3.73.5 $\int \frac{-4+e^{e^8}(4-4x^2)+e^{2e^8}(-1+6x^2-8x^3+3x^4)}{x^2}dx$

Optimal. Leaf size=20 $$\frac{{(2-e^{e^8}(-1+x{)}^2)}^2}{x}$$

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Rubi [B]  time = 0.04, antiderivative size = 56, normalized size of antiderivative = 2.80, number of steps used = 2, number of rules used = 1, integrand size = 44, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.023, Rules used = {14} $$\begin{array}{c}{e}^{2e^8}{x}^3-4e^{2e^8}{x}^2-2e^{e^8}(2-3e^{e^8})x+\frac{{(2-e^{e^8})}^2}{x}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(-4 + E^E^8*(4 - 4*x^2) + E^(2*E^8)*(-1 + 6*x^2 - 8*x^3 + 3*x^4))/x^2,x]

[Out]

(2 - E^E^8)^2/x - 2*E^E^8*(2 - 3*E^E^8)*x - 4*E^(2*E^8)*x^2 + E^(2*E^8)*x^3

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int (2e^{e^8}(-2+3e^{e^8})-\frac{{(-2+e^{e^8})}^2}{x^2}-8e^{2e^8}x+3e^{2e^8}{x}^2)dx\\ & =\frac{{(2-e^{e^8})}^2}{x}-2e^{e^8}(2-3e^{e^8})x-4e^{2e^8}{x}^2+e^{2e^8}{x}^3\end{array}\end{array}$$

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Mathematica [B]  time = 0.03, size = 41, normalized size = 2.05 $$\begin{array}{c}\frac{4-4e^{e^8}(1+x^2)+e^{2e^8}(1+6x^2-4x^3+x^4)}{x}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(-4 + E^E^8*(4 - 4*x^2) + E^(2*E^8)*(-1 + 6*x^2 - 8*x^3 + 3*x^4))/x^2,x]

[Out]

(4 - 4*E^E^8*(1 + x^2) + E^(2*E^8)*(1 + 6*x^2 - 4*x^3 + x^4))/x

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fricas [B]  time = 0.73, size = 37, normalized size = 1.85 $$\begin{array}{c}\frac{(x^4-4x^3+6x^2+1)e^{\left(2e^8\right)}-4(x^2+1)e^{\left(e^8\right)}+4}{x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x^4-8*x^3+6*x^2-1)*exp(exp(2)^4)^2+(-4*x^2+4)*exp(exp(2)^4)-4)/x^2,x, algorithm="fricas")

[Out]

((x^4 - 4*x^3 + 6*x^2 + 1)*e^(2*e^8) - 4*(x^2 + 1)*e^(e^8) + 4)/x

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giac [B]  time = 0.14, size = 50, normalized size = 2.50 $$\begin{array}{c}{x}^3{e}^{\left(2e^8\right)}-4x^2{e}^{\left(2e^8\right)}+6x{e}^{\left(2e^8\right)}-4x{e}^{\left(e^8\right)}+\frac{e^{\left(2e^8\right)}-4e^{\left(e^8\right)}+4}{x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x^4-8*x^3+6*x^2-1)*exp(exp(2)^4)^2+(-4*x^2+4)*exp(exp(2)^4)-4)/x^2,x, algorithm="giac")

[Out]

x^3*e^(2*e^8) - 4*x^2*e^(2*e^8) + 6*x*e^(2*e^8) - 4*x*e^(e^8) + (e^(2*e^8) - 4*e^(e^8) + 4)/x

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maple [B]  time = 0.06, size = 54, normalized size = 2.70

