\(\int \frac {3 e^4 \log (2)}{2 x^2} \, dx\) [4098]

Optimal result

Integrand size = 12, antiderivative size = 14 \[ \int \frac {3 e^4 \log (2)}{2 x^2} \, dx=-3-\frac {3 e^4 \log (2)}{2 x} \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 30} \[ \int \frac {3 e^4 \log (2)}{2 x^2} \, dx=-\frac {3 e^4 \log (2)}{2 x} \]

[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{align*} \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{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {3 e^4 \log (2)}{2 x^2} \, dx=-\frac {e^4 \log (8)}{2 x} \]

[In]

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

[Out]

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

Maple [A] (verified)

Time = 0.63 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71

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

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int \frac {3 e^4 \log (2)}{2 x^2} \, dx=-\frac {3 \, e^{4} \log \left (2\right )}{2 \, x} \]

[In]

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

[Out]

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

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {3 e^4 \log (2)}{2 x^2} \, dx=- \frac {3 e^{4} \log {\left (2 \right )}}{2 x} \]

[In]

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

[Out]

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

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int \frac {3 e^4 \log (2)}{2 x^2} \, dx=-\frac {3 \, e^{4} \log \left (2\right )}{2 \, x} \]

[In]

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

[Out]

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

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int \frac {3 e^4 \log (2)}{2 x^2} \, dx=-\frac {3 \, e^{4} \log \left (2\right )}{2 \, x} \]

[In]

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

[Out]

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

Mupad [B] (verification not implemented)

Time = 9.76 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int \frac {3 e^4 \log (2)}{2 x^2} \, dx=-\frac {3\,{\mathrm {e}}^4\,\ln \left (2\right )}{2\,x} \]

[In]

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

[Out]

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