3.41.98 \(\int \frac {3 e^4 \log (2)}{2 x^2} \, dx\)

Optimal. Leaf size=14 \[ -3-\frac {3 e^4 \log (2)}{2 x} \]

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Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 0.86, number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 30} \begin {gather*} -\frac {3 e^4 \log (2)}{2 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(3*E^4*Log[2])/(2*x^2),x]

[Out]

(-3*E^4*Log[2])/(2*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} &=\frac {1}{2} \left (3 e^4 \log (2)\right ) \int \frac {1}{x^2} \, dx\\ &=-\frac {3 e^4 \log (2)}{2 x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 0.86 \begin {gather*} -\frac {e^4 \log (8)}{2 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3*E^4*Log[2])/(2*x^2),x]

[Out]

-1/2*(E^4*Log[8])/x

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fricas [A]  time = 0.47, size = 9, normalized size = 0.64 \begin {gather*} -\frac {3 \, e^{4} \log \relax (2)}{2 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3/2*e^4*log(2)/x

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giac [A]  time = 0.21, size = 9, normalized size = 0.64 \begin {gather*} -\frac {3 \, e^{4} \log \relax (2)}{2 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3/2*e^4*log(2)/x

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maple [A]  time = 0.02, size = 10, normalized size = 0.71

method	result	size
gosper	\(-\frac {3 \,{\mathrm e}^{4} \ln \relax (2)}{2 x}\)	\(10\)
default	\(-\frac {3 \,{\mathrm e}^{4} \ln \relax (2)}{2 x}\)	\(10\)
norman	\(-\frac {3 \,{\mathrm e}^{4} \ln \relax (2)}{2 x}\)	\(10\)
risch	\(-\frac {3 \,{\mathrm e}^{4} \ln \relax (2)}{2 x}\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3/2*exp(4)/x*ln(2)

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maxima [A]  time = 0.36, size = 9, normalized size = 0.64 \begin {gather*} -\frac {3 \, e^{4} \log \relax (2)}{2 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3/2*e^4*log(2)/x

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mupad [B]  time = 2.97, size = 9, normalized size = 0.64 \begin {gather*} -\frac {3\,{\mathrm {e}}^4\,\ln \relax (2)}{2\,x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*exp(4)*log(2))/(2*x^2),x)

[Out]

-(3*exp(4)*log(2))/(2*x)

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sympy [A]  time = 0.05, size = 12, normalized size = 0.86 \begin {gather*} - \frac {3 e^{4} \log {\relax (2 )}}{2 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*exp(4)*log(2)/(2*x)

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