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

Optimal. Leaf size=14 \[ x \left (-1+\log ^2(2) \log \left (\log \left (\frac {23}{3}\right )\right )\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.14, number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {8} \begin {gather*} -x \left (1-\log ^2(2) \log \left (\log \left (\frac {23}{3}\right )\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[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 {gather*} \begin {aligned} \text {integral} &=-x \left (1-\log ^2(2) \log \left (\log \left (\frac {23}{3}\right )\right )\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 1.07 \begin {gather*} -x+x \log ^2(2) \log \left (\log \left (\frac {23}{3}\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-x + x*Log[2]^2*Log[Log[23/3]]

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fricas [A]  time = 0.62, size = 13, normalized size = 0.93 \begin {gather*} x \log \relax (2)^{2} \log \left (\log \left (\frac {23}{3}\right )\right ) - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*log(2)^2*log(log(23/3)) - x

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giac [A]  time = 0.25, size = 12, normalized size = 0.86 \begin {gather*} {\left (\log \relax (2)^{2} \log \left (\log \left (\frac {23}{3}\right )\right ) - 1\right )} x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(log(2)^2*log(log(23/3)) - 1)*x

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maple [A]  time = 0.02, size = 13, normalized size = 0.93

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.34, size = 12, normalized size = 0.86 \begin {gather*} {\left (\log \relax (2)^{2} \log \left (\log \left (\frac {23}{3}\right )\right ) - 1\right )} x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(log(2)^2*log(log(23/3)) - 1)*x

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mupad [B]  time = 0.00, size = 12, normalized size = 0.86 \begin {gather*} x\,\left ({\ln \relax (2)}^2\,\ln \left (\ln \left (\frac {23}{3}\right )\right )-1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(2)^2*log(log(23/3)) - 1,x)

[Out]

x*(log(2)^2*log(log(23/3)) - 1)

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sympy [A]  time = 0.06, size = 14, normalized size = 1.00 \begin {gather*} x \left (-1 + \log {\relax (2 )}^{2} \log {\left (\log {\left (\frac {23}{3} \right )} \right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*(-1 + log(2)**2*log(log(23/3)))

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