\(\int (1+e^{484+e^6+44 x+x^2+e^3 (44+2 x)} (44+2 e^3+2 x)) \, dx\) [1458]

Optimal result

Integrand size = 35, antiderivative size = 12 \[ \int \left (1+e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right )\right ) \, dx=e^{\left (22+e^3+x\right )^2}+x \]

[Out]

x+exp((x+22+exp(3))^2)

Rubi [A] (verified)

Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.057, Rules used = {2259, 2240} \[ \int \left (1+e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right )\right ) \, dx=x+e^{\left (x+e^3+22\right )^2} \]

[In]

Int[1 + E^(484 + E^6 + 44*x + x^2 + E^3*(44 + 2*x))*(44 + 2*E^3 + 2*x),x]

[Out]

E^(22 + E^3 + x)^2 + x

Rule 2240

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[(e + f*x)^n*(
F^(a + b*(c + d*x)^n)/(b*f*n*(c + d*x)^n*Log[F])), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rule 2259

Int[(u_.)*(F_)^((a_.) + (b_.)*(v_)), x_Symbol] :> Int[u*F^(a + b*NormalizePowerOfLinear[v, x]), x] /; FreeQ[{F
, a, b}, x] && PolynomialQ[u, x] && PowerOfLinearQ[v, x] &&  !PowerOfLinearMatchQ[v, x]

Rubi steps \begin{align*} \text {integral}& = x+\int e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right ) \, dx \\ & = x+\int e^{\left (22+e^3+x\right )^2} \left (44+2 e^3+2 x\right ) \, dx \\ & = e^{\left (22+e^3+x\right )^2}+x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \left (1+e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right )\right ) \, dx=e^{\left (22+e^3+x\right )^2}+x \]

[In]

Integrate[1 + E^(484 + E^6 + 44*x + x^2 + E^3*(44 + 2*x))*(44 + 2*E^3 + 2*x),x]

[Out]

E^(22 + E^3 + x)^2 + x

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(22\) vs. \(2(10)=20\).

Time = 0.06 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.92

method	result	size
risch	\(x +{\mathrm e}^{2 x \,{\mathrm e}^{3}+x^{2}+44 \,{\mathrm e}^{3}+{\mathrm e}^{6}+44 x +484}\)	\(23\)
norman	\(x +{\mathrm e}^{{\mathrm e}^{6}+\left (2 x +44\right ) {\mathrm e}^{3}+x^{2}+44 x +484}\)	\(24\)
parallelrisch	\(x +{\mathrm e}^{{\mathrm e}^{6}+\left (2 x +44\right ) {\mathrm e}^{3}+x^{2}+44 x +484}\)	\(24\)
default	\(x +2 \,{\mathrm e}^{{\mathrm e}^{6}} {\mathrm e}^{44 \,{\mathrm e}^{3}} {\mathrm e}^{484} \left (\frac {{\mathrm e}^{x^{2}+\left (2 \,{\mathrm e}^{3}+44\right ) x}}{2}+\frac {i \left (2 \,{\mathrm e}^{3}+44\right ) \sqrt {\pi }\, {\mathrm e}^{-\frac {\left (2 \,{\mathrm e}^{3}+44\right )^{2}}{4}} \operatorname {erf}\left (i x +\frac {i \left (2 \,{\mathrm e}^{3}+44\right )}{2}\right )}{4}\right )-i {\mathrm e}^{{\mathrm e}^{6}} {\mathrm e}^{44 \,{\mathrm e}^{3}} {\mathrm e}^{484} {\mathrm e}^{3} \sqrt {\pi }\, {\mathrm e}^{-\frac {\left (2 \,{\mathrm e}^{3}+44\right )^{2}}{4}} \operatorname {erf}\left (i x +\frac {i \left (2 \,{\mathrm e}^{3}+44\right )}{2}\right )-22 i {\mathrm e}^{{\mathrm e}^{6}} {\mathrm e}^{44 \,{\mathrm e}^{3}} {\mathrm e}^{484} \sqrt {\pi }\, {\mathrm e}^{-\frac {\left (2 \,{\mathrm e}^{3}+44\right )^{2}}{4}} \operatorname {erf}\left (i x +\frac {i \left (2 \,{\mathrm e}^{3}+44\right )}{2}\right )\)	\(161\)
parts	\(x +2 \,{\mathrm e}^{{\mathrm e}^{6}} {\mathrm e}^{44 \,{\mathrm e}^{3}} {\mathrm e}^{484} \left (\frac {{\mathrm e}^{x^{2}+\left (2 \,{\mathrm e}^{3}+44\right ) x}}{2}+\frac {i \left (2 \,{\mathrm e}^{3}+44\right ) \sqrt {\pi }\, {\mathrm e}^{-\frac {\left (2 \,{\mathrm e}^{3}+44\right )^{2}}{4}} \operatorname {erf}\left (i x +\frac {i \left (2 \,{\mathrm e}^{3}+44\right )}{2}\right )}{4}\right )-i {\mathrm e}^{{\mathrm e}^{6}} {\mathrm e}^{44 \,{\mathrm e}^{3}} {\mathrm e}^{484} {\mathrm e}^{3} \sqrt {\pi }\, {\mathrm e}^{-\frac {\left (2 \,{\mathrm e}^{3}+44\right )^{2}}{4}} \operatorname {erf}\left (i x +\frac {i \left (2 \,{\mathrm e}^{3}+44\right )}{2}\right )-22 i {\mathrm e}^{{\mathrm e}^{6}} {\mathrm e}^{44 \,{\mathrm e}^{3}} {\mathrm e}^{484} \sqrt {\pi }\, {\mathrm e}^{-\frac {\left (2 \,{\mathrm e}^{3}+44\right )^{2}}{4}} \operatorname {erf}\left (i x +\frac {i \left (2 \,{\mathrm e}^{3}+44\right )}{2}\right )\)	\(161\)

