Optimal. Leaf size=32 \[ -\frac{121}{25 (5 x+3)}+\frac{49}{3} \log (3 x+2)-\frac{407}{25} \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0412167, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{121}{25 (5 x+3)}+\frac{49}{3} \log (3 x+2)-\frac{407}{25} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2/((2 + 3*x)*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 6.29667, size = 26, normalized size = 0.81 \[ \frac{49 \log{\left (3 x + 2 \right )}}{3} - \frac{407 \log{\left (5 x + 3 \right )}}{25} - \frac{121}{25 \left (5 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2/(2+3*x)/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0330354, size = 32, normalized size = 1. \[ -\frac{121}{125 x+75}+\frac{49}{3} \log (3 x+2)-\frac{407}{25} \log (-3 (5 x+3)) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2/((2 + 3*x)*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.01, size = 27, normalized size = 0.8 \[ -{\frac{121}{75+125\,x}}+{\frac{49\,\ln \left ( 2+3\,x \right ) }{3}}-{\frac{407\,\ln \left ( 3+5\,x \right ) }{25}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2/(2+3*x)/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.34939, size = 35, normalized size = 1.09 \[ -\frac{121}{25 \,{\left (5 \, x + 3\right )}} - \frac{407}{25} \, \log \left (5 \, x + 3\right ) + \frac{49}{3} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^2*(3*x + 2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211267, size = 50, normalized size = 1.56 \[ -\frac{1221 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 1225 \,{\left (5 \, x + 3\right )} \log \left (3 \, x + 2\right ) + 363}{75 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^2*(3*x + 2)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.323972, size = 26, normalized size = 0.81 \[ - \frac{407 \log{\left (x + \frac{3}{5} \right )}}{25} + \frac{49 \log{\left (x + \frac{2}{3} \right )}}{3} - \frac{121}{125 x + 75} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2/(2+3*x)/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.212047, size = 58, normalized size = 1.81 \[ -\frac{121}{25 \,{\left (5 \, x + 3\right )}} - \frac{4}{75} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) + \frac{49}{3} \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^2*(3*x + 2)),x, algorithm="giac")
[Out]