\(\int \frac {1}{500} (500+379 \log (2)) \, dx\) [6481]

Optimal result

Integrand size = 10, antiderivative size = 12 \[ \int \frac {1}{500} (500+379 \log (2)) \, dx=x+\left (-4+\frac {379 x}{500}\right ) \log (2) \]

[Out]

x+(-4+379/500*x)*ln(2)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {8} \[ \int \frac {1}{500} (500+379 \log (2)) \, dx=\frac {1}{500} x (500+379 \log (2)) \]

[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{align*} \text {integral}& = \frac {1}{500} x (500+379 \log (2)) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int \frac {1}{500} (500+379 \log (2)) \, dx=x+\frac {379}{500} x \log (2) \]

[In]

Integrate[(500 + 379*Log[2])/500,x]

[Out]

x + (379*x*Log[2])/500

Maple [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67

method	result	size
risch	\(\frac {379 x \ln \left (2\right )}{500}+x\)	\(8\)
parts	\(\frac {379 x \ln \left (2\right )}{500}+x\)	\(8\)
norman	\(\left (\frac {379 \ln \left (2\right )}{500}+1\right ) x\)	\(9\)
parallelrisch	\(\left (\frac {379 \ln \left (2\right )}{500}+1\right ) x\)	\(9\)
default	\(\frac {x \left (379 \ln \left (2\right )+500\right )}{500}\)	\(10\)

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.58 \[ \int \frac {1}{500} (500+379 \log (2)) \, dx=\frac {379}{500} \, x \log \left (2\right ) + x \]

[In]

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

[Out]

379/500*x*log(2) + x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \frac {1}{500} (500+379 \log (2)) \, dx=x \left (\frac {379 \log {\left (2 \right )}}{500} + 1\right ) \]

[In]

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

[Out]

x*(379*log(2)/500 + 1)

Maxima [A] (verification not implemented)

none

Time = 0.17 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int \frac {1}{500} (500+379 \log (2)) \, dx=\frac {1}{500} \, x {\left (379 \, \log \left (2\right ) + 500\right )} \]

[In]

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

[Out]

1/500*x*(379*log(2) + 500)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int \frac {1}{500} (500+379 \log (2)) \, dx=\frac {1}{500} \, x {\left (379 \, \log \left (2\right ) + 500\right )} \]

[In]

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

[Out]

1/500*x*(379*log(2) + 500)

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \frac {1}{500} (500+379 \log (2)) \, dx=x\,\left (\frac {379\,\ln \left (2\right )}{500}+1\right ) \]

[In]

int((379*log(2))/500 + 1,x)

[Out]

x*((379*log(2))/500 + 1)