3.50.24 \(\int -\frac {3 e^{18}}{4 x^4} \, dx\)

Optimal. Leaf size=10 \[ \frac {e^{18}}{4 x^3} \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 30} \begin {gather*} \frac {e^{18}}{4 x^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-3*E^18)/(4*x^4),x]

[Out]

E^18/(4*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 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 (\frac {1}{4} \left (3 e^{18}\right ) \int \frac {1}{x^4} \, dx\right )\\ &=\frac {e^{18}}{4 x^3}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} \frac {e^{18}}{4 x^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-3*E^18)/(4*x^4),x]

[Out]

E^18/(4*x^3)

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fricas [A]  time = 0.77, size = 7, normalized size = 0.70 \begin {gather*} \frac {e^{18}}{4 \, x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/4*exp(9)^2/x^4,x, algorithm="fricas")

[Out]

1/4*e^18/x^3

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giac [A]  time = 0.12, size = 7, normalized size = 0.70 \begin {gather*} \frac {e^{18}}{4 \, x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/4*exp(9)^2/x^4,x, algorithm="giac")

[Out]

1/4*e^18/x^3

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maple [A]  time = 0.03, size = 8, normalized size = 0.80

method	result	size
risch	\(\frac {{\mathrm e}^{18}}{4 x^{3}}\)	\(8\)
gosper	\(\frac {{\mathrm e}^{18}}{4 x^{3}}\)	\(10\)
default	\(\frac {{\mathrm e}^{18}}{4 x^{3}}\)	\(10\)
norman	\(\frac {{\mathrm e}^{18}}{4 x^{3}}\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-3/4*exp(9)^2/x^4,x,method=_RETURNVERBOSE)

[Out]

1/4/x^3*exp(18)

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maxima [A]  time = 0.35, size = 7, normalized size = 0.70 \begin {gather*} \frac {e^{18}}{4 \, x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/4*exp(9)^2/x^4,x, algorithm="maxima")

[Out]

1/4*e^18/x^3

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mupad [B]  time = 0.02, size = 7, normalized size = 0.70 \begin {gather*} \frac {{\mathrm {e}}^{18}}{4\,x^3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(3*exp(18))/(4*x^4),x)

[Out]

exp(18)/(4*x^3)

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sympy [A]  time = 0.06, size = 7, normalized size = 0.70 \begin {gather*} \frac {e^{18}}{4 x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/4*exp(9)**2/x**4,x)

[Out]

exp(18)/(4*x**3)

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