3.11.59 \(\int \frac {e^x (3-3 x)}{x^2} \, dx\)

Optimal. Leaf size=18 \[ -\frac {3 e^x}{x}+130 \left (5+e^3+\log (2)\right ) \]

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Rubi [A]  time = 0.02, antiderivative size = 8, normalized size of antiderivative = 0.44, number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {2197} \begin {gather*} -\frac {3 e^x}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^x*(3 - 3*x))/x^2,x]

[Out]

(-3*E^x)/x

Rule 2197

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 {gather*} \begin {aligned} \text {integral} &=-\frac {3 e^x}{x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 0.44 \begin {gather*} -\frac {3 e^x}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^x*(3 - 3*x))/x^2,x]

[Out]

(-3*E^x)/x

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fricas [A]  time = 0.73, size = 7, normalized size = 0.39 \begin {gather*} -\frac {3 \, e^{x}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*e^x/x

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giac [A]  time = 0.27, size = 7, normalized size = 0.39 \begin {gather*} -\frac {3 \, e^{x}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*e^x/x

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maple [A]  time = 0.04, size = 8, normalized size = 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	\(-\frac {3 \,{\mathrm e}^{x}}{x}\)	\(8\)
meijerg	\(-3+\frac {3 x +3}{x}-\frac {3 \,{\mathrm e}^{x}}{x}-\frac {3}{x}\)	\(25\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*exp(x)/x

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maxima [C]  time = 0.41, size = 12, normalized size = 0.67 \begin {gather*} -3 \, {\rm Ei}\relax (x) + 3 \, \Gamma \left (-1, -x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*Ei(x) + 3*gamma(-1, -x)

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mupad [B]  time = 0.03, size = 7, normalized size = 0.39 \begin {gather*} -\frac {3\,{\mathrm {e}}^x}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(x)*(3*x - 3))/x^2,x)

[Out]

-(3*exp(x))/x

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sympy [A]  time = 0.08, size = 7, normalized size = 0.39 \begin {gather*} - \frac {3 e^{x}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*exp(x)/x

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