3.48.79 \(\int (-80 \log (5)+80 (i \pi +\log (\log (2)))) \, dx\)

Optimal. Leaf size=16 \[ 80 x (i \pi -\log (5)+\log (\log (2))) \]

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Rubi [A]  time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {8} \begin {gather*} 80 x \left (\log \left (\frac {\log (2)}{5}\right )+i \pi \right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-80*Log[5] + 80*(I*Pi + Log[Log[2]]),x]

[Out]

80*x*(I*Pi + Log[Log[2]/5])

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=80 x \left (i \pi +\log \left (\frac {\log (2)}{5}\right )\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 18, normalized size = 1.12 \begin {gather*} -80 x \log (5)+80 x (i \pi +\log (\log (2))) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-80*Log[5] + 80*(I*Pi + Log[Log[2]]),x]

[Out]

-80*x*Log[5] + 80*x*(I*Pi + Log[Log[2]])

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fricas [A]  time = 1.08, size = 14, normalized size = 0.88 \begin {gather*} -80 \, x \log \relax (5) + 80 \, x \log \left (-\log \relax (2)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(80*log(-log(2))-80*log(5),x, algorithm="fricas")

[Out]

-80*x*log(5) + 80*x*log(-log(2))

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giac [A]  time = 0.19, size = 13, normalized size = 0.81 \begin {gather*} -80 \, x {\left (\log \relax (5) - \log \left (-\log \relax (2)\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(80*log(-log(2))-80*log(5),x, algorithm="giac")

[Out]

-80*x*(log(5) - log(-log(2)))

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maple [A]  time = 0.02, size = 15, normalized size = 0.94

method	result	size
default	\(\left (80 \ln \left (-\ln \relax (2)\right )-80 \ln \relax (5)\right ) x\)	\(15\)
norman	\(\left (80 \ln \left (\ln \relax (2)\right )+80 i \pi -80 \ln \relax (5)\right ) x\)	\(17\)
risch	\(80 i x \pi -80 x \ln \relax (5)+80 x \ln \left (\ln \relax (2)\right )\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(80*ln(-ln(2))-80*ln(5),x,method=_RETURNVERBOSE)

[Out]

(80*ln(-ln(2))-80*ln(5))*x

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maxima [A]  time = 0.35, size = 13, normalized size = 0.81 \begin {gather*} -80 \, x {\left (\log \relax (5) - \log \left (-\log \relax (2)\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(80*log(-log(2))-80*log(5),x, algorithm="maxima")

[Out]

-80*x*(log(5) - log(-log(2)))

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mupad [B]  time = 0.00, size = 14, normalized size = 0.88 \begin {gather*} x\,\left (80\,\ln \left (-\ln \relax (2)\right )-80\,\ln \relax (5)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(80*log(-log(2)) - 80*log(5),x)

[Out]

x*(80*log(-log(2)) - 80*log(5))

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sympy [A]  time = 0.05, size = 17, normalized size = 1.06 \begin {gather*} x \left (- 80 \log {\relax (5 )} + 80 \log {\left (\log {\relax (2 )} \right )} + 80 i \pi \right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(80*ln(-ln(2))-80*ln(5),x)

[Out]

x*(-80*log(5) + 80*log(log(2)) + 80*I*pi)

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