Optimal. Leaf size=55 \[ -\frac{428}{243 (3 x+2)}+\frac{259}{81 (3 x+2)^2}-\frac{2009}{729 (3 x+2)^3}+\frac{343}{972 (3 x+2)^4}-\frac{40}{243} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0531095, antiderivative size = 55, 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 \[ -\frac{428}{243 (3 x+2)}+\frac{259}{81 (3 x+2)^2}-\frac{2009}{729 (3 x+2)^3}+\frac{343}{972 (3 x+2)^4}-\frac{40}{243} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^5,x]
[Out]
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Rubi in Sympy [A] time = 8.82551, size = 46, normalized size = 0.84 \[ - \frac{40 \log{\left (3 x + 2 \right )}}{243} - \frac{428}{243 \left (3 x + 2\right )} + \frac{259}{81 \left (3 x + 2\right )^{2}} - \frac{2009}{729 \left (3 x + 2\right )^{3}} + \frac{343}{972 \left (3 x + 2\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(3+5*x)/(2+3*x)**5,x)
[Out]
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Mathematica [A] time = 0.0256246, size = 41, normalized size = 0.75 \[ -\frac{138672 x^3+193428 x^2+97116 x+480 (3 x+2)^4 \log (6 x+4)+18835}{2916 (3 x+2)^4} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^5,x]
[Out]
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Maple [A] time = 0.01, size = 46, normalized size = 0.8 \[{\frac{343}{972\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{2009}{729\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{259}{81\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{428}{486+729\,x}}-{\frac{40\,\ln \left ( 2+3\,x \right ) }{243}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(3+5*x)/(2+3*x)^5,x)
[Out]
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Maxima [A] time = 1.34772, size = 65, normalized size = 1.18 \[ -\frac{138672 \, x^{3} + 193428 \, x^{2} + 97116 \, x + 18835}{2916 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} - \frac{40}{243} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)*(2*x - 1)^3/(3*x + 2)^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214389, size = 90, normalized size = 1.64 \[ -\frac{138672 \, x^{3} + 193428 \, x^{2} + 480 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 97116 \, x + 18835}{2916 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)*(2*x - 1)^3/(3*x + 2)^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.373495, size = 46, normalized size = 0.84 \[ - \frac{138672 x^{3} + 193428 x^{2} + 97116 x + 18835}{236196 x^{4} + 629856 x^{3} + 629856 x^{2} + 279936 x + 46656} - \frac{40 \log{\left (3 x + 2 \right )}}{243} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(3+5*x)/(2+3*x)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.216805, size = 74, normalized size = 1.35 \[ -\frac{428}{243 \,{\left (3 \, x + 2\right )}} + \frac{259}{81 \,{\left (3 \, x + 2\right )}^{2}} - \frac{2009}{729 \,{\left (3 \, x + 2\right )}^{3}} + \frac{343}{972 \,{\left (3 \, x + 2\right )}^{4}} + \frac{40}{243} \,{\rm ln}\left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)*(2*x - 1)^3/(3*x + 2)^5,x, algorithm="giac")
[Out]