Optimal. Leaf size=38 \[ -\frac{18 x}{125}-\frac{64}{625 (5 x+3)}-\frac{11}{1250 (5 x+3)^2}+\frac{87}{625} \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0472724, 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 \[ -\frac{18 x}{125}-\frac{64}{625 (5 x+3)}-\frac{11}{1250 (5 x+3)^2}+\frac{87}{625} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)*(2 + 3*x)^2)/(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{87 \log{\left (5 x + 3 \right )}}{625} + \int \left (- \frac{18}{125}\right )\, dx - \frac{64}{625 \left (5 x + 3\right )} - \frac{11}{1250 \left (5 x + 3\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)*(2+3*x)**2/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0276094, size = 39, normalized size = 1.03 \[ \frac{87}{625} \log (-3 (5 x+3))-\frac{900 x^3+1680 x^2+1172 x+295}{250 (5 x+3)^2} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)*(2 + 3*x)^2)/(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.008, size = 31, normalized size = 0.8 \[ -{\frac{18\,x}{125}}-{\frac{11}{1250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{64}{1875+3125\,x}}+{\frac{87\,\ln \left ( 3+5\,x \right ) }{625}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)*(2+3*x)^2/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.40266, size = 42, normalized size = 1.11 \[ -\frac{18}{125} \, x - \frac{128 \, x + 79}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{87}{625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^2*(2*x - 1)/(5*x + 3)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220602, size = 63, normalized size = 1.66 \[ -\frac{4500 \, x^{3} + 5400 \, x^{2} - 174 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 2260 \, x + 395}{1250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^2*(2*x - 1)/(5*x + 3)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.266315, size = 29, normalized size = 0.76 \[ - \frac{18 x}{125} - \frac{128 x + 79}{6250 x^{2} + 7500 x + 2250} + \frac{87 \log{\left (5 x + 3 \right )}}{625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)*(2+3*x)**2/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.212871, size = 36, normalized size = 0.95 \[ -\frac{18}{125} \, x - \frac{128 \, x + 79}{250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{87}{625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^2*(2*x - 1)/(5*x + 3)^3,x, algorithm="giac")
[Out]