3.55.38 \(\int -\frac {2 \log (20)}{15 x^3} \, dx\)

Optimal. Leaf size=9 \[ \frac {\log (20)}{15 x^2} \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 1.00, 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 {\log (20)}{15 x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-2*Log[20])/(15*x^3),x]

[Out]

Log[20]/(15*x^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} &=-\left (\frac {1}{15} (2 \log (20)) \int \frac {1}{x^3} \, dx\right )\\ &=\frac {\log (20)}{15 x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} \frac {\log (20)}{15 x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2*Log[20])/(15*x^3),x]

[Out]

Log[20]/(15*x^2)

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fricas [A]  time = 1.25, size = 7, normalized size = 0.78 \begin {gather*} \frac {\log \left (20\right )}{15 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/15*log(20)/x^3,x, algorithm="fricas")

[Out]

1/15*log(20)/x^2

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giac [A]  time = 0.22, size = 7, normalized size = 0.78 \begin {gather*} \frac {\log \left (20\right )}{15 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/15*log(20)/x^3,x, algorithm="giac")

[Out]

1/15*log(20)/x^2

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maple [A]  time = 0.02, size = 8, normalized size = 0.89

method	result	size
gosper	\(\frac {\ln \left (20\right )}{15 x^{2}}\)	\(8\)
default	\(\frac {\ln \left (20\right )}{15 x^{2}}\)	\(8\)
norman	\(\frac {\ln \left (20\right )}{15 x^{2}}\)	\(8\)
risch	\(\frac {2 \ln \relax (2)}{15 x^{2}}+\frac {\ln \relax (5)}{15 x^{2}}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2/15*ln(20)/x^3,x,method=_RETURNVERBOSE)

[Out]

1/15*ln(20)/x^2

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maxima [A]  time = 0.36, size = 7, normalized size = 0.78 \begin {gather*} \frac {\log \left (20\right )}{15 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/15*log(20)/x^3,x, algorithm="maxima")

[Out]

1/15*log(20)/x^2

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mupad [B]  time = 3.34, size = 7, normalized size = 0.78 \begin {gather*} \frac {\ln \left (20\right )}{15\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*log(20))/(15*x^3),x)

[Out]

log(20)/(15*x^2)

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sympy [A]  time = 0.05, size = 7, normalized size = 0.78 \begin {gather*} \frac {\log {\left (20 \right )}}{15 x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/15*ln(20)/x**3,x)

[Out]

log(20)/(15*x**2)

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