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

Optimal. Leaf size=17 \[ 2 \left (\frac {e^4}{4 x^2}-11 \log (3)\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.59, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 30} \begin {gather*} \frac {e^4}{2 x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-(E^4/x^3),x]

[Out]

E^4/(2*x^2)

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

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.59 \begin {gather*} \frac {e^4}{2 x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-(E^4/x^3),x]

[Out]

E^4/(2*x^2)

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fricas [A]  time = 0.52, size = 7, normalized size = 0.41 \begin {gather*} \frac {e^{4}}{2 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*e^4/x^2

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giac [A]  time = 0.14, size = 7, normalized size = 0.41 \begin {gather*} \frac {e^{4}}{2 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*e^4/x^2

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maple [A]  time = 0.01, size = 8, normalized size = 0.47

method	result	size
gosper	\(\frac {{\mathrm e}^{4}}{2 x^{2}}\)	\(8\)
default	\(\frac {{\mathrm e}^{4}}{2 x^{2}}\)	\(8\)
norman	\(\frac {{\mathrm e}^{4}}{2 x^{2}}\)	\(8\)
risch	\(\frac {{\mathrm e}^{4}}{2 x^{2}}\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*exp(4)/x^2

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maxima [A]  time = 0.41, size = 7, normalized size = 0.41 \begin {gather*} \frac {e^{4}}{2 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*e^4/x^2

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mupad [B]  time = 0.04, size = 7, normalized size = 0.41 \begin {gather*} \frac {{\mathrm {e}}^4}{2\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(4)/x^3,x)

[Out]

exp(4)/(2*x^2)

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sympy [A]  time = 0.05, size = 7, normalized size = 0.41 \begin {gather*} \frac {e^{4}}{2 x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(4)/(2*x**2)

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