3.56.64 \(\int (6+2 x+e^{e^x} (4+4 e^x x)) \, dx\)

Optimal. Leaf size=22 \[ -7+2 x+x^2-4 \left (-x-e^{e^x} x\right ) \]

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Rubi [A]  time = 0.02, antiderivative size = 15, normalized size of antiderivative = 0.68, number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {2288} \begin {gather*} x^2+4 e^{e^x} x+6 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[6 + 2*x + E^E^x*(4 + 4*E^x*x),x]

[Out]

6*x + 4*E^E^x*x + x^2

Rule 2288

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = (v*y)/(Log[F]*D[u, x])}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=6 x+x^2+\int e^{e^x} \left (4+4 e^x x\right ) \, dx\\ &=6 x+4 e^{e^x} x+x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 15, normalized size = 0.68 \begin {gather*} 6 x+4 e^{e^x} x+x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[6 + 2*x + E^E^x*(4 + 4*E^x*x),x]

[Out]

6*x + 4*E^E^x*x + x^2

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fricas [A]  time = 0.69, size = 13, normalized size = 0.59 \begin {gather*} x^{2} + 4 \, x e^{\left (e^{x}\right )} + 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*exp(x)*x+4)*exp(exp(x))+2*x+6,x, algorithm="fricas")

[Out]

x^2 + 4*x*e^(e^x) + 6*x

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giac [A]  time = 0.13, size = 13, normalized size = 0.59 \begin {gather*} x^{2} + 4 \, x e^{\left (e^{x}\right )} + 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*exp(x)*x+4)*exp(exp(x))+2*x+6,x, algorithm="giac")

[Out]

x^2 + 4*x*e^(e^x) + 6*x

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maple [A]  time = 0.03, size = 14, normalized size = 0.64

method	result	size
default	\(6 x +4 x \,{\mathrm e}^{{\mathrm e}^{x}}+x^{2}\)	\(14\)
norman	\(6 x +4 x \,{\mathrm e}^{{\mathrm e}^{x}}+x^{2}\)	\(14\)
risch	\(6 x +4 x \,{\mathrm e}^{{\mathrm e}^{x}}+x^{2}\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*exp(x)*x+4)*exp(exp(x))+2*x+6,x,method=_RETURNVERBOSE)

[Out]

6*x+4*x*exp(exp(x))+x^2

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maxima [A]  time = 0.37, size = 13, normalized size = 0.59 \begin {gather*} x^{2} + 4 \, x e^{\left (e^{x}\right )} + 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*exp(x)*x+4)*exp(exp(x))+2*x+6,x, algorithm="maxima")

[Out]

x^2 + 4*x*e^(e^x) + 6*x

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mupad [B]  time = 0.05, size = 10, normalized size = 0.45 \begin {gather*} x\,\left (x+4\,{\mathrm {e}}^{{\mathrm {e}}^x}+6\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + exp(exp(x))*(4*x*exp(x) + 4) + 6,x)

[Out]

x*(x + 4*exp(exp(x)) + 6)

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sympy [A]  time = 0.12, size = 14, normalized size = 0.64 \begin {gather*} x^{2} + 4 x e^{e^{x}} + 6 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*exp(x)*x+4)*exp(exp(x))+2*x+6,x)

[Out]

x**2 + 4*x*exp(exp(x)) + 6*x

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