3.32.85 \(\int (-1+12 x^3+e^{e^x} (4 x+2 e^x x^2)) \, dx\)

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

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Rubi [A]  time = 0.02, antiderivative size = 19, normalized size of antiderivative = 0.86, number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {2288} \begin {gather*} 3 x^4+2 e^{e^x} x^2-x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 + 12*x^3 + E^E^x*(4*x + 2*E^x*x^2),x]

[Out]

-x + 2*E^E^x*x^2 + 3*x^4

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

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Mathematica [A]  time = 0.01, size = 19, normalized size = 0.86 \begin {gather*} -x+2 e^{e^x} x^2+3 x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 + 12*x^3 + E^E^x*(4*x + 2*E^x*x^2),x]

[Out]

-x + 2*E^E^x*x^2 + 3*x^4

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fricas [A]  time = 0.53, size = 17, normalized size = 0.77 \begin {gather*} 3 \, x^{4} + 2 \, x^{2} e^{\left (e^{x}\right )} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(x)*x^2+4*x)*exp(exp(x))+12*x^3-1,x, algorithm="fricas")

[Out]

3*x^4 + 2*x^2*e^(e^x) - x

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giac [A]  time = 0.25, size = 17, normalized size = 0.77 \begin {gather*} 3 \, x^{4} + 2 \, x^{2} e^{\left (e^{x}\right )} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(x)*x^2+4*x)*exp(exp(x))+12*x^3-1,x, algorithm="giac")

[Out]

3*x^4 + 2*x^2*e^(e^x) - x

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maple [A]  time = 0.03, size = 18, normalized size = 0.82

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*exp(x)*x^2+4*x)*exp(exp(x))+12*x^3-1,x,method=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.42, size = 17, normalized size = 0.77 \begin {gather*} 3 \, x^{4} + 2 \, x^{2} e^{\left (e^{x}\right )} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(x)*x^2+4*x)*exp(exp(x))+12*x^3-1,x, algorithm="maxima")

[Out]

3*x^4 + 2*x^2*e^(e^x) - x

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mupad [B]  time = 0.06, size = 17, normalized size = 0.77 \begin {gather*} 2\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^x}-x+3\,x^4 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(12*x^3 + exp(exp(x))*(4*x + 2*x^2*exp(x)) - 1,x)

[Out]

2*x^2*exp(exp(x)) - x + 3*x^4

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sympy [A]  time = 0.13, size = 15, normalized size = 0.68 \begin {gather*} 3 x^{4} + 2 x^{2} e^{e^{x}} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(x)*x**2+4*x)*exp(exp(x))+12*x**3-1,x)

[Out]

3*x**4 + 2*x**2*exp(exp(x)) - x

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