Optimal. Leaf size=48 \[ \frac{675 x^4}{16}+\frac{945 x^3}{4}+\frac{21717 x^2}{32}+\frac{12973 x}{8}+\frac{41503}{64 (1-2 x)}+\frac{91091}{64} \log (1-2 x) \]
[Out]
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Rubi [A] time = 0.0641672, antiderivative size = 48, 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 \[ \frac{675 x^4}{16}+\frac{945 x^3}{4}+\frac{21717 x^2}{32}+\frac{12973 x}{8}+\frac{41503}{64 (1-2 x)}+\frac{91091}{64} \log (1-2 x) \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^3*(3 + 5*x)^2)/(1 - 2*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{675 x^{4}}{16} + \frac{945 x^{3}}{4} + \frac{91091 \log{\left (- 2 x + 1 \right )}}{64} + \int \frac{12973}{8}\, dx + \frac{21717 \int x\, dx}{16} + \frac{41503}{64 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**3*(3+5*x)**2/(1-2*x)**2,x)
[Out]
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Mathematica [A] time = 0.023865, size = 49, normalized size = 1.02 \[ \frac{21600 x^5+110160 x^4+286992 x^3+656536 x^2-933610 x+364364 (2 x-1) \log (1-2 x)+93225}{256 (2 x-1)} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^3*(3 + 5*x)^2)/(1 - 2*x)^2,x]
[Out]
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Maple [A] time = 0.009, size = 37, normalized size = 0.8 \[{\frac{675\,{x}^{4}}{16}}+{\frac{945\,{x}^{3}}{4}}+{\frac{21717\,{x}^{2}}{32}}+{\frac{12973\,x}{8}}-{\frac{41503}{-64+128\,x}}+{\frac{91091\,\ln \left ( -1+2\,x \right ) }{64}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^3*(3+5*x)^2/(1-2*x)^2,x)
[Out]
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Maxima [A] time = 1.33758, size = 49, normalized size = 1.02 \[ \frac{675}{16} \, x^{4} + \frac{945}{4} \, x^{3} + \frac{21717}{32} \, x^{2} + \frac{12973}{8} \, x - \frac{41503}{64 \,{\left (2 \, x - 1\right )}} + \frac{91091}{64} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^3/(2*x - 1)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205551, size = 63, normalized size = 1.31 \[ \frac{5400 \, x^{5} + 27540 \, x^{4} + 71748 \, x^{3} + 164134 \, x^{2} + 91091 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 103784 \, x - 41503}{64 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^3/(2*x - 1)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.219413, size = 41, normalized size = 0.85 \[ \frac{675 x^{4}}{16} + \frac{945 x^{3}}{4} + \frac{21717 x^{2}}{32} + \frac{12973 x}{8} + \frac{91091 \log{\left (2 x - 1 \right )}}{64} - \frac{41503}{128 x - 64} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**3*(3+5*x)**2/(1-2*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.214989, size = 89, normalized size = 1.85 \[ \frac{1}{256} \,{\left (2 \, x - 1\right )}^{4}{\left (\frac{10260}{2 \, x - 1} + \frac{70164}{{\left (2 \, x - 1\right )}^{2}} + \frac{319816}{{\left (2 \, x - 1\right )}^{3}} + 675\right )} - \frac{41503}{64 \,{\left (2 \, x - 1\right )}} - \frac{91091}{64} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^3/(2*x - 1)^2,x, algorithm="giac")
[Out]