Optimal. Leaf size=33 \[ -\frac{31}{125 (5 x+3)}-\frac{11}{250 (5 x+3)^2}-\frac{6}{125} \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0350468, antiderivative size = 33, 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 \[ -\frac{31}{125 (5 x+3)}-\frac{11}{250 (5 x+3)^2}-\frac{6}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)*(2 + 3*x))/(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 6.10584, size = 27, normalized size = 0.82 \[ - \frac{6 \log{\left (5 x + 3 \right )}}{125} - \frac{31}{125 \left (5 x + 3\right )} - \frac{11}{250 \left (5 x + 3\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)*(2+3*x)/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0123171, size = 33, normalized size = 1. \[ -\frac{31}{125 (5 x+3)}-\frac{11}{250 (5 x+3)^2}-\frac{6}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)*(2 + 3*x))/(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.008, size = 28, normalized size = 0.9 \[ -{\frac{11}{250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{31}{375+625\,x}}-{\frac{6\,\ln \left ( 3+5\,x \right ) }{125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)*(2+3*x)/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.35184, size = 38, normalized size = 1.15 \[ -\frac{310 \, x + 197}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} - \frac{6}{125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)*(2*x - 1)/(5*x + 3)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.226339, size = 50, normalized size = 1.52 \[ -\frac{12 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 310 \, x + 197}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)*(2*x - 1)/(5*x + 3)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.243395, size = 26, normalized size = 0.79 \[ - \frac{310 x + 197}{6250 x^{2} + 7500 x + 2250} - \frac{6 \log{\left (5 x + 3 \right )}}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)*(2+3*x)/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.207319, size = 32, normalized size = 0.97 \[ -\frac{310 \, x + 197}{250 \,{\left (5 \, x + 3\right )}^{2}} - \frac{6}{125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)*(2*x - 1)/(5*x + 3)^3,x, algorithm="giac")
[Out]