3.51.87 \(\int 2 \log (\frac {25}{4}) \, dx\) [5087]

Optimal. Leaf size=13 \[ -\left (\left (e^3-2 x\right ) \log \left (\frac {25}{4}\right )\right ) \]

[Out]

ln(4/25)*(exp(3)-2*x)

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Rubi [A]
time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.54, number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {8} \begin {gather*} 2 x \log \left (\frac {25}{4}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2*Log[25/4],x]

[Out]

2*x*Log[25/4]

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=2 x \log \left (\frac {25}{4}\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 7, normalized size = 0.54 \begin {gather*} 2 x \log \left (\frac {25}{4}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2*Log[25/4],x]

[Out]

2*x*Log[25/4]

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Maple [A]
time = 0.17, size = 6, normalized size = 0.46

method	result	size
default	\(-2 x \ln \left (\frac {4}{25}\right )\)	\(6\)
norman	\(\left (-4 \ln \left (2\right )+4 \ln \left (5\right )\right ) x\)	\(12\)
risch	\(-4 x \ln \left (2\right )+4 x \ln \left (5\right )\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2*ln(4/25),x,method=_RETURNVERBOSE)

[Out]

-2*x*ln(4/25)

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Maxima [A]
time = 0.30, size = 5, normalized size = 0.38 \begin {gather*} -2 \, x \log \left (\frac {4}{25}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*log(4/25),x, algorithm="maxima")

[Out]

-2*x*log(4/25)

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Fricas [A]
time = 0.35, size = 5, normalized size = 0.38 \begin {gather*} -2 \, x \log \left (\frac {4}{25}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*log(4/25),x, algorithm="fricas")

[Out]

-2*x*log(4/25)

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Sympy [A]
time = 0.00, size = 8, normalized size = 0.62 \begin {gather*} - 2 x \log {\left (\frac {4}{25} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*ln(4/25),x)

[Out]

-2*x*log(4/25)

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Giac [A]
time = 0.41, size = 5, normalized size = 0.38 \begin {gather*} -2 \, x \log \left (\frac {4}{25}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*log(4/25),x, algorithm="giac")

[Out]

-2*x*log(4/25)

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Mupad [B]
time = 0.00, size = 5, normalized size = 0.38 \begin {gather*} -2\,x\,\ln \left (\frac {4}{25}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2*log(4/25),x)

[Out]

-2*x*log(4/25)

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