\(\int -\frac {8 \log ^2(2)}{x} \, dx\) [9441]

Optimal result

Integrand size = 9, antiderivative size = 15 \[ \int -\frac {8 \log ^2(2)}{x} \, dx=-3+4 \log ^2(2) \log \left (\frac {\log (3)}{x^2}\right ) \]

[Out]

4*ln(2)^2*ln(1/x^2*ln(3))-3

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 29} \[ \int -\frac {8 \log ^2(2)}{x} \, dx=-8 \log ^2(2) \log (x) \]

[In]

Int[(-8*Log[2]^2)/x,x]

[Out]

-8*Log[2]^2*Log[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 29

Int[(x_)^(-1), x_Symbol] :> Simp[Log[x], x]

Rubi steps \begin{align*} \text {integral}& = -\left (\left (8 \log ^2(2)\right ) \int \frac {1}{x} \, dx\right ) \\ & = -8 \log ^2(2) \log (x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int -\frac {8 \log ^2(2)}{x} \, dx=-8 \log ^2(2) \log (x) \]

[In]

Integrate[(-8*Log[2]^2)/x,x]

[Out]

-8*Log[2]^2*Log[x]

Maple [A] (verified)

Time = 0.07 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.60

method	result	size
default	\(-8 \ln \left (x \right ) \ln \left (2\right )^{2}\)	\(9\)
norman	\(-8 \ln \left (x \right ) \ln \left (2\right )^{2}\)	\(9\)
risch	\(-8 \ln \left (x \right ) \ln \left (2\right )^{2}\)	\(9\)
parallelrisch	\(-8 \ln \left (x \right ) \ln \left (2\right )^{2}\)	\(9\)

[In]

int(-8*ln(2)^2/x,x,method=_RETURNVERBOSE)

[Out]

-8*ln(x)*ln(2)^2

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int -\frac {8 \log ^2(2)}{x} \, dx=-8 \, \log \left (2\right )^{2} \log \left (x\right ) \]

[In]

integrate(-8*log(2)^2/x,x, algorithm="fricas")

[Out]

-8*log(2)^2*log(x)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int -\frac {8 \log ^2(2)}{x} \, dx=- 8 \log {\left (2 \right )}^{2} \log {\left (x \right )} \]

[In]

integrate(-8*ln(2)**2/x,x)

[Out]

-8*log(2)**2*log(x)

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int -\frac {8 \log ^2(2)}{x} \, dx=-8 \, \log \left (2\right )^{2} \log \left (x\right ) \]

[In]

integrate(-8*log(2)^2/x,x, algorithm="maxima")

[Out]

-8*log(2)^2*log(x)

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.60 \[ \int -\frac {8 \log ^2(2)}{x} \, dx=-8 \, \log \left (2\right )^{2} \log \left ({\left | x \right |}\right ) \]

[In]

integrate(-8*log(2)^2/x,x, algorithm="giac")

[Out]

-8*log(2)^2*log(abs(x))

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int -\frac {8 \log ^2(2)}{x} \, dx=-8\,{\ln \left (2\right )}^2\,\ln \left (x\right ) \]

[In]

int(-(8*log(2)^2)/x,x)

[Out]

-8*log(2)^2*log(x)