\(\int (-1+\log ^2(2) \log (\log (\frac {23}{3}))) \, dx\) [6843]

Optimal result

Integrand size = 12, antiderivative size = 14 \[ \int \left (-1+\log ^2(2) \log \left (\log \left (\frac {23}{3}\right )\right )\right ) \, dx=x \left (-1+\log ^2(2) \log \left (\log \left (\frac {23}{3}\right )\right )\right ) \]

[Out]

(ln(2)^2*ln(ln(23/3))-1)*x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {8} \[ \int \left (-1+\log ^2(2) \log \left (\log \left (\frac {23}{3}\right )\right )\right ) \, dx=-x \left (1-\log ^2(2) \log \left (\log \left (\frac {23}{3}\right )\right )\right ) \]

[In]

Int[-1 + Log[2]^2*Log[Log[23/3]],x]

[Out]

-(x*(1 - Log[2]^2*Log[Log[23/3]]))

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps \begin{align*} \text {integral}& = -x \left (1-\log ^2(2) \log \left (\log \left (\frac {23}{3}\right )\right )\right ) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07 \[ \int \left (-1+\log ^2(2) \log \left (\log \left (\frac {23}{3}\right )\right )\right ) \, dx=-x+x \log ^2(2) \log \left (\log \left (\frac {23}{3}\right )\right ) \]

[In]

Integrate[-1 + Log[2]^2*Log[Log[23/3]],x]

[Out]

-x + x*Log[2]^2*Log[Log[23/3]]

Maple [A] (verified)

Time = 0.06 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93

method	result	size
default	\(\left (\ln \left (2\right )^{2} \ln \left (\ln \left (\frac {23}{3}\right )\right )-1\right ) x\)	\(13\)
parallelrisch	\(\left (\ln \left (2\right )^{2} \ln \left (\ln \left (\frac {23}{3}\right )\right )-1\right ) x\)	\(13\)
parts	\(-x +\ln \left (2\right )^{2} \ln \left (\ln \left (\frac {23}{3}\right )\right ) x\)	\(14\)
norman	\(\left (\ln \left (2\right )^{2} \ln \left (\ln \left (23\right )-\ln \left (3\right )\right )-1\right ) x\)	\(18\)
risch	\(\ln \left (2\right )^{2} \ln \left (\ln \left (23\right )-\ln \left (3\right )\right ) x -x\)	\(19\)

[In]

int(ln(2)^2*ln(ln(23/3))-1,x,method=_RETURNVERBOSE)

[Out]

(ln(2)^2*ln(ln(23/3))-1)*x

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93 \[ \int \left (-1+\log ^2(2) \log \left (\log \left (\frac {23}{3}\right )\right )\right ) \, dx=x \log \left (2\right )^{2} \log \left (\log \left (\frac {23}{3}\right )\right ) - x \]

[In]

integrate(log(2)^2*log(log(23/3))-1,x, algorithm="fricas")

[Out]

x*log(2)^2*log(log(23/3)) - x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \left (-1+\log ^2(2) \log \left (\log \left (\frac {23}{3}\right )\right )\right ) \, dx=x \left (-1 + \log {\left (2 \right )}^{2} \log {\left (\log {\left (\frac {23}{3} \right )} \right )}\right ) \]

[In]

integrate(ln(2)**2*ln(ln(23/3))-1,x)

[Out]

x*(-1 + log(2)**2*log(log(23/3)))

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \left (-1+\log ^2(2) \log \left (\log \left (\frac {23}{3}\right )\right )\right ) \, dx={\left (\log \left (2\right )^{2} \log \left (\log \left (\frac {23}{3}\right )\right ) - 1\right )} x \]

[In]

integrate(log(2)^2*log(log(23/3))-1,x, algorithm="maxima")

[Out]

(log(2)^2*log(log(23/3)) - 1)*x

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \left (-1+\log ^2(2) \log \left (\log \left (\frac {23}{3}\right )\right )\right ) \, dx={\left (\log \left (2\right )^{2} \log \left (\log \left (\frac {23}{3}\right )\right ) - 1\right )} x \]

[In]

integrate(log(2)^2*log(log(23/3))-1,x, algorithm="giac")

[Out]

(log(2)^2*log(log(23/3)) - 1)*x

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \left (-1+\log ^2(2) \log \left (\log \left (\frac {23}{3}\right )\right )\right ) \, dx=x\,\left ({\ln \left (2\right )}^2\,\ln \left (\ln \left (\frac {23}{3}\right )\right )-1\right ) \]

[In]

int(log(2)^2*log(log(23/3)) - 1,x)

[Out]

x*(log(2)^2*log(log(23/3)) - 1)