\(\int (2 x-e^2 \log (2)) \, dx\) [6486]

Optimal result

Integrand size = 11, antiderivative size = 22 \[ \int \left (2 x-e^2 \log (2)\right ) \, dx=x \left (x-\frac {e^2 (2+x \log (2)+5 \log (3))}{x}\right ) \]

[Out]

(x-(5*ln(3)+x*ln(2)+2)*exp(2)/x)*x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.55, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (2 x-e^2 \log (2)\right ) \, dx=x^2-e^2 x \log (2) \]

[In]

Int[2*x - E^2*Log[2],x]

[Out]

x^2 - E^2*x*Log[2]

Rubi steps \begin{align*} \text {integral}& = x^2-e^2 x \log (2) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.55 \[ \int \left (2 x-e^2 \log (2)\right ) \, dx=x^2-e^2 x \log (2) \]

[In]

Integrate[2*x - E^2*Log[2],x]

[Out]

x^2 - E^2*x*Log[2]

Maple [A] (verified)

Time = 0.04 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.55

method	result	size
default	\(-x \,{\mathrm e}^{2} \ln \left (2\right )+x^{2}\)	\(12\)
norman	\(-x \,{\mathrm e}^{2} \ln \left (2\right )+x^{2}\)	\(12\)
risch	\(-x \,{\mathrm e}^{2} \ln \left (2\right )+x^{2}\)	\(12\)
parallelrisch	\(-x \,{\mathrm e}^{2} \ln \left (2\right )+x^{2}\)	\(12\)
parts	\(-x \,{\mathrm e}^{2} \ln \left (2\right )+x^{2}\)	\(12\)
gosper	\(-x \left ({\mathrm e}^{2} \ln \left (2\right )-x \right )\)	\(13\)

[In]

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

[Out]

-x*exp(2)*ln(2)+x^2

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.50 \[ \int \left (2 x-e^2 \log (2)\right ) \, dx=-x e^{2} \log \left (2\right ) + x^{2} \]

[In]

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

[Out]

-x*e^2*log(2) + x^2

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.45 \[ \int \left (2 x-e^2 \log (2)\right ) \, dx=x^{2} - x e^{2} \log {\left (2 \right )} \]

[In]

integrate(-exp(2)*ln(2)+2*x,x)

[Out]

x**2 - x*exp(2)*log(2)

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.50 \[ \int \left (2 x-e^2 \log (2)\right ) \, dx=-x e^{2} \log \left (2\right ) + x^{2} \]

[In]

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

[Out]

-x*e^2*log(2) + x^2

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.50 \[ \int \left (2 x-e^2 \log (2)\right ) \, dx=-x e^{2} \log \left (2\right ) + x^{2} \]

[In]

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

[Out]

-x*e^2*log(2) + x^2

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.50 \[ \int \left (2 x-e^2 \log (2)\right ) \, dx=x^2-x\,{\mathrm {e}}^2\,\ln \left (2\right ) \]

[In]

int(2*x - exp(2)*log(2),x)

[Out]

x^2 - x*exp(2)*log(2)