dx \\ & = 2 \int \exp \left (-5+e^{-5+4 x+\frac {6 x}{e^{17}}+x^2}+4 \left (1+\frac {3}{2 e^{17}}\right ) x+x^2\right ) x \, dx+\left (2 \left (3+2 e^{17}\right )\right ) \int \exp \left (-22+e^{-5+4 x+\frac {6 x}{e^{17}}+x^2}+4 \left (1+\frac {3}{2 e^{17}}\right ) x+x^2\right ) \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.68 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int e^{-17+e^{\frac {6 x+e^{17} \left (-5+4 x+x^2\right )}{e^{17}}}+\frac {6 x+e^{17} \left (-5+4 x+x^2\right )}{e^{17}}} \left (6+e^{17} (4+2 x)\right ) \, dx=e^{e^{-5+4 x+\frac {6 x}{e^{17}}+x^2}} \]

[In]

Integrate[E^(-17 + E^((6*x + E^17*(-5 + 4*x + x^2))/E^17) + (6*x + E^17*(-5 + 4*x + x^2))/E^17)*(6 + E^17*(4 +
2*x)),x]

[Out]

E^E^(-5 + 4*x + (6*x)/E^17 + x^2)

Maple [A] (verified)

Time = 0.06 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.28

method	result	size
derivativedivides	\({\mathrm e}^{{\mathrm e}^{\left (\left (x^{2}+4 x -5\right ) {\mathrm e}^{17}+6 x \right ) {\mathrm e}^{-17}}}\)	\(23\)
default	\({\mathrm e}^{{\mathrm e}^{\left (\left (x^{2}+4 x -5\right ) {\mathrm e}^{17}+6 x \right ) {\mathrm e}^{-17}}}\)	\(23\)
norman	\({\mathrm e}^{{\mathrm e}^{\left (\left (x^{2}+4 x -5\right ) {\mathrm e}^{17}+6 x \right ) {\mathrm e}^{-17}}}\)	\(23\)
parallelrisch	\({\mathrm e}^{{\mathrm e}^{\left (\left (x^{2}+4 x -5\right ) {\mathrm e}^{17}+6 x \right ) {\mathrm e}^{-17}}}\)	\(23\)
risch	\({\mathrm e}^{{\mathrm e}^{\left ({\mathrm e}^{17} x^{2}+4 \,{\mathrm e}^{17} x -5 \,{\mathrm e}^{17}+6 x \right ) {\mathrm e}^{-17}}}\)	\(25\)

[In]

int(((4+2*x)*exp(17)+6)*exp(((x^2+4*x-5)*exp(17)+6*x)/exp(17))*exp(exp(((x^2+4*x-5)*exp(17)+6*x)/exp(17)))/exp
(17),x,method=_RETURNVERBOSE)

[Out]

exp(exp(((x^2+4*x-5)*exp(17)+6*x)/exp(17)))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (15) = 30\).

Time = 0.26 (sec) , antiderivative size = 61, normalized size of antiderivative = 3.39 \[ \int e^{-17+e^{\frac {6 x+e^{17} \left (-5+4 x+x^2\right )}{e^{17}}}+\frac {6 x+e^{17} \left (-5+4 x+x^2\right )}{e^{17}}} \left (6+e^{17} (4+2 x)\right ) \, dx=e^{\left (-{\left ({\left (x^{2} + 4 \, x - 5\right )} e^{17} + 6 \, x\right )} e^{\left (-17\right )} + {\left ({\left (x^{2} + 4 \, x - 22\right )} e^{17} + 6 \, x + e^{\left ({\left ({\left (x^{2} + 4 \, x - 5\right )} e^{17} + 6 \, x\right )} e^{\left (-17\right )} + 17\right )}\right )} e^{\left (-17\right )} + 17\right )} \]

[In]

integrate(((4+2*x)*exp(17)+6)*exp(((x^2+4*x-5)*exp(17)+6*x)/exp(17))*exp(exp(((x^2+4*x-5)*exp(17)+6*x)/exp(17)
))/exp(17),x, algorithm="fricas")

