\(\int \frac {e^x (3-3 x)}{x^2} \, dx\) [1059]

Optimal result

Integrand size = 12, antiderivative size = 18 \[ \int \frac {e^x (3-3 x)}{x^2} \, dx=-\frac {3 e^x}{x}+130 \left (5+e^3+\log (2)\right ) \]

[Out]

130*exp(3)+130*ln(2)+650-3*exp(x)/x

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.44, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {2228} \[ \int \frac {e^x (3-3 x)}{x^2} \, dx=-\frac {3 e^x}{x} \]

[In]

Int[(E^x*(3 - 3*x))/x^2,x]

[Out]

(-3*E^x)/x

Rule 2228

Int[(F_)^((c_.)*(v_))*(u_)^(m_.)*(w_), x_Symbol] :> With[{b = Coefficient[v, x, 1], d = Coefficient[u, x, 0],
e = Coefficient[u, x, 1], f = Coefficient[w, x, 0], g = Coefficient[w, x, 1]}, Simp[g*u^(m + 1)*(F^(c*v)/(b*c*
e*Log[F])), x] /; EqQ[e*g*(m + 1) - b*c*(e*f - d*g)*Log[F], 0]] /; FreeQ[{F, c, m}, x] && LinearQ[{u, v, w}, x
]

Rubi steps \begin{align*} \text {integral}& = -\frac {3 e^x}{x} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.44 \[ \int \frac {e^x (3-3 x)}{x^2} \, dx=-\frac {3 e^x}{x} \]

[In]

Integrate[(E^x*(3 - 3*x))/x^2,x]

[Out]

(-3*E^x)/x

Maple [A] (verified)

Time = 0.06 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.44

method	result	size
gosper	\(-\frac {3 \,{\mathrm e}^{x}}{x}\)	\(8\)
default	\(-\frac {3 \,{\mathrm e}^{x}}{x}\)	\(8\)
norman	\(-\frac {3 \,{\mathrm e}^{x}}{x}\)	\(8\)
risch	\(-\frac {3 \,{\mathrm e}^{x}}{x}\)	\(8\)
parallelrisch	\(-\frac {3 \,{\mathrm e}^{x}}{x}\)	\(8\)
meijerg	\(-3-\frac {3}{x}+\frac {3 x +3}{x}-\frac {3 \,{\mathrm e}^{x}}{x}\)	\(25\)

[In]

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

[Out]

-3*exp(x)/x

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.39 \[ \int \frac {e^x (3-3 x)}{x^2} \, dx=-\frac {3 \, e^{x}}{x} \]

[In]

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

[Out]

-3*e^x/x

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.39 \[ \int \frac {e^x (3-3 x)}{x^2} \, dx=- \frac {3 e^{x}}{x} \]

[In]

integrate((-3*x+3)*exp(x)/x**2,x)

[Out]

-3*exp(x)/x

Maxima [C] (verification not implemented)

Result contains higher order function than in optimal. Order 4 vs. order 3.

Time = 0.21 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.67 \[ \int \frac {e^x (3-3 x)}{x^2} \, dx=-3 \, {\rm Ei}\left (x\right ) + 3 \, \Gamma \left (-1, -x\right ) \]

[In]

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

[Out]

-3*Ei(x) + 3*gamma(-1, -x)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.39 \[ \int \frac {e^x (3-3 x)}{x^2} \, dx=-\frac {3 \, e^{x}}{x} \]

[In]

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

[Out]

-3*e^x/x

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.39 \[ \int \frac {e^x (3-3 x)}{x^2} \, dx=-\frac {3\,{\mathrm {e}}^x}{x} \]

[In]

int(-(exp(x)*(3*x - 3))/x^2,x)

[Out]

-(3*exp(x))/x