Optimal. Leaf size=60 \[ \frac{500 x}{243}-\frac{8285}{729 (3 x+2)}+\frac{4099}{1458 (3 x+2)^2}-\frac{763}{2187 (3 x+2)^3}+\frac{49}{2916 (3 x+2)^4}-\frac{3800}{729} \log (3 x+2) \]
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Rubi [A] time = 0.071009, antiderivative size = 60, 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 \[ \frac{500 x}{243}-\frac{8285}{729 (3 x+2)}+\frac{4099}{1458 (3 x+2)^2}-\frac{763}{2187 (3 x+2)^3}+\frac{49}{2916 (3 x+2)^4}-\frac{3800}{729} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^5,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{3800 \log{\left (3 x + 2 \right )}}{729} + \int \frac{500}{243}\, dx - \frac{8285}{729 \left (3 x + 2\right )} + \frac{4099}{1458 \left (3 x + 2\right )^{2}} - \frac{763}{2187 \left (3 x + 2\right )^{3}} + \frac{49}{2916 \left (3 x + 2\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(3+5*x)**3/(2+3*x)**5,x)
[Out]
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Mathematica [A] time = 0.0541261, size = 51, normalized size = 0.85 \[ \frac{1458000 x^5+4860000 x^4+3795660 x^3-827334 x^2-1853148 x-45600 (3 x+2)^4 \log (30 x+20)-510941}{8748 (3 x+2)^4} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^5,x]
[Out]
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Maple [A] time = 0.01, size = 49, normalized size = 0.8 \[{\frac{500\,x}{243}}+{\frac{49}{2916\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{763}{2187\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{4099}{1458\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{8285}{1458+2187\,x}}-{\frac{3800\,\ln \left ( 2+3\,x \right ) }{729}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(3+5*x)^3/(2+3*x)^5,x)
[Out]
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Maxima [A] time = 1.32572, size = 69, normalized size = 1.15 \[ \frac{500}{243} \, x - \frac{2684340 \, x^{3} + 5147334 \, x^{2} + 3293148 \, x + 702941}{8748 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} - \frac{3800}{729} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(2*x - 1)^2/(3*x + 2)^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.202303, size = 104, normalized size = 1.73 \[ \frac{1458000 \, x^{5} + 3888000 \, x^{4} + 1203660 \, x^{3} - 3419334 \, x^{2} - 45600 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) - 3005148 \, x - 702941}{8748 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(2*x - 1)^2/(3*x + 2)^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.381012, size = 49, normalized size = 0.82 \[ \frac{500 x}{243} - \frac{2684340 x^{3} + 5147334 x^{2} + 3293148 x + 702941}{708588 x^{4} + 1889568 x^{3} + 1889568 x^{2} + 839808 x + 139968} - \frac{3800 \log{\left (3 x + 2 \right )}}{729} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(3+5*x)**3/(2+3*x)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.218672, size = 80, normalized size = 1.33 \[ \frac{500}{243} \, x - \frac{8285}{729 \,{\left (3 \, x + 2\right )}} + \frac{4099}{1458 \,{\left (3 \, x + 2\right )}^{2}} - \frac{763}{2187 \,{\left (3 \, x + 2\right )}^{3}} + \frac{49}{2916 \,{\left (3 \, x + 2\right )}^{4}} + \frac{3800}{729} \,{\rm ln}\left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) + \frac{1000}{729} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(2*x - 1)^2/(3*x + 2)^5,x, algorithm="giac")
[Out]