\(\int (1+e^{e^{2 x}} (-3 x^2-2 e^{2 x} x^3)) \, dx\) [4264]

Optimal result

Integrand size = 26, antiderivative size = 22 \[ \int \left (1+e^{e^{2 x}} \left (-3 x^2-2 e^{2 x} x^3\right )\right ) \, dx=-3+e^3+x-e^{e^{2 x}} x^3-\log (3) \]

[Out]

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

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.64, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {2326} \[ \int \left (1+e^{e^{2 x}} \left (-3 x^2-2 e^{2 x} x^3\right )\right ) \, dx=x-e^{e^{2 x}} x^3 \]

[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 2326

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{align*} \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{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.64 \[ \int \left (1+e^{e^{2 x}} \left (-3 x^2-2 e^{2 x} x^3\right )\right ) \, dx=x-e^{e^{2 x}} x^3 \]

[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

Maple [A] (verified)

Time = 0.43 (sec) , antiderivative size = 13, normalized size of antiderivative = 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	\(x -x^{3} {\mathrm e}^{{\mathrm e}^{2 x}}\)	\(13\)
parallelrisch	\(x -x^{3} {\mathrm e}^{{\mathrm e}^{2 x}}\)	\(13\)

[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))

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.55 \[ \int \left (1+e^{e^{2 x}} \left (-3 x^2-2 e^{2 x} x^3\right )\right ) \, dx=-x^{3} e^{\left (e^{\left (2 \, x\right )}\right )} + x \]

[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

Sympy [A] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.45 \[ \int \left (1+e^{e^{2 x}} \left (-3 x^2-2 e^{2 x} x^3\right )\right ) \, dx=- x^{3} e^{e^{2 x}} + x \]

[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

Maxima [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.55 \[ \int \left (1+e^{e^{2 x}} \left (-3 x^2-2 e^{2 x} x^3\right )\right ) \, dx=-x^{3} e^{\left (e^{\left (2 \, x\right )}\right )} + x \]

[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

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.55 \[ \int \left (1+e^{e^{2 x}} \left (-3 x^2-2 e^{2 x} x^3\right )\right ) \, dx=-x^{3} e^{\left (e^{\left (2 \, x\right )}\right )} + x \]

[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

Mupad [B] (verification not implemented)

Time = 11.84 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.55 \[ \int \left (1+e^{e^{2 x}} \left (-3 x^2-2 e^{2 x} x^3\right )\right ) \, dx=x-x^3\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}} \]

[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))