[In]

int((2*exp(3)+2*x+44)*exp(exp(3)^2+(2*x+44)*exp(3)+x^2+44*x+484)+1,x,method=_RETURNVERBOSE)

[Out]

x+exp(2*x*exp(3)+x^2+44*exp(3)+exp(6)+44*x+484)

Fricas [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.67 \[ \int \left (1+e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right )\right ) \, dx=x + e^{\left (x^{2} + 2 \, {\left (x + 22\right )} e^{3} + 44 \, x + e^{6} + 484\right )} \]

[In]

integrate((2*exp(3)+2*x+44)*exp(exp(3)^2+(2*x+44)*exp(3)+x^2+44*x+484)+1,x, algorithm="fricas")

[Out]

x + e^(x^2 + 2*(x + 22)*e^3 + 44*x + e^6 + 484)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 22 vs. \(2 (10) = 20\).

Time = 0.05 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.83 \[ \int \left (1+e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right )\right ) \, dx=x + e^{x^{2} + 44 x + \left (2 x + 44\right ) e^{3} + e^{6} + 484} \]

[In]

integrate((2*exp(3)+2*x+44)*exp(exp(3)**2+(2*x+44)*exp(3)+x**2+44*x+484)+1,x)

[Out]

x + exp(x**2 + 44*x + (2*x + 44)*exp(3) + exp(6) + 484)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.67 \[ \int \left (1+e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right )\right ) \, dx=x + e^{\left (x^{2} + 2 \, {\left (x + 22\right )} e^{3} + 44 \, x + e^{6} + 484\right )} \]

[In]

integrate((2*exp(3)+2*x+44)*exp(exp(3)^2+(2*x+44)*exp(3)+x^2+44*x+484)+1,x, algorithm="maxima")

[Out]

x + e^(x^2 + 2*(x + 22)*e^3 + 44*x + e^6 + 484)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 22 vs. \(2 (10) = 20\).

Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.83 \[ \int \left (1+e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right )\right ) \, dx=x + e^{\left (x^{2} + 2 \, x e^{3} + 44 \, x + e^{6} + 44 \, e^{3} + 484\right )} \]

[In]

integrate((2*exp(3)+2*x+44)*exp(exp(3)^2+(2*x+44)*exp(3)+x^2+44*x+484)+1,x, algorithm="giac")

[Out]

x + e^(x^2 + 2*x*e^3 + 44*x + e^6 + 44*e^3 + 484)

Mupad [B] (verification not implemented)

Time = 7.52 (sec) , antiderivative size = 27, normalized size of antiderivative = 2.25 \[ \int \left (1+e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right )\right ) \, dx=x+{\mathrm {e}}^{44\,{\mathrm {e}}^3}\,{\mathrm {e}}^{44\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{484}\,{\mathrm {e}}^{2\,x\,{\mathrm {e}}^3}\,{\mathrm {e}}^{{\mathrm {e}}^6} \]

[In]

int(exp(44*x + exp(6) + x^2 + exp(3)*(2*x + 44) + 484)*(2*x + 2*exp(3) + 44) + 1,x)

[Out]

x + exp(44*exp(3))*exp(44*x)*exp(x^2)*exp(484)*exp(2*x*exp(3))*exp(exp(6))