3.27.75 \(\int \frac {-2 x+(-11+2 x) \log (3)}{\log (3)} \, dx\)

Optimal. Leaf size=18 \[ (-5+x)^2-x-\frac {x^2}{\log (3)} \]

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Rubi [A]  time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.17, number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {12} \begin {gather*} \frac {1}{4} (11-2 x)^2-\frac {x^2}{\log (3)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-2*x + (-11 + 2*x)*Log[3])/Log[3],x]

[Out]

(11 - 2*x)^2/4 - x^2/Log[3]

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int (-2 x+(-11+2 x) \log (3)) \, dx}{\log (3)}\\ &=\frac {1}{4} (11-2 x)^2-\frac {x^2}{\log (3)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 19, normalized size = 1.06 \begin {gather*} -11 x+\frac {x^2 (-2+\log (9))}{2 \log (3)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2*x + (-11 + 2*x)*Log[3])/Log[3],x]

[Out]

-11*x + (x^2*(-2 + Log[9]))/(2*Log[3])

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fricas [A]  time = 0.62, size = 21, normalized size = 1.17 \begin {gather*} -\frac {x^{2} - {\left (x^{2} - 11 \, x\right )} \log \relax (3)}{\log \relax (3)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x-11)*log(3)-2*x)/log(3),x, algorithm="fricas")

[Out]

-(x^2 - (x^2 - 11*x)*log(3))/log(3)

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giac [A]  time = 0.25, size = 21, normalized size = 1.17 \begin {gather*} -\frac {x^{2} - {\left (x^{2} - 11 \, x\right )} \log \relax (3)}{\log \relax (3)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x-11)*log(3)-2*x)/log(3),x, algorithm="giac")

[Out]

-(x^2 - (x^2 - 11*x)*log(3))/log(3)

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maple [A]  time = 0.02, size = 17, normalized size = 0.94

method	result	size
norman	\(\frac {\left (\ln \relax (3)-1\right ) x^{2}}{\ln \relax (3)}-11 x\)	\(17\)
risch	\(x^{2}-11 x -\frac {x^{2}}{\ln \relax (3)}\)	\(17\)
gosper	\(\frac {x \left (x \ln \relax (3)-11 \ln \relax (3)-x \right )}{\ln \relax (3)}\)	\(19\)
default	\(\frac {\ln \relax (3) \left (x^{2}-11 x \right )-x^{2}}{\ln \relax (3)}\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*x-11)*ln(3)-2*x)/ln(3),x,method=_RETURNVERBOSE)

[Out]

(ln(3)-1)/ln(3)*x^2-11*x

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maxima [A]  time = 0.35, size = 21, normalized size = 1.17 \begin {gather*} -\frac {x^{2} - {\left (x^{2} - 11 \, x\right )} \log \relax (3)}{\log \relax (3)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x-11)*log(3)-2*x)/log(3),x, algorithm="maxima")

[Out]

-(x^2 - (x^2 - 11*x)*log(3))/log(3)

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mupad [B]  time = 0.06, size = 16, normalized size = 0.89 \begin {gather*} \frac {x^2\,\left (\ln \relax (3)-1\right )}{\ln \relax (3)}-11\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*x - log(3)*(2*x - 11))/log(3),x)

[Out]

(x^2*(log(3) - 1))/log(3) - 11*x

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sympy [A]  time = 0.05, size = 14, normalized size = 0.78 \begin {gather*} \frac {x^{2} \left (-1 + \log {\relax (3 )}\right )}{\log {\relax (3 )}} - 11 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x-11)*ln(3)-2*x)/ln(3),x)

[Out]

x**2*(-1 + log(3))/log(3) - 11*x

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