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

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

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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} $$\begin{array}{c}-x(1-{\log }^2(2)\log (\log \left(\frac{23}{3}\right)))\end{array}$$

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =-x(1-{\log }^2(2)\log (\log \left(\frac{23}{3}\right)))\end{array}\end{array}$$

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

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 $$\begin{array}{c}x\log (2{)}^2\log (\log \left(\frac{23}{3}\right))-x\end{array}$$

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 $$\begin{array}{c}(\log (2{)}^2\log (\log \left(\frac{23}{3}\right))-1)x\end{array}$$

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	$(\ln (2{)}^2\ln (\ln \left(\frac{23}{3}\right))-1)x$	$13$
norman	$(\ln (2{)}^2\ln (\ln \left(23\right)-\ln (3))-1)x$	$18$
risch	$\ln (2{)}^2\ln (\ln \left(23\right)-\ln (3))x-x$	$19$

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 $$\begin{array}{c}(\log (2{)}^2\log (\log \left(\frac{23}{3}\right))-1)x\end{array}$$

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 $$\begin{array}{c}x({\ln (2)}^2\ln (\ln \left(\frac{23}{3}\right))-1)\end{array}$$

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 $$\begin{array}{c}x(-1+\log {(2)}^2\log (\log \left(\frac{23}{3}\right)))\end{array}$$

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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