3.84.85 \(\int (1+e^{e^{e^{e^{5+x}}}} (4+4 e^{5+e^{e^{5+x}}+e^{5+x}+x} x)) \, dx\)

Optimal. Leaf size=17 \[ \left (1+4 e^{e^{e^{e^{5+x}}}}\right ) x \]

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Rubi [A]  time = 0.05, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps used = 2, number of rules used = 1, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.028, Rules used = {2288} \begin {gather*} 4 e^{e^{e^{e^{x+5}}}} x+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 + E^E^E^E^(5 + x)*(4 + 4*E^(5 + E^E^(5 + x) + E^(5 + x) + x)*x),x]

[Out]

x + 4*E^E^E^E^(5 + x)*x

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

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Mathematica [A]  time = 0.03, size = 16, normalized size = 0.94 \begin {gather*} x+4 e^{e^{e^{e^{5+x}}}} x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 + E^E^E^E^(5 + x)*(4 + 4*E^(5 + E^E^(5 + x) + E^(5 + x) + x)*x),x]

[Out]

x + 4*E^E^E^E^(5 + x)*x

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fricas [A]  time = 0.67, size = 12, normalized size = 0.71 \begin {gather*} 4 \, x e^{\left (e^{\left (e^{\left (e^{\left (x + 5\right )}\right )}\right )}\right )} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x*exp(5+x)*exp(exp(5+x))*exp(exp(exp(5+x)))+4)*exp(exp(exp(exp(5+x))))+1,x, algorithm="fricas")

[Out]

4*x*e^(e^(e^(e^(x + 5)))) + x

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int 4 \, {\left (x e^{\left (x + e^{\left (x + 5\right )} + e^{\left (e^{\left (x + 5\right )}\right )} + 5\right )} + 1\right )} e^{\left (e^{\left (e^{\left (e^{\left (x + 5\right )}\right )}\right )}\right )} + 1\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x*exp(5+x)*exp(exp(5+x))*exp(exp(exp(5+x)))+4)*exp(exp(exp(exp(5+x))))+1,x, algorithm="giac")

[Out]

integrate(4*(x*e^(x + e^(x + 5) + e^(e^(x + 5)) + 5) + 1)*e^(e^(e^(e^(x + 5)))) + 1, x)

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maple [A]  time = 0.10, size = 13, normalized size = 0.76

method	result	size
risch	\(4 x \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{5+x}}}}+x\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*x*exp(5+x)*exp(exp(5+x))*exp(exp(exp(5+x)))+4)*exp(exp(exp(exp(5+x))))+1,x,method=_RETURNVERBOSE)

[Out]

4*x*exp(exp(exp(exp(5+x))))+x

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maxima [A]  time = 0.45, size = 12, normalized size = 0.71 \begin {gather*} 4 \, x e^{\left (e^{\left (e^{\left (e^{\left (x + 5\right )}\right )}\right )}\right )} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x*exp(5+x)*exp(exp(5+x))*exp(exp(exp(5+x)))+4)*exp(exp(exp(exp(5+x))))+1,x, algorithm="maxima")

[Out]

4*x*e^(e^(e^(e^(x + 5)))) + x

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mupad [B]  time = 5.37, size = 13, normalized size = 0.76 \begin {gather*} x+4\,x\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^5\,{\mathrm {e}}^x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(exp(exp(exp(x + 5))))*(4*x*exp(exp(exp(x + 5)))*exp(x + 5)*exp(exp(x + 5)) + 4) + 1,x)

[Out]

x + 4*x*exp(exp(exp(exp(5)*exp(x))))

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sympy [A]  time = 34.25, size = 14, normalized size = 0.82 \begin {gather*} 4 x e^{e^{e^{e^{x + 5}}}} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x*exp(5+x)*exp(exp(5+x))*exp(exp(exp(5+x)))+4)*exp(exp(exp(exp(5+x))))+1,x)

[Out]

4*x*exp(exp(exp(exp(x + 5)))) + x

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