3.10.83 \(\int \frac {2 x}{\log (2 e^{-4+\log ^2(2)})} \, dx\)

Optimal. Leaf size=21 \[ 2+\frac {1+x^2}{\log \left (2 e^{-4+\log ^2(2)}\right )} \]

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Rubi [A]  time = 0.01, antiderivative size = 19, normalized size of antiderivative = 0.90, number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 30} \begin {gather*} -\frac {x^2}{4-\log ^2(2)-\log (2)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(2*x)/Log[2*E^(-4 + Log[2]^2)],x]

[Out]

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

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Mathematica [A]  time = 0.00, size = 17, normalized size = 0.81 \begin {gather*} \frac {x^2}{\log \left (2 e^{-4+\log ^2(2)}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

x^2/Log[2*E^(-4 + Log[2]^2)]

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fricas [A]  time = 0.74, size = 14, normalized size = 0.67 \begin {gather*} \frac {x^{2}}{\log \relax (2)^{2} + \log \relax (2) - 4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^2/(log(2)^2 + log(2) - 4)

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giac [A]  time = 0.60, size = 16, normalized size = 0.76 \begin {gather*} \frac {x^{2}}{\log \left (2 \, e^{\left (\log \relax (2)^{2} - 4\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^2/log(2*e^(log(2)^2 - 4))

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maple [A]  time = 0.02, size = 15, normalized size = 0.71

method	result	size
norman	\(\frac {x^{2}}{\ln \relax (2)+\ln \relax (2)^{2}-4}\)	\(15\)
risch	\(\frac {x^{2}}{\ln \relax (2)+\ln \relax (2)^{2}-4}\)	\(15\)
gosper	\(\frac {x^{2}}{\ln \left (2 \,{\mathrm e}^{\ln \relax (2)^{2}-4}\right )}\)	\(17\)
default	\(\frac {x^{2}}{\ln \left (2 \,{\mathrm e}^{\ln \relax (2)^{2}-4}\right )}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/(ln(2)+ln(2)^2-4)*x^2

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maxima [A]  time = 0.44, size = 16, normalized size = 0.76 \begin {gather*} \frac {x^{2}}{\log \left (2 \, e^{\left (\log \relax (2)^{2} - 4\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^2/log(2*e^(log(2)^2 - 4))

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mupad [B]  time = 0.05, size = 14, normalized size = 0.67 \begin {gather*} \frac {x^2}{\ln \relax (2)+{\ln \relax (2)}^2-4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x)/log(2*exp(log(2)^2 - 4)),x)

[Out]

x^2/(log(2) + log(2)^2 - 4)

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sympy [A]  time = 0.06, size = 12, normalized size = 0.57 \begin {gather*} \frac {x^{2}}{-4 + \log {\relax (2 )}^{2} + \log {\relax (2 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x**2/(-4 + log(2)**2 + log(2))

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