3.11.94 \(\int -\frac {388129 \log (5)}{32 x^2} \, dx\)

Optimal. Leaf size=14 \[ 2+\frac {x+\frac {388129 \log (5)}{32}}{x} \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.64, 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 {388129 \log (5)}{32 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-388129*Log[5])/(32*x^2),x]

[Out]

(388129*Log[5])/(32*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} &=-\left (\frac {1}{32} (388129 \log (5)) \int \frac {1}{x^2} \, dx\right )\\ &=\frac {388129 \log (5)}{32 x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.64 \begin {gather*} \frac {388129 \log (5)}{32 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-388129*Log[5])/(32*x^2),x]

[Out]

(388129*Log[5])/(32*x)

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fricas [A]  time = 1.18, size = 7, normalized size = 0.50 \begin {gather*} \frac {388129 \, \log \relax (5)}{32 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-388129/32*log(5)/x^2,x, algorithm="fricas")

[Out]

388129/32*log(5)/x

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giac [A]  time = 0.29, size = 7, normalized size = 0.50 \begin {gather*} \frac {388129 \, \log \relax (5)}{32 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-388129/32*log(5)/x^2,x, algorithm="giac")

[Out]

388129/32*log(5)/x

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maple [A]  time = 0.01, size = 8, normalized size = 0.57

method	result	size
gosper	\(\frac {388129 \ln \relax (5)}{32 x}\)	\(8\)
default	\(\frac {388129 \ln \relax (5)}{32 x}\)	\(8\)
norman	\(\frac {388129 \ln \relax (5)}{32 x}\)	\(8\)
risch	\(\frac {388129 \ln \relax (5)}{32 x}\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-388129/32*ln(5)/x^2,x,method=_RETURNVERBOSE)

[Out]

388129/32*ln(5)/x

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maxima [A]  time = 0.65, size = 7, normalized size = 0.50 \begin {gather*} \frac {388129 \, \log \relax (5)}{32 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-388129/32*log(5)/x^2,x, algorithm="maxima")

[Out]

388129/32*log(5)/x

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mupad [B]  time = 0.67, size = 7, normalized size = 0.50 \begin {gather*} \frac {388129\,\ln \relax (5)}{32\,x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(388129*log(5))/(32*x^2),x)

[Out]

(388129*log(5))/(32*x)

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sympy [A]  time = 0.06, size = 7, normalized size = 0.50 \begin {gather*} \frac {388129 \log {\relax (5 )}}{32 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-388129/32*ln(5)/x**2,x)

[Out]

388129*log(5)/(32*x)

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