3.20.92 \(\int (2-2 x+\log (\frac {13}{2})) \, dx\)

Optimal. Leaf size=11 \[ x \left (2-x+\log \left (\frac {13}{2}\right )\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.27, number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x \left (2+\log \left (\frac {13}{2}\right )\right )-x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2 - 2*x + Log[13/2],x]

[Out]

-x^2 + x*(2 + Log[13/2])

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-x^2+x \left (2+\log \left (\frac {13}{2}\right )\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 1.36 \begin {gather*} 2 x-x^2+x \log \left (\frac {13}{2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2 - 2*x + Log[13/2],x]

[Out]

2*x - x^2 + x*Log[13/2]

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fricas [A]  time = 0.71, size = 14, normalized size = 1.27 \begin {gather*} -x^{2} - x \log \left (\frac {2}{13}\right ) + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-log(2/13)-2*x+2,x, algorithm="fricas")

[Out]

-x^2 - x*log(2/13) + 2*x

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giac [A]  time = 0.26, size = 14, normalized size = 1.27 \begin {gather*} -x^{2} - x \log \left (\frac {2}{13}\right ) + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-log(2/13)-2*x+2,x, algorithm="giac")

[Out]

-x^2 - x*log(2/13) + 2*x

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maple [A]  time = 0.02, size = 9, normalized size = 0.82

method	result	size
gosper	\(-x \left (x +\ln \left (\frac {2}{13}\right )-2\right )\)	\(9\)
default	\(-\ln \left (\frac {2}{13}\right ) x -x^{2}+2 x\)	\(15\)
norman	\(\left (-\ln \relax (2)+\ln \left (13\right )+2\right ) x -x^{2}\)	\(17\)
risch	\(-x \ln \relax (2)+x \ln \left (13\right )-x^{2}+2 x\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-ln(2/13)-2*x+2,x,method=_RETURNVERBOSE)

[Out]

-x*(x+ln(2/13)-2)

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maxima [A]  time = 0.46, size = 14, normalized size = 1.27 \begin {gather*} -x^{2} - x \log \left (\frac {2}{13}\right ) + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-log(2/13)-2*x+2,x, algorithm="maxima")

[Out]

-x^2 - x*log(2/13) + 2*x

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mupad [B]  time = 1.10, size = 12, normalized size = 1.09 \begin {gather*} x\,\left (\ln \left (\frac {13}{2}\right )+2\right )-x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2 - log(2/13) - 2*x,x)

[Out]

x*(log(13/2) + 2) - x^2

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sympy [A]  time = 0.05, size = 12, normalized size = 1.09 \begin {gather*} - x^{2} + x \left (- \log {\relax (2 )} + 2 + \log {\left (13 \right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-ln(2/13)-2*x+2,x)

[Out]

-x**2 + x*(-log(2) + 2 + log(13))

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