3.544 \(\int \frac{243+162 x+108 x^2+72 x^3+48 x^4+32 x^5}{729-64 x^6} \, dx\)

Optimal. Leaf size=10 \[ -\frac{1}{2} \log (3-2 x) \]

[Out]

-Log[3 - 2*x]/2

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Rubi [A]  time = 0.0158625, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 35, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.057 \[ -\frac{1}{2} \log (3-2 x) \]

Antiderivative was successfully verified.

[In]  Int[(243 + 162*x + 108*x^2 + 72*x^3 + 48*x^4 + 32*x^5)/(729 - 64*x^6),x]

[Out]

-Log[3 - 2*x]/2

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Rubi in Sympy [A]  time = 7.47107, size = 8, normalized size = 0.8 \[ - \frac{\log{\left (- 2 x + 3 \right )}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((32*x**5+48*x**4+72*x**3+108*x**2+162*x+243)/(-64*x**6+729),x)

[Out]

-log(-2*x + 3)/2

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Mathematica [A]  time = 0.00179574, size = 10, normalized size = 1. \[ -\frac{1}{2} \log (3-2 x) \]

Antiderivative was successfully verified.

[In]  Integrate[(243 + 162*x + 108*x^2 + 72*x^3 + 48*x^4 + 32*x^5)/(729 - 64*x^6),x]

[Out]

-Log[3 - 2*x]/2

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Maple [A]  time = 0.001, size = 9, normalized size = 0.9 \[ -{\frac{\ln \left ( -3+2\,x \right ) }{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((32*x^5+48*x^4+72*x^3+108*x^2+162*x+243)/(-64*x^6+729),x)

[Out]

-1/2*ln(-3+2*x)

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Maxima [A]  time = 1.40774, size = 11, normalized size = 1.1 \[ -\frac{1}{2} \, \log \left (2 \, x - 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(32*x^5 + 48*x^4 + 72*x^3 + 108*x^2 + 162*x + 243)/(64*x^6 - 729),x, algorithm="maxima")

[Out]

-1/2*log(2*x - 3)

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Fricas [A]  time = 0.20057, size = 11, normalized size = 1.1 \[ -\frac{1}{2} \, \log \left (2 \, x - 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(32*x^5 + 48*x^4 + 72*x^3 + 108*x^2 + 162*x + 243)/(64*x^6 - 729),x, algorithm="fricas")

[Out]

-1/2*log(2*x - 3)

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Sympy [A]  time = 0.062623, size = 8, normalized size = 0.8 \[ - \frac{\log{\left (2 x - 3 \right )}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((32*x**5+48*x**4+72*x**3+108*x**2+162*x+243)/(-64*x**6+729),x)

[Out]

-log(2*x - 3)/2

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GIAC/XCAS [A]  time = 0.217028, size = 12, normalized size = 1.2 \[ -\frac{1}{2} \,{\rm ln}\left ({\left | 2 \, x - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(32*x^5 + 48*x^4 + 72*x^3 + 108*x^2 + 162*x + 243)/(64*x^6 - 729),x, algorithm="giac")

[Out]

-1/2*ln(abs(2*x - 3))