3.64.52 \(\int 12 \log (\log (4+e^5)) \, dx\)

Optimal. Leaf size=19 \[ 3 \left (3+4 e^5+4 x \log \left (\log \left (4+e^5\right )\right )\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.53, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {8} \begin {gather*} 12 x \log \left (\log \left (4+e^5\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[12*Log[Log[4 + E^5]],x]

[Out]

12*x*Log[Log[4 + E^5]]

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=12 x \log \left (\log \left (4+e^5\right )\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.53 \begin {gather*} 12 x \log \left (\log \left (4+e^5\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[12*Log[Log[4 + E^5]],x]

[Out]

12*x*Log[Log[4 + E^5]]

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fricas [A]  time = 0.66, size = 9, normalized size = 0.47 \begin {gather*} 12 \, x \log \left (\log \left (e^{5} + 4\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(12*log(log(4+exp(5))),x, algorithm="fricas")

[Out]

12*x*log(log(e^5 + 4))

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giac [A]  time = 0.14, size = 9, normalized size = 0.47 \begin {gather*} 12 \, x \log \left (\log \left (e^{5} + 4\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(12*log(log(4+exp(5))),x, algorithm="giac")

[Out]

12*x*log(log(e^5 + 4))

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maple [A]  time = 0.03, size = 10, normalized size = 0.53

method	result	size
default	\(12 \ln \left (\ln \left (4+{\mathrm e}^{5}\right )\right ) x\)	\(10\)
norman	\(12 \ln \left (\ln \left (4+{\mathrm e}^{5}\right )\right ) x\)	\(10\)
risch	\(12 \ln \left (\ln \left (4+{\mathrm e}^{5}\right )\right ) x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(12*ln(ln(4+exp(5))),x,method=_RETURNVERBOSE)

[Out]

12*ln(ln(4+exp(5)))*x

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maxima [A]  time = 0.37, size = 9, normalized size = 0.47 \begin {gather*} 12 \, x \log \left (\log \left (e^{5} + 4\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(12*log(log(4+exp(5))),x, algorithm="maxima")

[Out]

12*x*log(log(e^5 + 4))

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mupad [B]  time = 0.00, size = 9, normalized size = 0.47 \begin {gather*} 12\,x\,\ln \left (\ln \left ({\mathrm {e}}^5+4\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(12*log(log(exp(5) + 4)),x)

[Out]

12*x*log(log(exp(5) + 4))

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sympy [A]  time = 0.05, size = 10, normalized size = 0.53 \begin {gather*} 12 x \log {\left (\log {\left (4 + e^{5} \right )} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(12*ln(ln(4+exp(5))),x)

[Out]

12*x*log(log(4 + exp(5)))

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