[Out]

e^(-((x^2 + 4*x - 5)*e^17 + 6*x)*e^(-17) + ((x^2 + 4*x - 22)*e^17 + 6*x + e^(((x^2 + 4*x - 5)*e^17 + 6*x)*e^(-
17) + 17))*e^(-17) + 17)

Sympy [A] (verification not implemented)

Time = 0.12 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int e^{-17+e^{\frac {6 x+e^{17} \left (-5+4 x+x^2\right )}{e^{17}}}+\frac {6 x+e^{17} \left (-5+4 x+x^2\right )}{e^{17}}} \left (6+e^{17} (4+2 x)\right ) \, dx=e^{e^{\frac {6 x + \left (x^{2} + 4 x - 5\right ) e^{17}}{e^{17}}}} \]

[In]

integrate(((4+2*x)*exp(17)+6)*exp(((x**2+4*x-5)*exp(17)+6*x)/exp(17))*exp(exp(((x**2+4*x-5)*exp(17)+6*x)/exp(1
7)))/exp(17),x)

[Out]

exp(exp((6*x + (x**2 + 4*x - 5)*exp(17))*exp(-17)))

Maxima [A] (verification not implemented)

none

Time = 0.49 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int e^{-17+e^{\frac {6 x+e^{17} \left (-5+4 x+x^2\right )}{e^{17}}}+\frac {6 x+e^{17} \left (-5+4 x+x^2\right )}{e^{17}}} \left (6+e^{17} (4+2 x)\right ) \, dx=e^{\left (e^{\left (x^{2} + 6 \, x e^{\left (-17\right )} + 4 \, x - 5\right )}\right )} \]

[In]

integrate(((4+2*x)*exp(17)+6)*exp(((x^2+4*x-5)*exp(17)+6*x)/exp(17))*exp(exp(((x^2+4*x-5)*exp(17)+6*x)/exp(17)
))/exp(17),x, algorithm="maxima")

[Out]

e^(e^(x^2 + 6*x*e^(-17) + 4*x - 5))

Giac [F]

\[ \int e^{-17+e^{\frac {6 x+e^{17} \left (-5+4 x+x^2\right )}{e^{17}}}+\frac {6 x+e^{17} \left (-5+4 x+x^2\right )}{e^{17}}} \left (6+e^{17} (4+2 x)\right ) \, dx=\int { 2 \, {\left ({\left (x + 2\right )} e^{17} + 3\right )} e^{\left ({\left ({\left (x^{2} + 4 \, x - 5\right )} e^{17} + 6 \, x\right )} e^{\left (-17\right )} + e^{\left ({\left ({\left (x^{2} + 4 \, x - 5\right )} e^{17} + 6 \, x\right )} e^{\left (-17\right )}\right )} - 17\right )} \,d x } \]

[In]

integrate(((4+2*x)*exp(17)+6)*exp(((x^2+4*x-5)*exp(17)+6*x)/exp(17))*exp(exp(((x^2+4*x-5)*exp(17)+6*x)/exp(17)
))/exp(17),x, algorithm="giac")

[Out]

integrate(2*((x + 2)*e^17 + 3)*e^(((x^2 + 4*x - 5)*e^17 + 6*x)*e^(-17) + e^(((x^2 + 4*x - 5)*e^17 + 6*x)*e^(-1
7)) - 17), x)

Mupad [B] (verification not implemented)

Time = 8.83 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int e^{-17+e^{\frac {6 x+e^{17} \left (-5+4 x+x^2\right )}{e^{17}}}+\frac {6 x+e^{17} \left (-5+4 x+x^2\right )}{e^{17}}} \left (6+e^{17} (4+2 x)\right ) \, dx={\mathrm {e}}^{{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-5}\,{\mathrm {e}}^{6\,x\,{\mathrm {e}}^{-17}}} \]

[In]

int(exp(exp(-17)*(6*x + exp(17)*(4*x + x^2 - 5)))*exp(-17)*exp(exp(exp(-17)*(6*x + exp(17)*(4*x + x^2 - 5))))*
(exp(17)*(2*x + 4) + 6),x)

[Out]

exp(exp(4*x)*exp(x^2)*exp(-5)*exp(6*x*exp(-17)))