3.25.60 \(\int \frac {-4 x+3 \log (\frac {5}{3})}{-2 x^2+(-1+3 x) \log (\frac {5}{3})} \, dx\)

Optimal. Leaf size=21 \[ \log \left (2 x+x \left (-5+\frac {1}{x}+\frac {2 x}{\log \left (\frac {5}{3}\right )}\right )\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 17, normalized size of antiderivative = 0.81, number of steps used = 1, number of rules used = 1, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {1587} \begin {gather*} \log \left (2 x^2+(1-3 x) \log \left (\frac {5}{3}\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-4*x + 3*Log[5/3])/(-2*x^2 + (-1 + 3*x)*Log[5/3]),x]

[Out]

Log[2*x^2 + (1 - 3*x)*Log[5/3]]

Rule 1587

Int[(Pp_)/(Qq_), x_Symbol] :> With[{p = Expon[Pp, x], q = Expon[Qq, x]}, Simp[(Coeff[Pp, x, p]*Log[RemoveConte
nt[Qq, x]])/(q*Coeff[Qq, x, q]), x] /; EqQ[p, q - 1] && EqQ[Pp, Simplify[(Coeff[Pp, x, p]*D[Qq, x])/(q*Coeff[Q
q, x, q])]]] /; PolyQ[Pp, x] && PolyQ[Qq, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\log \left (2 x^2+(1-3 x) \log \left (\frac {5}{3}\right )\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 18, normalized size = 0.86 \begin {gather*} \log \left (2 x^2+\log \left (\frac {5}{3}\right )-3 x \log \left (\frac {5}{3}\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-4*x + 3*Log[5/3])/(-2*x^2 + (-1 + 3*x)*Log[5/3]),x]

[Out]

Log[2*x^2 + Log[5/3] - 3*x*Log[5/3]]

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fricas [A]  time = 0.98, size = 16, normalized size = 0.76 \begin {gather*} \log \left (2 \, x^{2} - {\left (3 \, x - 1\right )} \log \left (\frac {5}{3}\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*log(5/3)-4*x)/((3*x-1)*log(5/3)-2*x^2),x, algorithm="fricas")

[Out]

log(2*x^2 - (3*x - 1)*log(5/3))

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giac [A]  time = 0.20, size = 14, normalized size = 0.67 \begin {gather*} \log \left (2 \, x^{2} - 3 \, x \log \left (\frac {5}{3}\right ) + \log \left (\frac {5}{3}\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*log(5/3)-4*x)/((3*x-1)*log(5/3)-2*x^2),x, algorithm="giac")

[Out]

log(2*x^2 - 3*x*log(5/3) + log(5/3))

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maple [A]  time = 0.73, size = 16, normalized size = 0.76

method	result	size
derivativedivides	\(\ln \left (\left (3 x -1\right ) \ln \left (\frac {5}{3}\right )-2 x^{2}\right )\)	\(16\)
default	\(\ln \left (3 \ln \left (\frac {5}{3}\right ) x -2 x^{2}-\ln \left (\frac {5}{3}\right )\right )\)	\(17\)
norman	\(\ln \left (3 \ln \left (\frac {5}{3}\right ) x -2 x^{2}-\ln \left (\frac {5}{3}\right )\right )\)	\(17\)
risch	\(\ln \left (2 x^{2}+\left (3 \ln \relax (3)-3 \ln \relax (5)\right ) x +\ln \relax (5)-\ln \relax (3)\right )\)	\(25\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*ln(5/3)-4*x)/((3*x-1)*ln(5/3)-2*x^2),x,method=_RETURNVERBOSE)

[Out]

ln((3*x-1)*ln(5/3)-2*x^2)

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maxima [A]  time = 0.42, size = 16, normalized size = 0.76 \begin {gather*} \log \left (2 \, x^{2} - {\left (3 \, x - 1\right )} \log \left (\frac {5}{3}\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*log(5/3)-4*x)/((3*x-1)*log(5/3)-2*x^2),x, algorithm="maxima")

[Out]

log(2*x^2 - (3*x - 1)*log(5/3))

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mupad [B]  time = 0.10, size = 14, normalized size = 0.67 \begin {gather*} \ln \left (2\,x^2-3\,\ln \left (\frac {5}{3}\right )\,x+\ln \left (\frac {5}{3}\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(4*x - 3*log(5/3))/(log(5/3)*(3*x - 1) - 2*x^2),x)

[Out]

log(log(5/3) - 3*x*log(5/3) + 2*x^2)

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sympy [A]  time = 0.23, size = 24, normalized size = 1.14 \begin {gather*} \log {\left (2 x^{2} + x \left (- 3 \log {\relax (5 )} + 3 \log {\relax (3 )}\right ) - \log {\relax (3 )} + \log {\relax (5 )} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*ln(5/3)-4*x)/((3*x-1)*ln(5/3)-2*x**2),x)

[Out]

log(2*x**2 + x*(-3*log(5) + 3*log(3)) - log(3) + log(5))

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