3.4.29 \(\int (1+2 x-2 \log (9)) \, dx\)

Optimal. Leaf size=13 \[ -\frac {19}{4}+x+x^2-2 x \log (9) \]

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Rubi [A]  time = 0.01, antiderivative size = 12, normalized size of antiderivative = 0.92, 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^2+x (1-2 \log (9)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 + 2*x - 2*Log[9],x]

[Out]

x^2 + x*(1 - 2*Log[9])

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x^2+x (1-2 \log (9))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.77 \begin {gather*} x+x^2-2 x \log (9) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 + 2*x - 2*Log[9],x]

[Out]

x + x^2 - 2*x*Log[9]

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fricas [A]  time = 0.71, size = 10, normalized size = 0.77 \begin {gather*} x^{2} - 4 \, x \log \relax (3) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*log(3)+2*x+1,x, algorithm="fricas")

[Out]

x^2 - 4*x*log(3) + x

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giac [A]  time = 0.28, size = 10, normalized size = 0.77 \begin {gather*} x^{2} - 4 \, x \log \relax (3) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*log(3)+2*x+1,x, algorithm="giac")

[Out]

x^2 - 4*x*log(3) + x

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maple [A]  time = 0.02, size = 11, normalized size = 0.85

method	result	size
default	\(-4 x \ln \relax (3)+x^{2}+x\)	\(11\)
risch	\(-4 x \ln \relax (3)+x^{2}+x\)	\(11\)
gosper	\(-x \left (-x +4 \ln \relax (3)-1\right )\)	\(13\)
norman	\(x^{2}+\left (-4 \ln \relax (3)+1\right ) x\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-4*ln(3)+2*x+1,x,method=_RETURNVERBOSE)

[Out]

-4*x*ln(3)+x^2+x

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maxima [A]  time = 0.52, size = 10, normalized size = 0.77 \begin {gather*} x^{2} - 4 \, x \log \relax (3) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*log(3)+2*x+1,x, algorithm="maxima")

[Out]

x^2 - 4*x*log(3) + x

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mupad [B]  time = 0.32, size = 11, normalized size = 0.85 \begin {gather*} x^2-x\,\left (\ln \left (81\right )-1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x - 4*log(3) + 1,x)

[Out]

x^2 - x*(log(81) - 1)

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sympy [A]  time = 0.06, size = 10, normalized size = 0.77 \begin {gather*} x^{2} + x \left (1 - 4 \log {\relax (3 )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*ln(3)+2*x+1,x)

[Out]

x**2 + x*(1 - 4*log(3))

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