Optimal. Leaf size=43 \[ \frac{1421}{27 (3 x+2)}+\frac{343}{54 (3 x+2)^2}-\frac{7189}{27} \log (3 x+2)+\frac{1331}{5} \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0508837, antiderivative size = 43, 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 \[ \frac{1421}{27 (3 x+2)}+\frac{343}{54 (3 x+2)^2}-\frac{7189}{27} \log (3 x+2)+\frac{1331}{5} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^3/((2 + 3*x)^3*(3 + 5*x)),x]
[Out]
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Rubi in Sympy [A] time = 7.3634, size = 36, normalized size = 0.84 \[ - \frac{7189 \log{\left (3 x + 2 \right )}}{27} + \frac{1331 \log{\left (5 x + 3 \right )}}{5} + \frac{1421}{27 \left (3 x + 2\right )} + \frac{343}{54 \left (3 x + 2\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3/(2+3*x)**3/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0410823, size = 39, normalized size = 0.91 \[ \frac{49 (58 x+41)}{18 (3 x+2)^2}-\frac{7189}{27} \log (5 (3 x+2))+\frac{1331}{5} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^3/((2 + 3*x)^3*(3 + 5*x)),x]
[Out]
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Maple [A] time = 0.011, size = 36, normalized size = 0.8 \[{\frac{343}{54\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{1421}{54+81\,x}}-{\frac{7189\,\ln \left ( 2+3\,x \right ) }{27}}+{\frac{1331\,\ln \left ( 3+5\,x \right ) }{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3/(2+3*x)^3/(3+5*x),x)
[Out]
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Maxima [A] time = 1.35044, size = 49, normalized size = 1.14 \[ \frac{49 \,{\left (58 \, x + 41\right )}}{18 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac{1331}{5} \, \log \left (5 \, x + 3\right ) - \frac{7189}{27} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)^3/((5*x + 3)*(3*x + 2)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.236078, size = 74, normalized size = 1.72 \[ \frac{71874 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (5 \, x + 3\right ) - 71890 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 42630 \, x + 30135}{270 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)^3/((5*x + 3)*(3*x + 2)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.388644, size = 34, normalized size = 0.79 \[ \frac{2842 x + 2009}{162 x^{2} + 216 x + 72} + \frac{1331 \log{\left (x + \frac{3}{5} \right )}}{5} - \frac{7189 \log{\left (x + \frac{2}{3} \right )}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3/(2+3*x)**3/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.209856, size = 45, normalized size = 1.05 \[ \frac{49 \,{\left (58 \, x + 41\right )}}{18 \,{\left (3 \, x + 2\right )}^{2}} + \frac{1331}{5} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{7189}{27} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)^3/((5*x + 3)*(3*x + 2)^3),x, algorithm="giac")
[Out]