3.22.87 \(\int \frac {e^{6-2 x} (-80-160 x)}{x^2} \, dx\)

Optimal. Leaf size=14 \[ 5+\frac {80 e^{6-2 x}}{x} \]

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Rubi [A]  time = 0.03, antiderivative size = 12, normalized size of antiderivative = 0.86, number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {2197} \begin {gather*} \frac {80 e^{6-2 x}}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^(6 - 2*x)*(-80 - 160*x))/x^2,x]

[Out]

(80*E^(6 - 2*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 {80 e^{6-2 x}}{x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 12, normalized size = 0.86 \begin {gather*} \frac {80 e^{6-2 x}}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(6 - 2*x)*(-80 - 160*x))/x^2,x]

[Out]

(80*E^(6 - 2*x))/x

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fricas [A]  time = 0.67, size = 11, normalized size = 0.79 \begin {gather*} \frac {80 \, e^{\left (-2 \, x + 6\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-160*x-80)*exp(3-x)^2/x^2,x, algorithm="fricas")

[Out]

80*e^(-2*x + 6)/x

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giac [A]  time = 0.16, size = 11, normalized size = 0.79 \begin {gather*} \frac {80 \, e^{\left (-2 \, x + 6\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-160*x-80)*exp(3-x)^2/x^2,x, algorithm="giac")

[Out]

80*e^(-2*x + 6)/x

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maple [A]  time = 0.06, size = 12, normalized size = 0.86

method	result	size
risch	\(\frac {80 \,{\mathrm e}^{6-2 x}}{x}\)	\(12\)
gosper	\(\frac {80 \,{\mathrm e}^{6-2 x}}{x}\)	\(14\)
derivativedivides	\(\frac {80 \,{\mathrm e}^{6-2 x}}{x}\)	\(14\)
default	\(\frac {80 \,{\mathrm e}^{6-2 x}}{x}\)	\(14\)
norman	\(\frac {80 \,{\mathrm e}^{6-2 x}}{x}\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-160*x-80)*exp(3-x)^2/x^2,x,method=_RETURNVERBOSE)

[Out]

80*exp(6-2*x)/x

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maxima [C]  time = 0.42, size = 18, normalized size = 1.29 \begin {gather*} -160 \, {\rm Ei}\left (-2 \, x\right ) e^{6} + 160 \, e^{6} \Gamma \left (-1, 2 \, x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-160*x-80)*exp(3-x)^2/x^2,x, algorithm="maxima")

[Out]

-160*Ei(-2*x)*e^6 + 160*e^6*gamma(-1, 2*x)

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mupad [B]  time = 1.23, size = 11, normalized size = 0.79 \begin {gather*} \frac {80\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^6}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(6 - 2*x)*(160*x + 80))/x^2,x)

[Out]

(80*exp(-2*x)*exp(6))/x

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sympy [A]  time = 0.09, size = 8, normalized size = 0.57 \begin {gather*} \frac {80 e^{6 - 2 x}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-160*x-80)*exp(3-x)**2/x**2,x)

[Out]

80*exp(6 - 2*x)/x

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