3.77.80 \(\int \frac {3-12 \log (2)}{\log (2)} \, dx\)

Optimal. Leaf size=20 \[ 5+2 (7 (5-x)+x)+\frac {3 x}{\log (2)} \]

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Rubi [A]  time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.65, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {8} \begin {gather*} \frac {3 x (1-4 \log (2))}{\log (2)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(3 - 12*Log[2])/Log[2],x]

[Out]

(3*x*(1 - 4*Log[2]))/Log[2]

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {3 x (1-4 \log (2))}{\log (2)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.55 \begin {gather*} -12 x+\frac {3 x}{\log (2)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3 - 12*Log[2])/Log[2],x]

[Out]

-12*x + (3*x)/Log[2]

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fricas [A]  time = 0.75, size = 15, normalized size = 0.75 \begin {gather*} -\frac {3 \, {\left (4 \, x \log \relax (2) - x\right )}}{\log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-12*log(2)+3)/log(2),x, algorithm="fricas")

[Out]

-3*(4*x*log(2) - x)/log(2)

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giac [A]  time = 0.16, size = 13, normalized size = 0.65 \begin {gather*} -\frac {3 \, x {\left (4 \, \log \relax (2) - 1\right )}}{\log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-12*log(2)+3)/log(2),x, algorithm="giac")

[Out]

-3*x*(4*log(2) - 1)/log(2)

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maple [A]  time = 0.01, size = 12, normalized size = 0.60

method	result	size
risch	\(-12 x +\frac {3 x}{\ln \relax (2)}\)	\(12\)
default	\(\frac {\left (-12 \ln \relax (2)+3\right ) x}{\ln \relax (2)}\)	\(13\)
norman	\(-\frac {3 \left (4 \ln \relax (2)-1\right ) x}{\ln \relax (2)}\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-12*ln(2)+3)/ln(2),x,method=_RETURNVERBOSE)

[Out]

-12*x+3*x/ln(2)

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maxima [A]  time = 0.36, size = 13, normalized size = 0.65 \begin {gather*} -\frac {3 \, x {\left (4 \, \log \relax (2) - 1\right )}}{\log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-12*log(2)+3)/log(2),x, algorithm="maxima")

[Out]

-3*x*(4*log(2) - 1)/log(2)

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mupad [B]  time = 0.00, size = 13, normalized size = 0.65 \begin {gather*} -\frac {x\,\left (12\,\ln \relax (2)-3\right )}{\ln \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(12*log(2) - 3)/log(2),x)

[Out]

-(x*(12*log(2) - 3))/log(2)

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sympy [A]  time = 0.04, size = 10, normalized size = 0.50 \begin {gather*} \frac {x \left (3 - 12 \log {\relax (2 )}\right )}{\log {\relax (2 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-12*ln(2)+3)/ln(2),x)

[Out]

x*(3 - 12*log(2))/log(2)

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