3.83.60 \(\int \frac {e^{15/x} (60-15 x+x^2)}{x^2} \, dx\)

Optimal. Leaf size=11 \[ e^{15/x} (-4+x) \]

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Rubi [A]  time = 0.03, antiderivative size = 14, normalized size of antiderivative = 1.27, number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {2288} \begin {gather*} -e^{15/x} (4-x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^(15/x)*(60 - 15*x + x^2))/x^2,x]

[Out]

-(E^(15/x)*(4 - x))

Rule 2288

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = (v*y)/(Log[F]*D[u, x])}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-e^{15/x} (4-x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 11, normalized size = 1.00 \begin {gather*} e^{15/x} (-4+x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(15/x)*(60 - 15*x + x^2))/x^2,x]

[Out]

E^(15/x)*(-4 + x)

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fricas [A]  time = 0.51, size = 10, normalized size = 0.91 \begin {gather*} {\left (x - 4\right )} e^{\frac {15}{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^2-15*x+60)*exp(15/x)/x^2,x, algorithm="fricas")

[Out]

(x - 4)*e^(15/x)

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giac [B]  time = 0.24, size = 23, normalized size = 2.09 \begin {gather*} -x {\left (\frac {4 \, e^{\frac {15}{x}}}{x} - e^{\frac {15}{x}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^2-15*x+60)*exp(15/x)/x^2,x, algorithm="giac")

[Out]

-x*(4*e^(15/x)/x - e^(15/x))

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maple [A]  time = 0.12, size = 11, normalized size = 1.00

method	result	size
gosper	\(\left (x -4\right ) {\mathrm e}^{\frac {15}{x}}\)	\(11\)
risch	\(\left (x -4\right ) {\mathrm e}^{\frac {15}{x}}\)	\(11\)
derivativedivides	\({\mathrm e}^{\frac {15}{x}} x -4 \,{\mathrm e}^{\frac {15}{x}}\)	\(18\)
default	\({\mathrm e}^{\frac {15}{x}} x -4 \,{\mathrm e}^{\frac {15}{x}}\)	\(18\)
norman	\(\frac {x^{2} {\mathrm e}^{\frac {15}{x}}-4 \,{\mathrm e}^{\frac {15}{x}} x}{x}\)	\(25\)
meijerg	\(x +19-\frac {x \left (2+\frac {30}{x}\right )}{2}+{\mathrm e}^{\frac {15}{x}} x -4 \,{\mathrm e}^{\frac {15}{x}}\)	\(30\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x^2-15*x+60)*exp(15/x)/x^2,x,method=_RETURNVERBOSE)

[Out]

(x-4)*exp(15/x)

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maxima [C]  time = 0.38, size = 26, normalized size = 2.36 \begin {gather*} 15 \, {\rm Ei}\left (\frac {15}{x}\right ) - 4 \, e^{\frac {15}{x}} - 15 \, \Gamma \left (-1, -\frac {15}{x}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^2-15*x+60)*exp(15/x)/x^2,x, algorithm="maxima")

[Out]

15*Ei(15/x) - 4*e^(15/x) - 15*gamma(-1, -15/x)

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mupad [B]  time = 4.81, size = 10, normalized size = 0.91 \begin {gather*} {\mathrm {e}}^{15/x}\,\left (x-4\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(15/x)*(x^2 - 15*x + 60))/x^2,x)

[Out]

exp(15/x)*(x - 4)

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sympy [A]  time = 0.11, size = 7, normalized size = 0.64 \begin {gather*} \left (x - 4\right ) e^{\frac {15}{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x**2-15*x+60)*exp(15/x)/x**2,x)

[Out]

(x - 4)*exp(15/x)

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