method	result	size
default	${\mathrm{e}}^{2{\mathrm{e}}^8}{x}^3-4{\mathrm{e}}^{2{\mathrm{e}}^8}{x}^2+6{\mathrm{e}}^{2{\mathrm{e}}^8}x-4{\mathrm{e}}^{{\mathrm{e}}^8}x-\frac{-{\mathrm{e}}^{2{\mathrm{e}}^8}+4{\mathrm{e}}^{{\mathrm{e}}^8}-4}{x}$	$54$
risch	${\mathrm{e}}^{2{\mathrm{e}}^8}{x}^3-4{\mathrm{e}}^{2{\mathrm{e}}^8}{x}^2+6{\mathrm{e}}^{2{\mathrm{e}}^8}x-4{\mathrm{e}}^{{\mathrm{e}}^8}x+\frac{{\mathrm{e}}^{2{\mathrm{e}}^8}}{x}-\frac{4{\mathrm{e}}^{{\mathrm{e}}^8}}{x}+\frac{4}{x}$	$57$
norman	$\frac{{\mathrm{e}}^{2{\mathrm{e}}^8}{x}^4-4{\mathrm{e}}^{2{\mathrm{e}}^8}{x}^3+(6{\mathrm{e}}^{2{\mathrm{e}}^8}-4{\mathrm{e}}^{{\mathrm{e}}^8})x^2+4+{\mathrm{e}}^{2{\mathrm{e}}^8}-4{\mathrm{e}}^{{\mathrm{e}}^8}}{x}$	$65$
gosper	$\frac{{\mathrm{e}}^{2{\mathrm{e}}^8}{x}^4-4{\mathrm{e}}^{2{\mathrm{e}}^8}{x}^3+6{\mathrm{e}}^{2{\mathrm{e}}^8}{x}^2-4{\mathrm{e}}^{{\mathrm{e}}^8}{x}^2+{\mathrm{e}}^{2{\mathrm{e}}^8}-4{\mathrm{e}}^{{\mathrm{e}}^8}+4}{x}$	$66$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((3*x^4-8*x^3+6*x^2-1)*exp(exp(2)^4)^2+(-4*x^2+4)*exp(exp(2)^4)-4)/x^2,x,method=_RETURNVERBOSE)

[Out]

exp(2*exp(8))*x^3-4*exp(2*exp(8))*x^2+6*exp(2*exp(8))*x-4*exp(exp(8))*x-(-exp(2*exp(8))+4*exp(exp(8))-4)/x

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maxima [B]  time = 0.37, size = 52, normalized size = 2.60 $$\begin{array}{c}{x}^3{e}^{\left(2e^8\right)}-4x^2{e}^{\left(2e^8\right)}+2x(3e^{\left(2e^8\right)}-2e^{\left(e^8\right)})+\frac{e^{\left(2e^8\right)}-4e^{\left(e^8\right)}+4}{x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x^4-8*x^3+6*x^2-1)*exp(exp(2)^4)^2+(-4*x^2+4)*exp(exp(2)^4)-4)/x^2,x, algorithm="maxima")

[Out]

x^3*e^(2*e^8) - 4*x^2*e^(2*e^8) + 2*x*(3*e^(2*e^8) - 2*e^(e^8)) + (e^(2*e^8) - 4*e^(e^8) + 4)/x

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mupad [B]  time = 4.34, size = 49, normalized size = 2.45 $$\begin{array}{c}{x}^3{\mathrm{e}}^{2{\mathrm{e}}^8}-4x^2{\mathrm{e}}^{2{\mathrm{e}}^8}+\frac{{\mathrm{e}}^{2{\mathrm{e}}^8}-4{\mathrm{e}}^{{\mathrm{e}}^8}+4}{x}+2x{\mathrm{e}}^{{\mathrm{e}}^8}(3{\mathrm{e}}^{{\mathrm{e}}^8}-2)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(exp(8))*(4*x^2 - 4) - exp(2*exp(8))*(6*x^2 - 8*x^3 + 3*x^4 - 1) + 4)/x^2,x)

[Out]

x^3*exp(2*exp(8)) - 4*x^2*exp(2*exp(8)) + (exp(2*exp(8)) - 4*exp(exp(8)) + 4)/x + 2*x*exp(exp(8))*(3*exp(exp(8
)) - 2)

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sympy [B]  time = 0.17, size = 54, normalized size = 2.70 $$\begin{array}{c}{x}^3{e}^{2e^8}-4x^2{e}^{2e^8}+x(-4e^{e^8}+6e^{2e^8})+\frac{4-4e^{e^8}+e^{2e^8}}{x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x**4-8*x**3+6*x**2-1)*exp(exp(2)**4)**2+(-4*x**2+4)*exp(exp(2)**4)-4)/x**2,x)

[Out]

x**3*exp(2*exp(8)) - 4*x**2*exp(2*exp(8)) + x*(-4*exp(exp(8)) + 6*exp(2*exp(8))) + (4 - 4*exp(exp(8)) + exp(2*
exp(8)))/x

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