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

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

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Rubi [A]  time = 0.02, antiderivative size = 14, normalized size of antiderivative = 0.64, number of steps used = 2, number of rules used = 1, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {2288} \begin {gather*} x-e^{e^{2 x}} x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

x - E^E^(2*x)*x^3

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

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Mathematica [A]  time = 0.01, size = 14, normalized size = 0.64 \begin {gather*} x-e^{e^{2 x}} x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

x - E^E^(2*x)*x^3

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fricas [A]  time = 0.55, size = 12, normalized size = 0.55 \begin {gather*} -x^{3} e^{\left (e^{\left (2 \, x\right )}\right )} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x^3*e^(e^(2*x)) + x

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giac [A]  time = 0.12, size = 12, normalized size = 0.55 \begin {gather*} -x^{3} e^{\left (e^{\left (2 \, x\right )}\right )} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x^3*e^(e^(2*x)) + x

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maple [A]  time = 0.03, size = 13, normalized size = 0.59

method	result	size
default	\(x -x^{3} {\mathrm e}^{{\mathrm e}^{2 x}}\)	\(13\)
norman	\(x -x^{3} {\mathrm e}^{{\mathrm e}^{2 x}}\)	\(13\)
risch	\(x -x^{3} {\mathrm e}^{{\mathrm e}^{2 x}}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.38, size = 12, normalized size = 0.55 \begin {gather*} -x^{3} e^{\left (e^{\left (2 \, x\right )}\right )} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x^3*e^(e^(2*x)) + x

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mupad [B]  time = 3.03, size = 12, normalized size = 0.55 \begin {gather*} x-x^3\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x - x^3*exp(exp(2*x))

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sympy [A]  time = 0.14, size = 10, normalized size = 0.45 \begin {gather*} - x^{3} e^{e^{2 x}} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x**3*exp(exp(2*x)) + x

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