3.162 \(\int \frac{1}{(5-6 x)^2 x^2} \, dx\)

Optimal. Leaf size=35 \[ \frac{6}{25 (5-6 x)}-\frac{1}{25 x}-\frac{12}{125} \log (5-6 x)+\frac{12 \log (x)}{125} \]

[Out]

6/(25*(5 - 6*x)) - 1/(25*x) - (12*Log[5 - 6*x])/125 + (12*Log[x])/125

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Rubi [A]  time = 0.0324588, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{6}{25 (5-6 x)}-\frac{1}{25 x}-\frac{12}{125} \log (5-6 x)+\frac{12 \log (x)}{125} \]

Antiderivative was successfully verified.

[In]  Int[1/((5 - 6*x)^2*x^2),x]

[Out]

6/(25*(5 - 6*x)) - 1/(25*x) - (12*Log[5 - 6*x])/125 + (12*Log[x])/125

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Rubi in Sympy [A]  time = 2.39384, size = 27, normalized size = 0.77 \[ \frac{12 \log{\left (x \right )}}{125} - \frac{12 \log{\left (- 6 x + 5 \right )}}{125} + \frac{6}{25 \left (- 6 x + 5\right )} - \frac{1}{25 x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(5-6*x)**2/x**2,x)

[Out]

12*log(x)/125 - 12*log(-6*x + 5)/125 + 6/(25*(-6*x + 5)) - 1/(25*x)

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Mathematica [A]  time = 0.0280564, size = 31, normalized size = 0.89 \[ \frac{1}{125} \left (\frac{30}{5-6 x}-\frac{5}{x}-12 \log (5-6 x)+12 \log (x)\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[1/((5 - 6*x)^2*x^2),x]

[Out]

(30/(5 - 6*x) - 5/x - 12*Log[5 - 6*x] + 12*Log[x])/125

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Maple [A]  time = 0.013, size = 28, normalized size = 0.8 \[ -{\frac{6}{-125+150\,x}}-{\frac{12\,\ln \left ( -5+6\,x \right ) }{125}}-{\frac{1}{25\,x}}+{\frac{12\,\ln \left ( x \right ) }{125}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(5-6*x)^2/x^2,x)

[Out]

-6/25/(-5+6*x)-12/125*ln(-5+6*x)-1/25/x+12/125*ln(x)

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Maxima [A]  time = 1.79919, size = 42, normalized size = 1.2 \[ -\frac{12 \, x - 5}{25 \,{\left (6 \, x^{2} - 5 \, x\right )}} - \frac{12}{125} \, \log \left (6 \, x - 5\right ) + \frac{12}{125} \, \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((6*x - 5)^2*x^2),x, algorithm="maxima")

[Out]

-1/25*(12*x - 5)/(6*x^2 - 5*x) - 12/125*log(6*x - 5) + 12/125*log(x)

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Fricas [A]  time = 0.214233, size = 65, normalized size = 1.86 \[ -\frac{12 \,{\left (6 \, x^{2} - 5 \, x\right )} \log \left (6 \, x - 5\right ) - 12 \,{\left (6 \, x^{2} - 5 \, x\right )} \log \left (x\right ) + 60 \, x - 25}{125 \,{\left (6 \, x^{2} - 5 \, x\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((6*x - 5)^2*x^2),x, algorithm="fricas")

[Out]

-1/125*(12*(6*x^2 - 5*x)*log(6*x - 5) - 12*(6*x^2 - 5*x)*log(x) + 60*x - 25)/(6*
x^2 - 5*x)

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Sympy [A]  time = 0.138363, size = 29, normalized size = 0.83 \[ - \frac{12 x - 5}{150 x^{2} - 125 x} + \frac{12 \log{\left (x \right )}}{125} - \frac{12 \log{\left (x - \frac{5}{6} \right )}}{125} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(5-6*x)**2/x**2,x)

[Out]

-(12*x - 5)/(150*x**2 - 125*x) + 12*log(x)/125 - 12*log(x - 5/6)/125

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GIAC/XCAS [A]  time = 0.209292, size = 54, normalized size = 1.54 \[ -\frac{6}{25 \,{\left (6 \, x - 5\right )}} + \frac{6}{125 \,{\left (\frac{5}{6 \, x - 5} + 1\right )}} + \frac{12}{125} \,{\rm ln}\left ({\left | -\frac{5}{6 \, x - 5} - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((6*x - 5)^2*x^2),x, algorithm="giac")

[Out]

-6/25/(6*x - 5) + 6/125/(5/(6*x - 5) + 1) + 12/125*ln(abs(-5/(6*x - 5) - 1))