3.65.81 \(\int \frac {1}{500} (500+379 \log (2)) \, dx\)

Optimal. Leaf size=12 \[ x+\left (-4+\frac {379 x}{500}\right ) \log (2) \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.92, number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {8} \begin {gather*} \frac {1}{500} x (500+379 \log (2)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(500 + 379*Log[2])/500,x]

[Out]

(x*(500 + 379*Log[2]))/500

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{500} x (500+379 \log (2))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.75 \begin {gather*} x+\frac {379}{500} x \log (2) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(500 + 379*Log[2])/500,x]

[Out]

x + (379*x*Log[2])/500

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fricas [A]  time = 0.75, size = 7, normalized size = 0.58 \begin {gather*} \frac {379}{500} \, x \log \relax (2) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(379/500*log(2)+1,x, algorithm="fricas")

[Out]

379/500*x*log(2) + x

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giac [A]  time = 0.13, size = 9, normalized size = 0.75 \begin {gather*} \frac {1}{500} \, x {\left (379 \, \log \relax (2) + 500\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(379/500*log(2)+1,x, algorithm="giac")

[Out]

1/500*x*(379*log(2) + 500)

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maple [A]  time = 0.03, size = 8, normalized size = 0.67

method	result	size
risch	\(\frac {379 x \ln \relax (2)}{500}+x\)	\(8\)
default	\(\left (\frac {379 \ln \relax (2)}{500}+1\right ) x\)	\(9\)
norman	\(\left (\frac {379 \ln \relax (2)}{500}+1\right ) x\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(379/500*ln(2)+1,x,method=_RETURNVERBOSE)

[Out]

379/500*x*ln(2)+x

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maxima [A]  time = 0.36, size = 9, normalized size = 0.75 \begin {gather*} \frac {1}{500} \, x {\left (379 \, \log \relax (2) + 500\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(379/500*log(2)+1,x, algorithm="maxima")

[Out]

1/500*x*(379*log(2) + 500)

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mupad [B]  time = 0.00, size = 8, normalized size = 0.67 \begin {gather*} x\,\left (\frac {379\,\ln \relax (2)}{500}+1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((379*log(2))/500 + 1,x)

[Out]

x*((379*log(2))/500 + 1)

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sympy [A]  time = 0.04, size = 8, normalized size = 0.67 \begin {gather*} x \left (\frac {379 \log {\relax (2 )}}{500} + 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(379/500*ln(2)+1,x)

[Out]

x*(379*log(2)/500 + 1)

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