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

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

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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} $$\begin{array}{c}-\frac{3e^4\log (2)}{2x}\end{array}$$

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\frac{1}{2}(3e^4\log (2))\int \frac{1}{x^2}dx\\ & =-\frac{3e^4\log (2)}{2x}\end{array}\end{array}$$

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

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 $$\begin{array}{c}-\frac{3e^4\log (2)}{2x}\end{array}$$

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 $$\begin{array}{c}-\frac{3e^4\log (2)}{2x}\end{array}$$

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	$-\frac{3{\mathrm{e}}^4\ln (2)}{2x}$	$10$
default	$-\frac{3{\mathrm{e}}^4\ln (2)}{2x}$	$10$
norman	$-\frac{3{\mathrm{e}}^4\ln (2)}{2x}$	$10$
risch	$-\frac{3{\mathrm{e}}^4\ln (2)}{2x}$	$10$

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 $$\begin{array}{c}-\frac{3e^4\log (2)}{2x}\end{array}$$

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 $$\begin{array}{c}-\frac{3{\mathrm{e}}^4\ln (2)}{2x}\end{array}$$

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 $$\begin{array}{c}-\frac{3e^4\log (2)}{2x}\end{array}$$

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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