3.85.37 \(\int (7-6 \log (4)) \, dx\)

Optimal. Leaf size=11 \[ x+6 (x-x \log (4)) \]

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.73, 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*} x (7-6 \log (4)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[7 - 6*Log[4],x]

[Out]

x*(7 - 6*Log[4])

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x (7-6 \log (4))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.82 \begin {gather*} 7 x-6 x \log (4) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[7 - 6*Log[4],x]

[Out]

7*x - 6*x*Log[4]

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fricas [A]  time = 0.90, size = 9, normalized size = 0.82 \begin {gather*} -12 \, x \log \relax (2) + 7 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12*log(2)+7,x, algorithm="fricas")

[Out]

-12*x*log(2) + 7*x

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giac [A]  time = 0.20, size = 9, normalized size = 0.82 \begin {gather*} -x {\left (12 \, \log \relax (2) - 7\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12*log(2)+7,x, algorithm="giac")

[Out]

-x*(12*log(2) - 7)

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maple [A]  time = 0.01, size = 9, normalized size = 0.82

method	result	size
default	\(\left (-12 \ln \relax (2)+7\right ) x\)	\(9\)
norman	\(\left (-12 \ln \relax (2)+7\right ) x\)	\(9\)
risch	\(7 x -12 x \ln \relax (2)\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-12*ln(2)+7,x,method=_RETURNVERBOSE)

[Out]

(-12*ln(2)+7)*x

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maxima [A]  time = 0.36, size = 9, normalized size = 0.82 \begin {gather*} -x {\left (12 \, \log \relax (2) - 7\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12*log(2)+7,x, algorithm="maxima")

[Out]

-x*(12*log(2) - 7)

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mupad [B]  time = 0.00, size = 9, normalized size = 0.82 \begin {gather*} -x\,\left (12\,\ln \relax (2)-7\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(7 - 12*log(2),x)

[Out]

-x*(12*log(2) - 7)

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sympy [A]  time = 0.05, size = 7, normalized size = 0.64 \begin {gather*} x \left (7 - 12 \log {\relax (2 )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12*ln(2)+7,x)

[Out]

x*(7 - 12*log(2))

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