3.115 \(\int \frac{3+2 x}{(-2+x) (5+x)} \, dx\)

Optimal. Leaf size=11 \[ \log (2-x)+\log (x+5) \]

[Out]

Log[2 - x] + Log[5 + x]

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Rubi [A]  time = 0.0182272, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ \log (2-x)+\log (x+5) \]

Antiderivative was successfully verified.

[In]  Int[(3 + 2*x)/((-2 + x)*(5 + x)),x]

[Out]

Log[2 - x] + Log[5 + x]

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Rubi in Sympy [A]  time = 1.47666, size = 8, normalized size = 0.73 \[ \log{\left (- x + 2 \right )} + \log{\left (x + 5 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((3+2*x)/(-2+x)/(5+x),x)

[Out]

log(-x + 2) + log(x + 5)

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Mathematica [A]  time = 0.00550531, size = 9, normalized size = 0.82 \[ \log (x-2)+\log (x+5) \]

Antiderivative was successfully verified.

[In]  Integrate[(3 + 2*x)/((-2 + x)*(5 + x)),x]

[Out]

Log[-2 + x] + Log[5 + x]

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Maple [A]  time = 0.002, size = 9, normalized size = 0.8 \[ \ln \left ( \left ( -2+x \right ) \left ( 5+x \right ) \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+2*x)/(-2+x)/(5+x),x)

[Out]

ln((-2+x)*(5+x))

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Maxima [A]  time = 1.34278, size = 12, normalized size = 1.09 \[ \log \left (x + 5\right ) + \log \left (x - 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x + 3)/((x + 5)*(x - 2)),x, algorithm="maxima")

[Out]

log(x + 5) + log(x - 2)

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Fricas [A]  time = 0.18985, size = 12, normalized size = 1.09 \[ \log \left (x^{2} + 3 \, x - 10\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x + 3)/((x + 5)*(x - 2)),x, algorithm="fricas")

[Out]

log(x^2 + 3*x - 10)

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Sympy [A]  time = 0.083926, size = 8, normalized size = 0.73 \[ \log{\left (x^{2} + 3 x - 10 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3+2*x)/(-2+x)/(5+x),x)

[Out]

log(x**2 + 3*x - 10)

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GIAC/XCAS [A]  time = 0.224585, size = 15, normalized size = 1.36 \[{\rm ln}\left ({\left | x + 5 \right |}\right ) +{\rm ln}\left ({\left | x - 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x + 3)/((x + 5)*(x - 2)),x, algorithm="giac")

[Out]

ln(abs(x + 5)) + ln(abs(x - 2))