3.97.34 \(\int \frac {1}{2} (8-3 x+2 \log (3)) \, dx\)

Optimal. Leaf size=23 \[ 3+x \left (4-x+\frac {\left (\frac {x}{2}+\log (3)\right )^2}{x}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.57, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {9} \begin {gather*} -\frac {1}{12} (-3 x+8+\log (9))^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(8 - 3*x + 2*Log[3])/2,x]

[Out]

-1/12*(8 - 3*x + Log[9])^2

Rule 9

Int[(a_)*((b_) + (c_.)*(x_)), x_Symbol] :> Simp[(a*(b + c*x)^2)/(2*c), x] /; FreeQ[{a, b, c}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {1}{12} (8-3 x+\log (9))^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 0.65 \begin {gather*} 4 x-\frac {3 x^2}{4}+x \log (3) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(8 - 3*x + 2*Log[3])/2,x]

[Out]

4*x - (3*x^2)/4 + x*Log[3]

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fricas [A]  time = 0.47, size = 13, normalized size = 0.57 \begin {gather*} -\frac {3}{4} \, x^{2} + x \log \relax (3) + 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3/4*x^2 + x*log(3) + 4*x

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giac [A]  time = 0.15, size = 13, normalized size = 0.57 \begin {gather*} -\frac {3}{4} \, x^{2} + x \log \relax (3) + 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3/4*x^2 + x*log(3) + 4*x

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maple [A]  time = 0.02, size = 13, normalized size = 0.57

method	result	size
gosper	\(\frac {x \left (-3 x +4 \ln \relax (3)+16\right )}{4}\)	\(13\)
norman	\(\left (\ln \relax (3)+4\right ) x -\frac {3 x^{2}}{4}\)	\(13\)
default	\(x \ln \relax (3)-\frac {3 x^{2}}{4}+4 x\)	\(14\)
risch	\(x \ln \relax (3)-\frac {3 x^{2}}{4}+4 x\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/4*x*(-3*x+4*ln(3)+16)

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maxima [A]  time = 0.34, size = 13, normalized size = 0.57 \begin {gather*} -\frac {3}{4} \, x^{2} + x \log \relax (3) + 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3/4*x^2 + x*log(3) + 4*x

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mupad [B]  time = 6.11, size = 12, normalized size = 0.52 \begin {gather*} x\,\left (\ln \relax (3)+4\right )-\frac {3\,x^2}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(3) - (3*x)/2 + 4,x)

[Out]

x*(log(3) + 4) - (3*x^2)/4

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sympy [A]  time = 0.05, size = 12, normalized size = 0.52 \begin {gather*} - \frac {3 x^{2}}{4} + x \left (\log {\relax (3 )} + 4\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*x**2/4 + x*(log(3) + 4)

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