Optimal. Leaf size=55 \[ \frac{740}{243 (3 x+2)}-\frac{503}{162 (3 x+2)^2}+\frac{518}{729 (3 x+2)^3}-\frac{49}{972 (3 x+2)^4}+\frac{100}{243} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0556127, antiderivative size = 55, 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 \[ \frac{740}{243 (3 x+2)}-\frac{503}{162 (3 x+2)^2}+\frac{518}{729 (3 x+2)^3}-\frac{49}{972 (3 x+2)^4}+\frac{100}{243} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^5,x]
[Out]
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Rubi in Sympy [A] time = 9.27585, size = 46, normalized size = 0.84 \[ \frac{100 \log{\left (3 x + 2 \right )}}{243} + \frac{740}{243 \left (3 x + 2\right )} - \frac{503}{162 \left (3 x + 2\right )^{2}} + \frac{518}{729 \left (3 x + 2\right )^{3}} - \frac{49}{972 \left (3 x + 2\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(3+5*x)**2/(2+3*x)**5,x)
[Out]
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Mathematica [A] time = 0.0224023, size = 41, normalized size = 0.75 \[ \frac{239760 x^3+398034 x^2+217248 x+1200 (3 x+2)^4 \log (3 x+2)+38821}{2916 (3 x+2)^4} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^5,x]
[Out]
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Maple [A] time = 0.009, size = 46, normalized size = 0.8 \[ -{\frac{49}{972\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{518}{729\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{503}{162\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{740}{486+729\,x}}+{\frac{100\,\ln \left ( 2+3\,x \right ) }{243}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(3+5*x)^2/(2+3*x)^5,x)
[Out]
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Maxima [A] time = 1.33718, size = 65, normalized size = 1.18 \[ \frac{239760 \, x^{3} + 398034 \, x^{2} + 217248 \, x + 38821}{2916 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac{100}{243} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(2*x - 1)^2/(3*x + 2)^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218813, size = 90, normalized size = 1.64 \[ \frac{239760 \, x^{3} + 398034 \, x^{2} + 1200 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 217248 \, x + 38821}{2916 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(2*x - 1)^2/(3*x + 2)^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.382947, size = 44, normalized size = 0.8 \[ \frac{239760 x^{3} + 398034 x^{2} + 217248 x + 38821}{236196 x^{4} + 629856 x^{3} + 629856 x^{2} + 279936 x + 46656} + \frac{100 \log{\left (3 x + 2 \right )}}{243} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(3+5*x)**2/(2+3*x)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.209017, size = 74, normalized size = 1.35 \[ \frac{740}{243 \,{\left (3 \, x + 2\right )}} - \frac{503}{162 \,{\left (3 \, x + 2\right )}^{2}} + \frac{518}{729 \,{\left (3 \, x + 2\right )}^{3}} - \frac{49}{972 \,{\left (3 \, x + 2\right )}^{4}} - \frac{100}{243} \,{\rm ln}\left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(2*x - 1)^2/(3*x + 2)^5,x, algorithm="giac")
[Out]