3.62.25 \(\int \frac {115 \log (2)}{4 x^2} \, dx\)

Optimal. Leaf size=19 \[ \log (2) \left (\frac {5}{4} \left (16-\frac {23}{x}\right )-\log (4)\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.47, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 30} \begin {gather*} -\frac {115 \log (2)}{4 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(115*Log[2])/(4*x^2),x]

[Out]

(-115*Log[2])/(4*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}{4} (115 \log (2)) \int \frac {1}{x^2} \, dx\\ &=-\frac {115 \log (2)}{4 x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.47 \begin {gather*} -\frac {115 \log (2)}{4 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(115*Log[2])/(4*x^2),x]

[Out]

(-115*Log[2])/(4*x)

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fricas [A]  time = 0.57, size = 7, normalized size = 0.37 \begin {gather*} -\frac {115 \, \log \relax (2)}{4 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(115/4*log(2)/x^2,x, algorithm="fricas")

[Out]

-115/4*log(2)/x

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giac [A]  time = 0.16, size = 7, normalized size = 0.37 \begin {gather*} -\frac {115 \, \log \relax (2)}{4 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(115/4*log(2)/x^2,x, algorithm="giac")

[Out]

-115/4*log(2)/x

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maple [A]  time = 0.02, size = 8, normalized size = 0.42

method	result	size
gosper	\(-\frac {115 \ln \relax (2)}{4 x}\)	\(8\)
default	\(-\frac {115 \ln \relax (2)}{4 x}\)	\(8\)
norman	\(-\frac {115 \ln \relax (2)}{4 x}\)	\(8\)
risch	\(-\frac {115 \ln \relax (2)}{4 x}\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(115/4*ln(2)/x^2,x,method=_RETURNVERBOSE)

[Out]

-115/4*ln(2)/x

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maxima [A]  time = 0.35, size = 7, normalized size = 0.37 \begin {gather*} -\frac {115 \, \log \relax (2)}{4 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(115/4*log(2)/x^2,x, algorithm="maxima")

[Out]

-115/4*log(2)/x

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mupad [B]  time = 0.03, size = 7, normalized size = 0.37 \begin {gather*} -\frac {115\,\ln \relax (2)}{4\,x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((115*log(2))/(4*x^2),x)

[Out]

-(115*log(2))/(4*x)

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sympy [A]  time = 0.05, size = 8, normalized size = 0.42 \begin {gather*} - \frac {115 \log {\relax (2 )}}{4 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(115/4*ln(2)/x**2,x)

[Out]

-115*log(2)/(4*x)

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