3.63.54 \(\int \frac {27 e^{17}-4 x^2}{6 x^2} \, dx\)

Optimal. Leaf size=17 \[ 21-\frac {9 e^{17}}{2 x}-\frac {2 x}{3} \]

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Rubi [A]  time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 14} \begin {gather*} -\frac {2 x}{3}-\frac {9 e^{17}}{2 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(27*E^17 - 4*x^2)/(6*x^2),x]

[Out]

(-9*E^17)/(2*x) - (2*x)/3

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, 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 {gather*} \begin {aligned} \text {integral} &=\frac {1}{6} \int \frac {27 e^{17}-4 x^2}{x^2} \, dx\\ &=\frac {1}{6} \int \left (-4+\frac {27 e^{17}}{x^2}\right ) \, dx\\ &=-\frac {9 e^{17}}{2 x}-\frac {2 x}{3}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 16, normalized size = 0.94 \begin {gather*} -\frac {9 e^{17}}{2 x}-\frac {2 x}{3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(27*E^17 - 4*x^2)/(6*x^2),x]

[Out]

(-9*E^17)/(2*x) - (2*x)/3

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fricas [A]  time = 0.55, size = 15, normalized size = 0.88 \begin {gather*} -\frac {4 \, x^{2} + 27 \, e^{17}}{6 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/6*(27*exp(17)-4*x^2)/x^2,x, algorithm="fricas")

[Out]

-1/6*(4*x^2 + 27*e^17)/x

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giac [A]  time = 0.73, size = 11, normalized size = 0.65 \begin {gather*} -\frac {2}{3} \, x - \frac {9 \, e^{17}}{2 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/6*(27*exp(17)-4*x^2)/x^2,x, algorithm="giac")

[Out]

-2/3*x - 9/2*e^17/x

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maple [A]  time = 0.05, size = 12, normalized size = 0.71

method	result	size
default	\(-\frac {2 x}{3}-\frac {9 \,{\mathrm e}^{17}}{2 x}\)	\(12\)
risch	\(-\frac {2 x}{3}-\frac {9 \,{\mathrm e}^{17}}{2 x}\)	\(12\)
norman	\(\frac {-\frac {2 x^{2}}{3}-\frac {9 \,{\mathrm e}^{17}}{2}}{x}\)	\(15\)
gosper	\(-\frac {4 x^{2}+27 \,{\mathrm e}^{17}}{6 x}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/6*(27*exp(17)-4*x^2)/x^2,x,method=_RETURNVERBOSE)

[Out]

-2/3*x-9/2/x*exp(17)

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maxima [A]  time = 0.39, size = 11, normalized size = 0.65 \begin {gather*} -\frac {2}{3} \, x - \frac {9 \, e^{17}}{2 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/6*(27*exp(17)-4*x^2)/x^2,x, algorithm="maxima")

[Out]

-2/3*x - 9/2*e^17/x

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mupad [B]  time = 4.02, size = 11, normalized size = 0.65 \begin {gather*} -\frac {2\,x}{3}-\frac {9\,{\mathrm {e}}^{17}}{2\,x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((9*exp(17))/2 - (2*x^2)/3)/x^2,x)

[Out]

- (2*x)/3 - (9*exp(17))/(2*x)

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sympy [A]  time = 0.08, size = 14, normalized size = 0.82 \begin {gather*} - \frac {2 x}{3} - \frac {9 e^{17}}{2 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/6*(27*exp(17)-4*x**2)/x**2,x)

[Out]

-2*x/3 - 9*exp(17)/(2*x)

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