3.65.86 \(\int (2 x-e^2 \log (2)) \, dx\)

Optimal. Leaf size=22 \[ x \left (x-\frac {e^2 (2+x \log (2)+5 \log (3))}{x}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 0.55, number of steps used = 1, number of rules used = 0, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x^2-e^2 x \log (2) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2*x - E^2*Log[2],x]

[Out]

x^2 - E^2*x*Log[2]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x^2-e^2 x \log (2)\\ \end {aligned} \end {gather*}

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

Antiderivative was successfully verified.

[In]

Integrate[2*x - E^2*Log[2],x]

[Out]

x^2 - E^2*x*Log[2]

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fricas [A]  time = 0.79, size = 11, normalized size = 0.50 \begin {gather*} -x e^{2} \log \relax (2) + x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x*e^2*log(2) + x^2

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giac [A]  time = 0.16, size = 11, normalized size = 0.50 \begin {gather*} -x e^{2} \log \relax (2) + x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x*e^2*log(2) + x^2

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maple [A]  time = 0.04, size = 12, normalized size = 0.55

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.38, size = 11, normalized size = 0.50 \begin {gather*} -x e^{2} \log \relax (2) + x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x*e^2*log(2) + x^2

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mupad [B]  time = 0.04, size = 11, normalized size = 0.50 \begin {gather*} x^2-x\,{\mathrm {e}}^2\,\ln \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x - exp(2)*log(2),x)

[Out]

x^2 - x*exp(2)*log(2)

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sympy [A]  time = 0.05, size = 10, normalized size = 0.45 \begin {gather*} x^{2} - x e^{2} \log {\relax (2 )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x**2 - x*exp(2)*log(2)

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