3.73.21 $\int \frac{1}{2}{e}^{-e^4}(2x+e^{e^4}(3+11e^{\frac{11x^3}{6}}{x}^2))dx$

Optimal. Leaf size=26 $$e^{\frac{11x^3}{6}}+\frac{1}{2}x(3+e^{-e^4}x)$$

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Rubi [A]  time = 0.03, antiderivative size = 29, normalized size of antiderivative = 1.12, number of steps used = 4, number of rules used = 2, integrand size = 37, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.054, Rules used = {12, 2209} $$\begin{array}{c}{e}^{\frac{11x^3}{6}}+\frac{1}{2}{e}^{-e^4}{x}^2+\frac{3x}{2}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(2*x + E^E^4*(3 + 11*E^((11*x^3)/6)*x^2))/(2*E^E^4),x]

[Out]

E^((11*x^3)/6) + (3*x)/2 + x^2/(2*E^E^4)

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2209

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[((e + f*x)^n*
F^(a + b*(c + d*x)^n))/(b*f*n*(c + d*x)^n*Log[F]), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\frac{1}{2}{e}^{-e^4}\int (2x+e^{e^4}(3+11e^{\frac{11x^3}{6}}{x}^2))dx\\ & =\frac{1}{2}{e}^{-e^4}{x}^2+\frac{1}{2}\int (3+11e^{\frac{11x^3}{6}}{x}^2)dx\\ & =\frac{3x}{2}+\frac{1}{2}{e}^{-e^4}{x}^2+\frac{11}{2}\int e^{\frac{11x^3}{6}}{x}^{2}dx\\ & =e^{\frac{11x^3}{6}}+\frac{3x}{2}+\frac{1}{2}{e}^{-e^4}{x}^2\end{array}\end{array}$$

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Mathematica [A]  time = 0.01, size = 29, normalized size = 1.12 $$\begin{array}{c}{e}^{\frac{11x^3}{6}}+\frac{3x}{2}+\frac{1}{2}{e}^{-e^4}{x}^2\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(2*x + E^E^4*(3 + 11*E^((11*x^3)/6)*x^2))/(2*E^E^4),x]

[Out]

E^((11*x^3)/6) + (3*x)/2 + x^2/(2*E^E^4)

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fricas [A]  time = 0.75, size = 27, normalized size = 1.04 $$\begin{array}{c}\frac{1}{2}(x^2+(3x+2e^{\left(\frac{11}{6}{x}^3\right)})e^{\left(e^4\right)})e^{(-e^4)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*((11*x^2*exp(11/6*x^3)+3)*exp(exp(4))+2*x)/exp(exp(4)),x, algorithm="fricas")

[Out]

1/2*(x^2 + (3*x + 2*e^(11/6*x^3))*e^(e^4))*e^(-e^4)

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giac [A]  time = 0.18, size = 27, normalized size = 1.04 $$\begin{array}{c}\frac{1}{2}(x^2+(3x+2e^{\left(\frac{11}{6}{x}^3\right)})e^{\left(e^4\right)})e^{(-e^4)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*((11*x^2*exp(11/6*x^3)+3)*exp(exp(4))+2*x)/exp(exp(4)),x, algorithm="giac")

[Out]

1/2*(x^2 + (3*x + 2*e^(11/6*x^3))*e^(e^4))*e^(-e^4)

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maple [A]  time = 0.03, size = 21, normalized size = 0.81

method	result	size
norman	$\frac{3x}{2}+\frac{{\mathrm{e}}^{-{\mathrm{e}}^4}{x}^2}{2}+{\mathrm{e}}^{\frac{11x^3}{6}}$	$21$
risch	$\frac{3x}{2}+\frac{{\mathrm{e}}^{-{\mathrm{e}}^4}{x}^2}{2}+{\mathrm{e}}^{\frac{11x^3}{6}}$	$21$
default	$\frac{{\mathrm{e}}^{-{\mathrm{e}}^4}({\mathrm{e}}^{{\mathrm{e}}^4}(3x+2{\mathrm{e}}^{\frac{11x^3}{6}})+x^2)}{2}$	$28$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/2*((11*x^2*exp(11/6*x^3)+3)*exp(exp(4))+2*x)/exp(exp(4)),x,method=_RETURNVERBOSE)

[Out]

3/2*x+1/2/exp(exp(4))*x^2+exp(11/6*x^3)

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maxima [A]  time = 0.35, size = 27, normalized size = 1.04 $$\begin{array}{c}\frac{1}{2}(x^2+(3x+2e^{\left(\frac{11}{6}{x}^3\right)})e^{\left(e^4\right)})e^{(-e^4)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*((11*x^2*exp(11/6*x^3)+3)*exp(exp(4))+2*x)/exp(exp(4)),x, algorithm="maxima")

[Out]

1/2*(x^2 + (3*x + 2*e^(11/6*x^3))*e^(e^4))*e^(-e^4)

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mupad [B]  time = 0.07, size = 20, normalized size = 0.77 $$\begin{array}{c}\frac{3x}{2}+{\mathrm{e}}^{\frac{11x^3}{6}}+\frac{x^2{\mathrm{e}}^{-{\mathrm{e}}^4}}{2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-exp(4))*(x + (exp(exp(4))*(11*x^2*exp((11*x^3)/6) + 3))/2),x)

[Out]

(3*x)/2 + exp((11*x^3)/6) + (x^2*exp(-exp(4)))/2

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sympy [A]  time = 0.12, size = 22, normalized size = 0.85 $$\begin{array}{c}\frac{x^2}{2e^{e^4}}+\frac{3x}{2}+e^{\frac{11x^3}{6}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*((11*x**2*exp(11/6*x**3)+3)*exp(exp(4))+2*x)/exp(exp(4)),x)

[Out]

x**2*exp(-exp(4))/2 + 3*x/2 + exp(11*x**3/6)

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