Optimal. Leaf size=38 \[ \frac{12 x}{125}-\frac{319}{625 (5 x+3)}-\frac{121}{1250 (5 x+3)^2}-\frac{128}{625} \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0466938, antiderivative size = 38, 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 \[ \frac{12 x}{125}-\frac{319}{625 (5 x+3)}-\frac{121}{1250 (5 x+3)^2}-\frac{128}{625} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^2*(2 + 3*x))/(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{128 \log{\left (5 x + 3 \right )}}{625} + \int \frac{12}{125}\, dx - \frac{319}{625 \left (5 x + 3\right )} - \frac{121}{1250 \left (5 x + 3\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(2+3*x)/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0267467, size = 37, normalized size = 0.97 \[ \frac{\frac{5 \left (600 x^3+420 x^2-782 x-515\right )}{(5 x+3)^2}-256 \log (10 x+6)}{1250} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^2*(2 + 3*x))/(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.009, size = 31, normalized size = 0.8 \[{\frac{12\,x}{125}}-{\frac{121}{1250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{319}{1875+3125\,x}}-{\frac{128\,\ln \left ( 3+5\,x \right ) }{625}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(2+3*x)/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.35592, size = 42, normalized size = 1.11 \[ \frac{12}{125} \, x - \frac{11 \,{\left (58 \, x + 37\right )}}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} - \frac{128}{625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)*(2*x - 1)^2/(5*x + 3)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207649, size = 63, normalized size = 1.66 \[ \frac{3000 \, x^{3} + 3600 \, x^{2} - 256 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 2110 \, x - 2035}{1250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)*(2*x - 1)^2/(5*x + 3)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.265727, size = 29, normalized size = 0.76 \[ \frac{12 x}{125} - \frac{638 x + 407}{6250 x^{2} + 7500 x + 2250} - \frac{128 \log{\left (5 x + 3 \right )}}{625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(2+3*x)/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.205795, size = 36, normalized size = 0.95 \[ \frac{12}{125} \, x - \frac{11 \,{\left (58 \, x + 37\right )}}{250 \,{\left (5 \, x + 3\right )}^{2}} - \frac{128}{625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)*(2*x - 1)^2/(5*x + 3)^3,x, algorithm="giac")
[Out]