Optimal. Leaf size=67 \[ -\frac{500 x^2}{243}+\frac{9100 x}{729}-\frac{66193}{2187 (3 x+2)}+\frac{10073}{1458 (3 x+2)^2}-\frac{1813}{2187 (3 x+2)^3}+\frac{343}{8748 (3 x+2)^4}-\frac{14390}{729} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0812738, antiderivative size = 67, 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 \[ -\frac{500 x^2}{243}+\frac{9100 x}{729}-\frac{66193}{2187 (3 x+2)}+\frac{10073}{1458 (3 x+2)^2}-\frac{1813}{2187 (3 x+2)^3}+\frac{343}{8748 (3 x+2)^4}-\frac{14390}{729} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^3*(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. \[ - \frac{14390 \log{\left (3 x + 2 \right )}}{729} + \int \frac{9100}{729}\, dx - \frac{1000 \int x\, dx}{243} - \frac{66193}{2187 \left (3 x + 2\right )} + \frac{10073}{1458 \left (3 x + 2\right )^{2}} - \frac{1813}{2187 \left (3 x + 2\right )^{3}} + \frac{343}{8748 \left (3 x + 2\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(3+5*x)**3/(2+3*x)**5,x)
[Out]
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Mathematica [A] time = 0.0344561, size = 56, normalized size = 0.84 \[ \frac{-1458000 x^6+4957200 x^5+26244000 x^4+32163156 x^3+13894254 x^2+675708 x-172680 (3 x+2)^4 \log (3 x+2)-597785}{8748 (3 x+2)^4} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^5,x]
[Out]
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Maple [A] time = 0.012, size = 54, normalized size = 0.8 \[{\frac{9100\,x}{729}}-{\frac{500\,{x}^{2}}{243}}+{\frac{343}{8748\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{1813}{2187\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{10073}{1458\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{66193}{4374+6561\,x}}-{\frac{14390\,\ln \left ( 2+3\,x \right ) }{729}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(3+5*x)^3/(2+3*x)^5,x)
[Out]
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Maxima [A] time = 1.34897, size = 76, normalized size = 1.13 \[ -\frac{500}{243} \, x^{2} + \frac{9100}{729} \, x - \frac{2382948 \, x^{3} + 4584582 \, x^{2} + 2942764 \, x + 630195}{2916 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} - \frac{14390}{729} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(2*x - 1)^3/(3*x + 2)^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22046, size = 111, normalized size = 1.66 \[ -\frac{486000 \, x^{6} - 1652400 \, x^{5} - 6566400 \, x^{4} - 4903452 \, x^{3} + 1186182 \, x^{2} + 57560 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 2360364 \, x + 630195}{2916 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(2*x - 1)^3/(3*x + 2)^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.398208, size = 56, normalized size = 0.84 \[ - \frac{500 x^{2}}{243} + \frac{9100 x}{729} - \frac{2382948 x^{3} + 4584582 x^{2} + 2942764 x + 630195}{236196 x^{4} + 629856 x^{3} + 629856 x^{2} + 279936 x + 46656} - \frac{14390 \log{\left (3 x + 2 \right )}}{729} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(3+5*x)**3/(2+3*x)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.210537, size = 101, normalized size = 1.51 \[ \frac{100}{2187} \,{\left (3 \, x + 2\right )}^{2}{\left (\frac{111}{3 \, x + 2} - 5\right )} - \frac{66193}{2187 \,{\left (3 \, x + 2\right )}} + \frac{10073}{1458 \,{\left (3 \, x + 2\right )}^{2}} - \frac{1813}{2187 \,{\left (3 \, x + 2\right )}^{3}} + \frac{343}{8748 \,{\left (3 \, x + 2\right )}^{4}} + \frac{14390}{729} \,{\rm ln}\left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(2*x - 1)^3/(3*x + 2)^5,x, algorithm="giac")
[Out]