3.58.70 \(\int \frac {4 \log (3)}{5} \, dx\)

Optimal. Leaf size=15 \[ -\left (\left (-x+\frac {5+x}{5}\right ) \log (3)\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.47, 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*} \frac {4}{5} x \log (3) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(4*Log[3])/5,x]

[Out]

(4*x*Log[3])/5

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {4}{5} x \log (3)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 0.47 \begin {gather*} \frac {4}{5} x \log (3) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(4*Log[3])/5,x]

[Out]

(4*x*Log[3])/5

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fricas [A]  time = 0.87, size = 5, normalized size = 0.33 \begin {gather*} \frac {4}{5} \, x \log \relax (3) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4/5*log(3),x, algorithm="fricas")

[Out]

4/5*x*log(3)

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giac [A]  time = 0.11, size = 5, normalized size = 0.33 \begin {gather*} \frac {4}{5} \, x \log \relax (3) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4/5*log(3),x, algorithm="giac")

[Out]

4/5*x*log(3)

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maple [A]  time = 0.01, size = 6, normalized size = 0.40

method	result	size
default	\(\frac {4 x \ln \relax (3)}{5}\)	\(6\)
norman	\(\frac {4 x \ln \relax (3)}{5}\)	\(6\)
risch	\(\frac {4 x \ln \relax (3)}{5}\)	\(6\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4/5*ln(3),x,method=_RETURNVERBOSE)

[Out]

4/5*x*ln(3)

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maxima [A]  time = 0.35, size = 5, normalized size = 0.33 \begin {gather*} \frac {4}{5} \, x \log \relax (3) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4/5*log(3),x, algorithm="maxima")

[Out]

4/5*x*log(3)

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mupad [B]  time = 0.00, size = 5, normalized size = 0.33 \begin {gather*} \frac {4\,x\,\ln \relax (3)}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*log(3))/5,x)

[Out]

(4*x*log(3))/5

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sympy [A]  time = 0.01, size = 7, normalized size = 0.47 \begin {gather*} \frac {4 x \log {\relax (3 )}}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4/5*ln(3),x)

[Out]

4*x*log(3)/5

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