3.51.45 \(\int \frac {-34+40 x}{-35-17 x+10 x^2+7 \log (3)} \, dx\)

Optimal. Leaf size=21 \[ \log \left (\left (5+x+\frac {10}{7} \left (x-x^2\right )-\log (3)\right )^2\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 20, normalized size of antiderivative = 0.95, number of steps used = 1, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {628} \begin {gather*} 2 \log \left (-10 x^2+17 x+7 (5-\log (3))\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-34 + 40*x)/(-35 - 17*x + 10*x^2 + 7*Log[3]),x]

[Out]

2*Log[17*x - 10*x^2 + 7*(5 - Log[3])]

Rule 628

Int[((d_) + (e_.)*(x_))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Simp[(d*Log[RemoveContent[a + b*x +
c*x^2, x]])/b, x] /; FreeQ[{a, b, c, d, e}, x] && EqQ[2*c*d - b*e, 0]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=2 \log \left (17 x-10 x^2+7 (5-\log (3))\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 18, normalized size = 0.86 \begin {gather*} 2 \log \left (-17 x+10 x^2+7 (-5+\log (3))\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-34 + 40*x)/(-35 - 17*x + 10*x^2 + 7*Log[3]),x]

[Out]

2*Log[-17*x + 10*x^2 + 7*(-5 + Log[3])]

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fricas [A]  time = 1.03, size = 17, normalized size = 0.81 \begin {gather*} 2 \, \log \left (10 \, x^{2} - 17 \, x + 7 \, \log \relax (3) - 35\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((40*x-34)/(7*log(3)+10*x^2-17*x-35),x, algorithm="fricas")

[Out]

2*log(10*x^2 - 17*x + 7*log(3) - 35)

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giac [A]  time = 0.14, size = 18, normalized size = 0.86 \begin {gather*} 2 \, \log \left ({\left | 10 \, x^{2} - 17 \, x + 7 \, \log \relax (3) - 35 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((40*x-34)/(7*log(3)+10*x^2-17*x-35),x, algorithm="giac")

[Out]

2*log(abs(10*x^2 - 17*x + 7*log(3) - 35))

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maple [A]  time = 0.27, size = 18, normalized size = 0.86

method	result	size
default	\(2 \ln \left (7 \ln \relax (3)+10 x^{2}-17 x -35\right )\)	\(18\)
norman	\(2 \ln \left (7 \ln \relax (3)+10 x^{2}-17 x -35\right )\)	\(18\)
risch	\(2 \ln \left (7 \ln \relax (3)+10 x^{2}-17 x -35\right )\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((40*x-34)/(7*ln(3)+10*x^2-17*x-35),x,method=_RETURNVERBOSE)

[Out]

2*ln(7*ln(3)+10*x^2-17*x-35)

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maxima [A]  time = 0.35, size = 17, normalized size = 0.81 \begin {gather*} 2 \, \log \left (10 \, x^{2} - 17 \, x + 7 \, \log \relax (3) - 35\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((40*x-34)/(7*log(3)+10*x^2-17*x-35),x, algorithm="maxima")

[Out]

2*log(10*x^2 - 17*x + 7*log(3) - 35)

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mupad [B]  time = 0.08, size = 17, normalized size = 0.81 \begin {gather*} 2\,\ln \left (10\,x^2-17\,x+7\,\ln \relax (3)-35\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(40*x - 34)/(17*x - 7*log(3) - 10*x^2 + 35),x)

[Out]

2*log(7*log(3) - 17*x + 10*x^2 - 35)

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sympy [A]  time = 0.15, size = 17, normalized size = 0.81 \begin {gather*} 2 \log {\left (10 x^{2} - 17 x - 35 + 7 \log {\relax (3 )} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((40*x-34)/(7*ln(3)+10*x**2-17*x-35),x)

[Out]

2*log(10*x**2 - 17*x - 35 + 7*log(3))

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