\(\int -\frac {2 \log (20)}{15 x^3} \, dx\) [5438]

Optimal result

Integrand size = 9, antiderivative size = 9 \[ \int -\frac {2 \log (20)}{15 x^3} \, dx=\frac {\log (20)}{15 x^2} \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 30} \[ \int -\frac {2 \log (20)}{15 x^3} \, dx=\frac {\log (20)}{15 x^2} \]

[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{align*} \text {integral}& = -\left (\frac {1}{15} (2 \log (20)) \int \frac {1}{x^3} \, dx\right ) \\ & = \frac {\log (20)}{15 x^2} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int -\frac {2 \log (20)}{15 x^3} \, dx=\frac {\log (20)}{15 x^2} \]

[In]

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

[Out]

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

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 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	\(\frac {\ln \left (20\right )}{15 x^{2}}\)	\(8\)
parallelrisch	\(\frac {\ln \left (20\right )}{15 x^{2}}\)	\(8\)
risch	\(\frac {2 \ln \left (2\right )}{15 x^{2}}+\frac {\ln \left (5\right )}{15 x^{2}}\)	\(16\)

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int -\frac {2 \log (20)}{15 x^3} \, dx=\frac {\log \left (20\right )}{15 \, x^{2}} \]

[In]

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

[Out]

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

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int -\frac {2 \log (20)}{15 x^3} \, dx=\frac {\log {\left (20 \right )}}{15 x^{2}} \]

[In]

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

[Out]

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

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int -\frac {2 \log (20)}{15 x^3} \, dx=\frac {\log \left (20\right )}{15 \, x^{2}} \]

[In]

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

[Out]

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

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int -\frac {2 \log (20)}{15 x^3} \, dx=\frac {\log \left (20\right )}{15 \, x^{2}} \]

[In]

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

[Out]

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

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int -\frac {2 \log (20)}{15 x^3} \, dx=\frac {\ln \left (20\right )}{15\,x^2} \]

[In]

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

[Out]

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