Optimal. Leaf size=15 \[ 2 \log (1-x)+3 \log (x+3) \]
[Out]
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Rubi [A] time = 0.0148709, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ 2 \log (1-x)+3 \log (x+3) \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)/(-3 + 2*x + x^2),x]
[Out]
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Rubi in Sympy [A] time = 2.01697, size = 12, normalized size = 0.8 \[ 2 \log{\left (- x + 1 \right )} + 3 \log{\left (x + 3 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)/(x**2+2*x-3),x)
[Out]
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Mathematica [A] time = 0.00618239, size = 15, normalized size = 1. \[ 2 \log (1-x)+3 \log (x+3) \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)/(-3 + 2*x + x^2),x]
[Out]
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Maple [A] time = 0.007, size = 14, normalized size = 0.9 \[ 2\,\ln \left ( -1+x \right ) +3\,\ln \left ( 3+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)/(x^2+2*x-3),x)
[Out]
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Maxima [A] time = 1.37797, size = 18, normalized size = 1.2 \[ 3 \, \log \left (x + 3\right ) + 2 \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)/(x^2 + 2*x - 3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.197893, size = 18, normalized size = 1.2 \[ 3 \, \log \left (x + 3\right ) + 2 \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)/(x^2 + 2*x - 3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.114409, size = 12, normalized size = 0.8 \[ 2 \log{\left (x - 1 \right )} + 3 \log{\left (x + 3 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)/(x**2+2*x-3),x)
[Out]
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GIAC/XCAS [A] time = 0.221742, size = 20, normalized size = 1.33 \[ 3 \,{\rm ln}\left ({\left | x + 3 \right |}\right ) + 2 \,{\rm ln}\left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)/(x^2 + 2*x - 3),x, algorithm="giac")
[Out]