3.12.65 \(\int e^{e^x} (10 x^4+6 x^5+e^x (2 x^5+x^6)) \, dx\)

Optimal. Leaf size=12 \[ e^{e^x} x^5 (2+x) \]

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Rubi [A]  time = 0.03, antiderivative size = 15, normalized size of antiderivative = 1.25, number of steps used = 1, number of rules used = 1, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {2288} \begin {gather*} e^{e^x} \left (x^6+2 x^5\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^E^x*(10*x^4 + 6*x^5 + E^x*(2*x^5 + x^6)),x]

[Out]

E^E^x*(2*x^5 + x^6)

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} &=e^{e^x} \left (2 x^5+x^6\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.12, size = 12, normalized size = 1.00 \begin {gather*} e^{e^x} x^5 (2+x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^E^x*(10*x^4 + 6*x^5 + E^x*(2*x^5 + x^6)),x]

[Out]

E^E^x*x^5*(2 + x)

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fricas [A]  time = 0.85, size = 13, normalized size = 1.08 \begin {gather*} {\left (x^{6} + 2 \, x^{5}\right )} e^{\left (e^{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^6+2*x^5)*exp(x)+6*x^5+10*x^4)*exp(exp(x)),x, algorithm="fricas")

[Out]

(x^6 + 2*x^5)*e^(e^x)

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giac [B]  time = 0.42, size = 25, normalized size = 2.08 \begin {gather*} {\left (x^{6} e^{\left (x + e^{x}\right )} + 2 \, x^{5} e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^6+2*x^5)*exp(x)+6*x^5+10*x^4)*exp(exp(x)),x, algorithm="giac")

[Out]

(x^6*e^(x + e^x) + 2*x^5*e^(x + e^x))*e^(-x)

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maple [A]  time = 0.03, size = 11, normalized size = 0.92

method	result	size
risch	\(\left (2+x \right ) x^{5} {\mathrm e}^{{\mathrm e}^{x}}\)	\(11\)
norman	\(x^{6} {\mathrm e}^{{\mathrm e}^{x}}+2 x^{5} {\mathrm e}^{{\mathrm e}^{x}}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((x^6+2*x^5)*exp(x)+6*x^5+10*x^4)*exp(exp(x)),x,method=_RETURNVERBOSE)

[Out]

(2+x)*x^5*exp(exp(x))

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maxima [A]  time = 0.47, size = 13, normalized size = 1.08 \begin {gather*} {\left (x^{6} + 2 \, x^{5}\right )} e^{\left (e^{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^6+2*x^5)*exp(x)+6*x^5+10*x^4)*exp(exp(x)),x, algorithm="maxima")

[Out]

(x^6 + 2*x^5)*e^(e^x)

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mupad [B]  time = 0.81, size = 10, normalized size = 0.83 \begin {gather*} x^5\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (x+2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(exp(x))*(exp(x)*(2*x^5 + x^6) + 10*x^4 + 6*x^5),x)

[Out]

x^5*exp(exp(x))*(x + 2)

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sympy [A]  time = 0.15, size = 12, normalized size = 1.00 \begin {gather*} \left (x^{6} + 2 x^{5}\right ) e^{e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x**6+2*x**5)*exp(x)+6*x**5+10*x**4)*exp(exp(x)),x)

[Out]

(x**6 + 2*x**5)*exp(exp(x))

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