Optimal. Leaf size=30 \[ \frac{4 x^3}{5}-\frac{28 x^2}{25}+\frac{43 x}{125}+\frac{121}{625} \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0312799, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{4 x^3}{5}-\frac{28 x^2}{25}+\frac{43 x}{125}+\frac{121}{625} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^2*(2 + 3*x))/(3 + 5*x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{4 x^{3}}{5} + \frac{121 \log{\left (5 x + 3 \right )}}{625} + \int \frac{43}{125}\, dx - \frac{56 \int x\, dx}{25} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(2+3*x)/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0157787, size = 27, normalized size = 0.9 \[ \frac{1}{625} \left (500 x^3-700 x^2+215 x+121 \log (5 x+3)+489\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^2*(2 + 3*x))/(3 + 5*x),x]
[Out]
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Maple [A] time = 0.005, size = 23, normalized size = 0.8 \[{\frac{43\,x}{125}}-{\frac{28\,{x}^{2}}{25}}+{\frac{4\,{x}^{3}}{5}}+{\frac{121\,\ln \left ( 3+5\,x \right ) }{625}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(2+3*x)/(3+5*x),x)
[Out]
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Maxima [A] time = 1.35114, size = 30, normalized size = 1. \[ \frac{4}{5} \, x^{3} - \frac{28}{25} \, x^{2} + \frac{43}{125} \, x + \frac{121}{625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)*(2*x - 1)^2/(5*x + 3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212832, size = 30, normalized size = 1. \[ \frac{4}{5} \, x^{3} - \frac{28}{25} \, x^{2} + \frac{43}{125} \, x + \frac{121}{625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)*(2*x - 1)^2/(5*x + 3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.151231, size = 27, normalized size = 0.9 \[ \frac{4 x^{3}}{5} - \frac{28 x^{2}}{25} + \frac{43 x}{125} + \frac{121 \log{\left (5 x + 3 \right )}}{625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(2+3*x)/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.20628, size = 31, normalized size = 1.03 \[ \frac{4}{5} \, x^{3} - \frac{28}{25} \, x^{2} + \frac{43}{125} \, x + \frac{121}{625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)*(2*x - 1)^2/(5*x + 3),x, algorithm="giac")
[Out]