3.74.35 \(\int e^{3+e^x-x+x^2+3 \log ^4(4)} (-1+e^x+2 x) \, dx\)

Optimal. Leaf size=19 \[ e^{3+e^x-x+x^2+3 \log ^4(4)} \]

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Rubi [A]  time = 0.09, antiderivative size = 20, normalized size of antiderivative = 1.05, number of steps used = 1, number of rules used = 1, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {6706} \begin {gather*} e^{x^2-x+e^x+3 \left (1+\log ^4(4)\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

E^(E^x - x + x^2 + 3*(1 + Log[4]^4))

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=e^{e^x-x+x^2+3 \left (1+\log ^4(4)\right )}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.12, size = 19, normalized size = 1.00 \begin {gather*} e^{3+e^x-x+x^2+3 \log ^4(4)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(3 + E^x - x + x^2 + 3*Log[4]^4)*(-1 + E^x + 2*x),x]

[Out]

E^(3 + E^x - x + x^2 + 3*Log[4]^4)

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fricas [A]  time = 0.67, size = 17, normalized size = 0.89 \begin {gather*} e^{\left (48 \, \log \relax (2)^{4} + x^{2} - x + e^{x} + 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(x)+2*x-1)*exp(exp(x)+48*log(2)^4+x^2-x+3),x, algorithm="fricas")

[Out]

e^(48*log(2)^4 + x^2 - x + e^x + 3)

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giac [A]  time = 0.12, size = 17, normalized size = 0.89 \begin {gather*} e^{\left (48 \, \log \relax (2)^{4} + x^{2} - x + e^{x} + 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(x)+2*x-1)*exp(exp(x)+48*log(2)^4+x^2-x+3),x, algorithm="giac")

[Out]

e^(48*log(2)^4 + x^2 - x + e^x + 3)

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maple [A]  time = 0.02, size = 18, normalized size = 0.95

method	result	size
derivativedivides	\({\mathrm e}^{{\mathrm e}^{x}+48 \ln \relax (2)^{4}+x^{2}-x +3}\)	\(18\)
default	\({\mathrm e}^{{\mathrm e}^{x}+48 \ln \relax (2)^{4}+x^{2}-x +3}\)	\(18\)
norman	\({\mathrm e}^{{\mathrm e}^{x}+48 \ln \relax (2)^{4}+x^{2}-x +3}\)	\(18\)
risch	\({\mathrm e}^{{\mathrm e}^{x}+48 \ln \relax (2)^{4}+x^{2}-x +3}\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x)+2*x-1)*exp(exp(x)+48*ln(2)^4+x^2-x+3),x,method=_RETURNVERBOSE)

[Out]

exp(exp(x)+48*ln(2)^4+x^2-x+3)

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maxima [A]  time = 0.36, size = 17, normalized size = 0.89 \begin {gather*} e^{\left (48 \, \log \relax (2)^{4} + x^{2} - x + e^{x} + 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(x)+2*x-1)*exp(exp(x)+48*log(2)^4+x^2-x+3),x, algorithm="maxima")

[Out]

e^(48*log(2)^4 + x^2 - x + e^x + 3)

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mupad [B]  time = 4.97, size = 21, normalized size = 1.11 \begin {gather*} {\mathrm {e}}^{-x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^3\,{\mathrm {e}}^{48\,{\ln \relax (2)}^4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(exp(x) - x + 48*log(2)^4 + x^2 + 3)*(2*x + exp(x) - 1),x)

[Out]

exp(-x)*exp(x^2)*exp(exp(x))*exp(3)*exp(48*log(2)^4)

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sympy [A]  time = 0.17, size = 17, normalized size = 0.89 \begin {gather*} e^{x^{2} - x + e^{x} + 3 + 48 \log {\relax (2 )}^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(x)+2*x-1)*exp(exp(x)+48*ln(2)**4+x**2-x+3),x)

[Out]

exp(x**2 - x + exp(x) + 3 + 48*log(2)**4)

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