3.177 \(\int \frac{x}{-5+x} \, dx\)

Optimal. Leaf size=10 \[ x+5 \log (5-x) \]

[Out]

x + 5*Log[5 - x]

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Rubi [A]  time = 0.0118842, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ x+5 \log (5-x) \]

Antiderivative was successfully verified.

[In]  Int[x/(-5 + x),x]

[Out]

x + 5*Log[5 - x]

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Rubi in Sympy [A]  time = 1.06624, size = 7, normalized size = 0.7 \[ x + 5 \log{\left (- x + 5 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x/(-5+x),x)

[Out]

x + 5*log(-x + 5)

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Mathematica [A]  time = 0.00193654, size = 8, normalized size = 0.8 \[ x+5 \log (x-5) \]

Antiderivative was successfully verified.

[In]  Integrate[x/(-5 + x),x]

[Out]

x + 5*Log[-5 + x]

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Maple [A]  time = 0.003, size = 9, normalized size = 0.9 \[ x+5\,\ln \left ( -5+x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x/(-5+x),x)

[Out]

x+5*ln(-5+x)

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Maxima [A]  time = 1.3611, size = 11, normalized size = 1.1 \[ x + 5 \, \log \left (x - 5\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(x - 5),x, algorithm="maxima")

[Out]

x + 5*log(x - 5)

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Fricas [A]  time = 0.195011, size = 11, normalized size = 1.1 \[ x + 5 \, \log \left (x - 5\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(x - 5),x, algorithm="fricas")

[Out]

x + 5*log(x - 5)

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Sympy [A]  time = 0.0566, size = 7, normalized size = 0.7 \[ x + 5 \log{\left (x - 5 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(-5+x),x)

[Out]

x + 5*log(x - 5)

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GIAC/XCAS [A]  time = 0.208451, size = 12, normalized size = 1.2 \[ x + 5 \,{\rm ln}\left ({\left | x - 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(x - 5),x, algorithm="giac")

[Out]

x + 5*ln(abs(x - 5))