Optimal. Leaf size=27 \[ -\frac{6 x}{25}-\frac{11}{125 (5 x+3)}+\frac{31}{125} \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0330552, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ -\frac{6 x}{25}-\frac{11}{125 (5 x+3)}+\frac{31}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)*(2 + 3*x))/(3 + 5*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{31 \log{\left (5 x + 3 \right )}}{125} + \int \left (- \frac{6}{25}\right )\, dx - \frac{11}{125 \left (5 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)*(2+3*x)/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0171671, size = 26, normalized size = 0.96 \[ \frac{1}{125} \left (-30 x-\frac{11}{5 x+3}+31 \log (5 x+3)-18\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)*(2 + 3*x))/(3 + 5*x)^2,x]
[Out]
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Maple [A] time = 0.01, size = 22, normalized size = 0.8 \[ -{\frac{6\,x}{25}}-{\frac{11}{375+625\,x}}+{\frac{31\,\ln \left ( 3+5\,x \right ) }{125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)*(2+3*x)/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.3431, size = 28, normalized size = 1.04 \[ -\frac{6}{25} \, x - \frac{11}{125 \,{\left (5 \, x + 3\right )}} + \frac{31}{125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)*(2*x - 1)/(5*x + 3)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213126, size = 43, normalized size = 1.59 \[ -\frac{150 \, x^{2} - 31 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 90 \, x + 11}{125 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)*(2*x - 1)/(5*x + 3)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.188679, size = 20, normalized size = 0.74 \[ - \frac{6 x}{25} + \frac{31 \log{\left (5 x + 3 \right )}}{125} - \frac{11}{625 x + 375} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)*(2+3*x)/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.211597, size = 43, normalized size = 1.59 \[ -\frac{6}{25} \, x - \frac{11}{125 \,{\left (5 \, x + 3\right )}} - \frac{31}{125} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) - \frac{18}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)*(2*x - 1)/(5*x + 3)^2,x, algorithm="giac")
[Out]