3.99.21 \(\int (1+10 \log (\log (2))) \, dx\)

Optimal. Leaf size=14 \[ x+5 \left (\frac {619}{125}+2 x\right ) \log (\log (2)) \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.64, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {8} \begin {gather*} x (1+10 \log (\log (2))) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 + 10*Log[Log[2]],x]

[Out]

x*(1 + 10*Log[Log[2]])

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x (1+10 \log (\log (2)))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 0.57 \begin {gather*} x+10 x \log (\log (2)) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 + 10*Log[Log[2]],x]

[Out]

x + 10*x*Log[Log[2]]

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fricas [A]  time = 0.92, size = 8, normalized size = 0.57 \begin {gather*} 10 \, x \log \left (\log \relax (2)\right ) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*log(log(2))+1,x, algorithm="fricas")

[Out]

10*x*log(log(2)) + x

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giac [A]  time = 0.13, size = 9, normalized size = 0.64 \begin {gather*} x {\left (10 \, \log \left (\log \relax (2)\right ) + 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*log(log(2))+1,x, algorithm="giac")

[Out]

x*(10*log(log(2)) + 1)

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maple [A]  time = 0.01, size = 9, normalized size = 0.64

method	result	size
risch	\(10 x \ln \left (\ln \relax (2)\right )+x\)	\(9\)
default	\(\left (10 \ln \left (\ln \relax (2)\right )+1\right ) x\)	\(10\)
norman	\(\left (10 \ln \left (\ln \relax (2)\right )+1\right ) x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10*ln(ln(2))+1,x,method=_RETURNVERBOSE)

[Out]

10*x*ln(ln(2))+x

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maxima [A]  time = 0.44, size = 9, normalized size = 0.64 \begin {gather*} x {\left (10 \, \log \left (\log \relax (2)\right ) + 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*log(log(2))+1,x, algorithm="maxima")

[Out]

x*(10*log(log(2)) + 1)

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mupad [B]  time = 0.00, size = 9, normalized size = 0.64 \begin {gather*} x\,\left (10\,\ln \left (\ln \relax (2)\right )+1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10*log(log(2)) + 1,x)

[Out]

x*(10*log(log(2)) + 1)

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sympy [A]  time = 0.05, size = 8, normalized size = 0.57 \begin {gather*} x \left (10 \log {\left (\log {\relax (2 )} \right )} + 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*ln(ln(2))+1,x)

[Out]

x*(10*log(log(2)) + 1)

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