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

Optimal. Leaf size=12 \[ e^{\left (22+e^3+x\right )^2}+x \]

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Rubi [A]  time = 0.09, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.057, Rules used = {2227, 2209} \begin {gather*} x+e^{\left (x+e^3+22\right )^2} \end {gather*}

Antiderivative was successfully verified.

[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 2209

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 2227

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 {gather*} \begin {aligned} \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 {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 12, normalized size = 1.00 \begin {gather*} e^{\left (22+e^3+x\right )^2}+x \end {gather*}

Antiderivative was successfully verified.

[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

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fricas [A]  time = 1.48, size = 20, normalized size = 1.67 \begin {gather*} x + e^{\left (x^{2} + 2 \, {\left (x + 22\right )} e^{3} + 44 \, x + e^{6} + 484\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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giac [B]  time = 0.58, size = 22, normalized size = 1.83 \begin {gather*} x + e^{\left (x^{2} + 2 \, x e^{3} + 44 \, x + e^{6} + 44 \, e^{3} + 484\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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maple [B]  time = 0.04, size = 23, normalized size = 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	\(x +{\mathrm e}^{{\mathrm e}^{6}+\left (2 x +44\right ) {\mathrm e}^{3}+x^{2}+44 x +484}\)	\(24\)
default	\(x +{\mathrm e}^{x^{2}+\left (2 \,{\mathrm e}^{3}+44\right ) x +44 \,{\mathrm e}^{3}+{\mathrm e}^{6}+484}+\frac {i \left (2 \,{\mathrm e}^{3}+44\right ) \sqrt {\pi }\, {\mathrm e}^{44 \,{\mathrm e}^{3}+{\mathrm e}^{6}+484-\frac {\left (2 \,{\mathrm e}^{3}+44\right )^{2}}{4}} \erf \left (i x +\frac {i \left (2 \,{\mathrm e}^{3}+44\right )}{2}\right )}{2}-i \sqrt {\pi }\, {\mathrm e}^{44 \,{\mathrm e}^{3}+{\mathrm e}^{6}+487-\frac {\left (2 \,{\mathrm e}^{3}+44\right )^{2}}{4}} \erf \left (i x +\frac {i \left (2 \,{\mathrm e}^{3}+44\right )}{2}\right )-22 i \sqrt {\pi }\, {\mathrm e}^{44 \,{\mathrm e}^{3}+{\mathrm e}^{6}+484-\frac {\left (2 \,{\mathrm e}^{3}+44\right )^{2}}{4}} \erf \left (i x +\frac {i \left (2 \,{\mathrm e}^{3}+44\right )}{2}\right )\)	\(149\)

Verification of antiderivative is not currently implemented for this CAS.

[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)

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maxima [A]  time = 0.39, size = 20, normalized size = 1.67 \begin {gather*} x + e^{\left (x^{2} + 2 \, {\left (x + 22\right )} e^{3} + 44 \, x + e^{6} + 484\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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mupad [B]  time = 0.13, size = 27, normalized size = 2.25 \begin {gather*} 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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))

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sympy [B]  time = 0.11, size = 22, normalized size = 1.83 \begin {gather*} x + e^{x^{2} + 44 x + \left (2 x + 44\right ) e^{3} + e^{6} + 484} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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