3.54.42 \(\int \frac {4-e^3}{x^2} \, dx\)

Optimal. Leaf size=9 \[ \frac {-4+e^3}{x} \]

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Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.33, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 30} \begin {gather*} -\frac {4-e^3}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(4 - E^3)/x^2,x]

[Out]

-((4 - E^3)/x)

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\left (4-e^3\right ) \int \frac {1}{x^2} \, dx\\ &=-\frac {4-e^3}{x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 1.33 \begin {gather*} -\frac {4-e^3}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(4 - E^3)/x^2,x]

[Out]

-((4 - E^3)/x)

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fricas [A]  time = 0.63, size = 8, normalized size = 0.89 \begin {gather*} \frac {e^{3} - 4}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4-exp(3))/x^2,x, algorithm="fricas")

[Out]

(e^3 - 4)/x

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giac [A]  time = 0.15, size = 8, normalized size = 0.89 \begin {gather*} \frac {e^{3} - 4}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4-exp(3))/x^2,x, algorithm="giac")

[Out]

(e^3 - 4)/x

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maple [A]  time = 0.02, size = 9, normalized size = 1.00

method	result	size
gosper	\(\frac {{\mathrm e}^{3}-4}{x}\)	\(9\)
norman	\(\frac {{\mathrm e}^{3}-4}{x}\)	\(9\)
default	\(-\frac {4-{\mathrm e}^{3}}{x}\)	\(12\)
risch	\(-\frac {4}{x}+\frac {{\mathrm e}^{3}}{x}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4-exp(3))/x^2,x,method=_RETURNVERBOSE)

[Out]

(exp(3)-4)/x

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maxima [A]  time = 0.43, size = 8, normalized size = 0.89 \begin {gather*} \frac {e^{3} - 4}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4-exp(3))/x^2,x, algorithm="maxima")

[Out]

(e^3 - 4)/x

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mupad [B]  time = 3.38, size = 8, normalized size = 0.89 \begin {gather*} \frac {{\mathrm {e}}^3-4}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(3) - 4)/x^2,x)

[Out]

(exp(3) - 4)/x

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sympy [A]  time = 0.05, size = 7, normalized size = 0.78 \begin {gather*} - \frac {4 - e^{3}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4-exp(3))/x**2,x)

[Out]

-(4 - exp(3))/x

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