\(\int \frac {-3+400 e^{e^5}-2 x^2}{x^2} \, dx\) [7774]

Optimal result

Integrand size = 18, antiderivative size = 27 \[ \int \frac {-3+400 e^{e^5}-2 x^2}{x^2} \, dx=4+16 \left (4+e^{e^5} \left (3-\frac {25}{x}\right )\right )+\frac {3}{x}-2 x \]

[Out]

68+3/x+16*(3-25/x)*exp(exp(5))-2*x

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.63, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {14} \[ \int \frac {-3+400 e^{e^5}-2 x^2}{x^2} \, dx=\frac {3-400 e^{e^5}}{x}-2 x \]

[In]

Int[(-3 + 400*E^E^5 - 2*x^2)/x^2,x]

[Out]

(3 - 400*E^E^5)/x - 2*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}& = \int \left (-2+\frac {-3+400 e^{e^5}}{x^2}\right ) \, dx \\ & = \frac {3-400 e^{e^5}}{x}-2 x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.67 \[ \int \frac {-3+400 e^{e^5}-2 x^2}{x^2} \, dx=-\frac {-3+400 e^{e^5}}{x}-2 x \]

[In]

Integrate[(-3 + 400*E^E^5 - 2*x^2)/x^2,x]

[Out]

-((-3 + 400*E^E^5)/x) - 2*x

Maple [A] (verified)

Time = 0.04 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.63

method	result	size
default	\(-2 x -\frac {400 \,{\mathrm e}^{{\mathrm e}^{5}}-3}{x}\)	\(17\)
norman	\(\frac {-2 x^{2}+3-400 \,{\mathrm e}^{{\mathrm e}^{5}}}{x}\)	\(17\)
gosper	\(-\frac {2 x^{2}+400 \,{\mathrm e}^{{\mathrm e}^{5}}-3}{x}\)	\(18\)
risch	\(-2 x -\frac {400 \,{\mathrm e}^{{\mathrm e}^{5}}}{x}+\frac {3}{x}\)	\(18\)
parallelrisch	\(-\frac {2 x^{2}+400 \,{\mathrm e}^{{\mathrm e}^{5}}-3}{x}\)	\(18\)

[In]

int((400*exp(exp(5))-2*x^2-3)/x^2,x,method=_RETURNVERBOSE)

[Out]

-2*x-(400*exp(exp(5))-3)/x

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.63 \[ \int \frac {-3+400 e^{e^5}-2 x^2}{x^2} \, dx=-\frac {2 \, x^{2} + 400 \, e^{\left (e^{5}\right )} - 3}{x} \]

[In]

integrate((400*exp(exp(5))-2*x^2-3)/x^2,x, algorithm="fricas")

[Out]

-(2*x^2 + 400*e^(e^5) - 3)/x

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.52 \[ \int \frac {-3+400 e^{e^5}-2 x^2}{x^2} \, dx=- 2 x - \frac {-3 + 400 e^{e^{5}}}{x} \]

[In]

integrate((400*exp(exp(5))-2*x**2-3)/x**2,x)

[Out]

-2*x - (-3 + 400*exp(exp(5)))/x

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.59 \[ \int \frac {-3+400 e^{e^5}-2 x^2}{x^2} \, dx=-2 \, x - \frac {400 \, e^{\left (e^{5}\right )} - 3}{x} \]

[In]

integrate((400*exp(exp(5))-2*x^2-3)/x^2,x, algorithm="maxima")

[Out]

-2*x - (400*e^(e^5) - 3)/x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.59 \[ \int \frac {-3+400 e^{e^5}-2 x^2}{x^2} \, dx=-2 \, x - \frac {400 \, e^{\left (e^{5}\right )} - 3}{x} \]

[In]

integrate((400*exp(exp(5))-2*x^2-3)/x^2,x, algorithm="giac")

[Out]

-2*x - (400*e^(e^5) - 3)/x

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.59 \[ \int \frac {-3+400 e^{e^5}-2 x^2}{x^2} \, dx=-2\,x-\frac {400\,{\mathrm {e}}^{{\mathrm {e}}^5}-3}{x} \]

[In]

int(-(2*x^2 - 400*exp(exp(5)) + 3)/x^2,x)

[Out]

- 2*x - (400*exp(exp(5)) - 3)/x