\(\int \frac {3 e^{e^{-e} (4+5 e^e)}-10 x^2}{10 x^2} \, dx\) [5871]

Optimal result

Integrand size = 30, antiderivative size = 25 \[ \int \frac {3 e^{e^{-e} \left (4+5 e^e\right )}-10 x^2}{10 x^2} \, dx=6-\frac {3 e^{5+4 e^{-e}}}{10 x}-x+\log (2) \]

[Out]

6+ln(2)-x-3/10*exp(5+4/exp(exp(1)))/x

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.88, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12, 14} \[ \int \frac {3 e^{e^{-e} \left (4+5 e^e\right )}-10 x^2}{10 x^2} \, dx=-x-\frac {3 e^{5+4 e^{-e}}}{10 x} \]

[In]

Int[(3*E^((4 + 5*E^E)/E^E) - 10*x^2)/(10*x^2),x]

[Out]

(-3*E^(5 + 4/E^E))/(10*x) - x

Rule 12

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

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{align*} \text {integral}& = \frac {1}{10} \int \frac {3 e^{e^{-e} \left (4+5 e^e\right )}-10 x^2}{x^2} \, dx \\ & = \frac {1}{10} \int \left (-10+\frac {3 e^{5+4 e^{-e}}}{x^2}\right ) \, dx \\ & = -\frac {3 e^{5+4 e^{-e}}}{10 x}-x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.88 \[ \int \frac {3 e^{e^{-e} \left (4+5 e^e\right )}-10 x^2}{10 x^2} \, dx=-\frac {3 e^{5+4 e^{-e}}}{10 x}-x \]

[In]

Integrate[(3*E^((4 + 5*E^E)/E^E) - 10*x^2)/(10*x^2),x]

[Out]

(-3*E^(5 + 4/E^E))/(10*x) - x

Maple [A] (verified)

Time = 0.08 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.80

method	result	size
risch	\(-x -\frac {3 \,{\mathrm e}^{5+4 \,{\mathrm e}^{-{\mathrm e}}}}{10 x}\)	\(20\)
default	\(-x -\frac {3 \,{\mathrm e}^{\left (5 \,{\mathrm e}^{{\mathrm e}}+4\right ) {\mathrm e}^{-{\mathrm e}}}}{10 x}\)	\(24\)
gosper	\(-\frac {10 x^{2}+3 \,{\mathrm e}^{\left (5 \,{\mathrm e}^{{\mathrm e}}+4\right ) {\mathrm e}^{-{\mathrm e}}}}{10 x}\)	\(28\)
parallelrisch	\(-\frac {10 x^{2}+3 \,{\mathrm e}^{\left (5 \,{\mathrm e}^{{\mathrm e}}+4\right ) {\mathrm e}^{-{\mathrm e}}}}{10 x}\)	\(28\)

[In]

int(1/10*(3*exp((5*exp(exp(1))+4)/exp(exp(1)))-10*x^2)/x^2,x,method=_RETURNVERBOSE)

[Out]

-x-3/10/x*exp(5+4*exp(-exp(1)))

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {3 e^{e^{-e} \left (4+5 e^e\right )}-10 x^2}{10 x^2} \, dx=-\frac {10 \, x^{2} + 3 \, e^{\left ({\left (5 \, e^{e} + 4\right )} e^{\left (-e\right )}\right )}}{10 \, x} \]

[In]

integrate(1/10*(3*exp((5*exp(exp(1))+4)/exp(exp(1)))-10*x^2)/x^2,x, algorithm="fricas")

[Out]

-1/10*(10*x^2 + 3*e^((5*e^e + 4)*e^(-e)))/x

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.76 \[ \int \frac {3 e^{e^{-e} \left (4+5 e^e\right )}-10 x^2}{10 x^2} \, dx=- x - \frac {3 e^{5} e^{\frac {4}{e^{e}}}}{10 x} \]

[In]

integrate(1/10*(3*exp((5*exp(exp(1))+4)/exp(exp(1)))-10*x**2)/x**2,x)

[Out]

-x - 3*exp(5)*exp(4*exp(-E))/(10*x)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92 \[ \int \frac {3 e^{e^{-e} \left (4+5 e^e\right )}-10 x^2}{10 x^2} \, dx=-x - \frac {3 \, e^{\left ({\left (5 \, e^{e} + 4\right )} e^{\left (-e\right )}\right )}}{10 \, x} \]

[In]

integrate(1/10*(3*exp((5*exp(exp(1))+4)/exp(exp(1)))-10*x^2)/x^2,x, algorithm="maxima")

[Out]

-x - 3/10*e^((5*e^e + 4)*e^(-e))/x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92 \[ \int \frac {3 e^{e^{-e} \left (4+5 e^e\right )}-10 x^2}{10 x^2} \, dx=-x - \frac {3 \, e^{\left ({\left (5 \, e^{e} + 4\right )} e^{\left (-e\right )}\right )}}{10 \, x} \]

[In]

integrate(1/10*(3*exp((5*exp(exp(1))+4)/exp(exp(1)))-10*x^2)/x^2,x, algorithm="giac")

[Out]

-x - 3/10*e^((5*e^e + 4)*e^(-e))/x

Mupad [B] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.76 \[ \int \frac {3 e^{e^{-e} \left (4+5 e^e\right )}-10 x^2}{10 x^2} \, dx=-x-\frac {3\,{\mathrm {e}}^{4\,{\mathrm {e}}^{-\mathrm {e}}+5}}{10\,x} \]

[In]

int(((3*exp(exp(-exp(1))*(5*exp(exp(1)) + 4)))/10 - x^2)/x^2,x)

[Out]

- x - (3*exp(4*exp(-exp(1)) + 5))/(10*x)