Optimal. Leaf size=23 \[ \frac{2 x^2}{5}-\frac{32 x}{25}+\frac{121}{125} \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0217076, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{2 x^2}{5}-\frac{32 x}{25}+\frac{121}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2/(3 + 5*x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{121 \log{\left (5 x + 3 \right )}}{125} + \int \left (- \frac{32}{25}\right )\, dx + \frac{4 \int x\, dx}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.00856435, size = 22, normalized size = 0.96 \[ \frac{1}{125} \left (50 x^2-160 x+121 \log (5 x+3)-114\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2/(3 + 5*x),x]
[Out]
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Maple [A] time = 0.003, size = 18, normalized size = 0.8 \[ -{\frac{32\,x}{25}}+{\frac{2\,{x}^{2}}{5}}+{\frac{121\,\ln \left ( 3+5\,x \right ) }{125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2/(3+5*x),x)
[Out]
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Maxima [A] time = 1.35199, size = 23, normalized size = 1. \[ \frac{2}{5} \, x^{2} - \frac{32}{25} \, x + \frac{121}{125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/(5*x + 3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.209169, size = 23, normalized size = 1. \[ \frac{2}{5} \, x^{2} - \frac{32}{25} \, x + \frac{121}{125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/(5*x + 3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.131266, size = 20, normalized size = 0.87 \[ \frac{2 x^{2}}{5} - \frac{32 x}{25} + \frac{121 \log{\left (5 x + 3 \right )}}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.212493, size = 24, normalized size = 1.04 \[ \frac{2}{5} \, x^{2} - \frac{32}{25} \, x + \frac{121}{125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/(5*x + 3),x, algorithm="giac")
[Out]