Optimal. Leaf size=33 \[ -\frac{125 x^2}{12}-\frac{1225 x}{36}-\frac{1331}{56} \log (1-2 x)-\frac{1}{189} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0413524, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{125 x^2}{12}-\frac{1225 x}{36}-\frac{1331}{56} \log (1-2 x)-\frac{1}{189} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{1331 \log{\left (- 2 x + 1 \right )}}{56} - \frac{\log{\left (3 x + 2 \right )}}{189} + \int \left (- \frac{1225}{36}\right )\, dx - \frac{125 \int x\, dx}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**3/(1-2*x)/(2+3*x),x)
[Out]
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Mathematica [A] time = 0.0259938, size = 35, normalized size = 1.06 \[ \frac{-1050 \left (15 x^2+49 x+24\right )-35937 \log (5-10 x)-8 \log (5 (3 x+2))}{1512} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)),x]
[Out]
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Maple [A] time = 0.009, size = 26, normalized size = 0.8 \[ -{\frac{125\,{x}^{2}}{12}}-{\frac{1225\,x}{36}}-{\frac{\ln \left ( 2+3\,x \right ) }{189}}-{\frac{1331\,\ln \left ( -1+2\,x \right ) }{56}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^3/(1-2*x)/(2+3*x),x)
[Out]
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Maxima [A] time = 1.34615, size = 34, normalized size = 1.03 \[ -\frac{125}{12} \, x^{2} - \frac{1225}{36} \, x - \frac{1}{189} \, \log \left (3 \, x + 2\right ) - \frac{1331}{56} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3/((3*x + 2)*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218029, size = 34, normalized size = 1.03 \[ -\frac{125}{12} \, x^{2} - \frac{1225}{36} \, x - \frac{1}{189} \, \log \left (3 \, x + 2\right ) - \frac{1331}{56} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3/((3*x + 2)*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.28835, size = 31, normalized size = 0.94 \[ - \frac{125 x^{2}}{12} - \frac{1225 x}{36} - \frac{1331 \log{\left (x - \frac{1}{2} \right )}}{56} - \frac{\log{\left (x + \frac{2}{3} \right )}}{189} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)**3/(1-2*x)/(2+3*x),x)
[Out]
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GIAC/XCAS [A] time = 0.20986, size = 36, normalized size = 1.09 \[ -\frac{125}{12} \, x^{2} - \frac{1225}{36} \, x - \frac{1}{189} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{1331}{56} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3/((3*x + 2)*(2*x - 1)),x, algorithm="giac")
[Out]