3.42 \(\int \frac{B^2+B C x+C^2 x^2}{-B^3+C^3 x^3} \, dx\)

Optimal. Leaf size=11 \[ \frac{\log (B-C x)}{C} \]

[Out]

Log[B - C*x]/C

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Rubi [A]  time = 0.0200754, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 31, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.065 \[ \frac{\log (B-C x)}{C} \]

Antiderivative was successfully verified.

[In]  Int[(B^2 + B*C*x + C^2*x^2)/(-B^3 + C^3*x^3),x]

[Out]

Log[B - C*x]/C

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Rubi in Sympy [A]  time = 6.53793, size = 7, normalized size = 0.64 \[ \frac{\log{\left (B - C x \right )}}{C} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((C**2*x**2+B*C*x+B**2)/(C**3*x**3-B**3),x)

[Out]

log(B - C*x)/C

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Mathematica [A]  time = 0.00257394, size = 12, normalized size = 1.09 \[ \frac{\log (C x-B)}{C} \]

Antiderivative was successfully verified.

[In]  Integrate[(B^2 + B*C*x + C^2*x^2)/(-B^3 + C^3*x^3),x]

[Out]

Log[-B + C*x]/C

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Maple [A]  time = 0.003, size = 12, normalized size = 1.1 \[{\frac{\ln \left ( -Cx+B \right ) }{C}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((C^2*x^2+B*C*x+B^2)/(C^3*x^3-B^3),x)

[Out]

ln(-C*x+B)/C

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Maxima [A]  time = 1.3649, size = 16, normalized size = 1.45 \[ \frac{\log \left (C x - B\right )}{C} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((C^2*x^2 + B*C*x + B^2)/(C^3*x^3 - B^3),x, algorithm="maxima")

[Out]

log(C*x - B)/C

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Fricas [A]  time = 0.229778, size = 16, normalized size = 1.45 \[ \frac{\log \left (C x - B\right )}{C} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((C^2*x^2 + B*C*x + B^2)/(C^3*x^3 - B^3),x, algorithm="fricas")

[Out]

log(C*x - B)/C

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Sympy [A]  time = 0.062702, size = 7, normalized size = 0.64 \[ \frac{\log{\left (- B + C x \right )}}{C} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((C**2*x**2+B*C*x+B**2)/(C**3*x**3-B**3),x)

[Out]

log(-B + C*x)/C

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GIAC/XCAS [A]  time = 0.233571, size = 18, normalized size = 1.64 \[ \frac{{\rm ln}\left ({\left | C x - B \right |}\right )}{C} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((C^2*x^2 + B*C*x + B^2)/(C^3*x^3 - B^3),x, algorithm="giac")

[Out]

ln(abs(C*x - B))/C