3.18.95 \(\int (-2 e^x+e^{-20+e^{e^3} (-5+x)+5 x} (5+e^{e^3})) \, dx\)

Optimal. Leaf size=22 \[ -2-2 e^x+e^{\left (4+e^{e^3}\right ) (-5+x)+x} \]

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Rubi [A]  time = 0.06, antiderivative size = 27, normalized size of antiderivative = 1.23, number of steps used = 4, number of rules used = 2, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {2194, 2227} \begin {gather*} e^{\left (5+e^{e^3}\right ) x-5 \left (4+e^{e^3}\right )}-2 e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-2*E^x + E^(-20 + E^E^3*(-5 + x) + 5*x)*(5 + E^E^3),x]

[Out]

-2*E^x + E^(-5*(4 + E^E^3) + (5 + E^E^3)*x)

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

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} &=-\left (2 \int e^x \, dx\right )+\left (5+e^{e^3}\right ) \int e^{-20+e^{e^3} (-5+x)+5 x} \, dx\\ &=-2 e^x+\left (5+e^{e^3}\right ) \int e^{-5 \left (4+e^{e^3}\right )+\left (5+e^{e^3}\right ) x} \, dx\\ &=-2 e^x+e^{-5 \left (4+e^{e^3}\right )+\left (5+e^{e^3}\right ) x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.07, size = 23, normalized size = 1.05 \begin {gather*} e^{e^{e^3} (-5+x)+5 (-4+x)}-2 e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-2*E^x + E^(-20 + E^E^3*(-5 + x) + 5*x)*(5 + E^E^3),x]

[Out]

E^(E^E^3*(-5 + x) + 5*(-4 + x)) - 2*E^x

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fricas [A]  time = 0.82, size = 18, normalized size = 0.82 \begin {gather*} e^{\left ({\left (x - 5\right )} e^{\left (e^{3}\right )} + 5 \, x - 20\right )} - 2 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(exp(3))+5)*exp((x-5)*exp(exp(3))+5*x-20)-2*exp(x),x, algorithm="fricas")

[Out]

e^((x - 5)*e^(e^3) + 5*x - 20) - 2*e^x

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giac [A]  time = 0.25, size = 18, normalized size = 0.82 \begin {gather*} e^{\left ({\left (x - 5\right )} e^{\left (e^{3}\right )} + 5 \, x - 20\right )} - 2 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(exp(3))+5)*exp((x-5)*exp(exp(3))+5*x-20)-2*exp(x),x, algorithm="giac")

[Out]

e^((x - 5)*e^(e^3) + 5*x - 20) - 2*e^x

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maple [A]  time = 0.04, size = 19, normalized size = 0.86

method	result	size
default	\({\mathrm e}^{\left (x -5\right ) {\mathrm e}^{{\mathrm e}^{3}}+5 x -20}-2 \,{\mathrm e}^{x}\)	\(19\)
norman	\({\mathrm e}^{\left (x -5\right ) {\mathrm e}^{{\mathrm e}^{3}}+5 x -20}-2 \,{\mathrm e}^{x}\)	\(19\)
risch	\({\mathrm e}^{x \,{\mathrm e}^{{\mathrm e}^{3}}-5 \,{\mathrm e}^{{\mathrm e}^{3}}+5 x -20}-2 \,{\mathrm e}^{x}\)	\(22\)
meijerg	\(\frac {\left ({\mathrm e}^{{\mathrm e}^{3}-5 \,{\mathrm e}^{{\mathrm e}^{3}}-20}+5 \,{\mathrm e}^{-5 \,{\mathrm e}^{{\mathrm e}^{3}}-20}\right ) \left (1-{\mathrm e}^{-x \left (-{\mathrm e}^{{\mathrm e}^{3}}-5\right )}\right )}{-{\mathrm e}^{{\mathrm e}^{3}}-5}+2-2 \,{\mathrm e}^{x}\)	\(53\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp(3))+5)*exp((x-5)*exp(exp(3))+5*x-20)-2*exp(x),x,method=_RETURNVERBOSE)

[Out]

exp((x-5)*exp(exp(3))+5*x-20)-2*exp(x)

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maxima [A]  time = 0.35, size = 18, normalized size = 0.82 \begin {gather*} e^{\left ({\left (x - 5\right )} e^{\left (e^{3}\right )} + 5 \, x - 20\right )} - 2 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(exp(3))+5)*exp((x-5)*exp(exp(3))+5*x-20)-2*exp(x),x, algorithm="maxima")

[Out]

e^((x - 5)*e^(e^3) + 5*x - 20) - 2*e^x

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mupad [B]  time = 0.11, size = 24, normalized size = 1.09 \begin {gather*} {\mathrm {e}}^{x\,{\mathrm {e}}^{{\mathrm {e}}^3}}\,{\mathrm {e}}^{5\,x}\,{\mathrm {e}}^{-20}\,{\mathrm {e}}^{-5\,{\mathrm {e}}^{{\mathrm {e}}^3}}-2\,{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(5*x + exp(exp(3))*(x - 5) - 20)*(exp(exp(3)) + 5) - 2*exp(x),x)

[Out]

exp(x*exp(exp(3)))*exp(5*x)*exp(-20)*exp(-5*exp(exp(3))) - 2*exp(x)

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sympy [A]  time = 0.12, size = 19, normalized size = 0.86 \begin {gather*} - 2 e^{x} + e^{5 x + \left (x - 5\right ) e^{e^{3}} - 20} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(exp(3))+5)*exp((x-5)*exp(exp(3))+5*x-20)-2*exp(x),x)

[Out]

-2*exp(x) + exp(5*x + (x - 5)*exp(exp(3)) - 20)

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