Optimal. Leaf size=71 \[ -\frac{1000 x}{729}+\frac{14390}{729 (3 x+2)}-\frac{66193}{4374 (3 x+2)^2}+\frac{10073}{2187 (3 x+2)^3}-\frac{1813}{2916 (3 x+2)^4}+\frac{343}{10935 (3 x+2)^5}+\frac{3700}{729} \log (3 x+2) \]
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Rubi [A] time = 0.0805253, antiderivative size = 71, 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 \[ -\frac{1000 x}{729}+\frac{14390}{729 (3 x+2)}-\frac{66193}{4374 (3 x+2)^2}+\frac{10073}{2187 (3 x+2)^3}-\frac{1813}{2916 (3 x+2)^4}+\frac{343}{10935 (3 x+2)^5}+\frac{3700}{729} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^6,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{3700 \log{\left (3 x + 2 \right )}}{729} + \int \left (- \frac{1000}{729}\right )\, dx + \frac{14390}{729 \left (3 x + 2\right )} - \frac{66193}{4374 \left (3 x + 2\right )^{2}} + \frac{10073}{2187 \left (3 x + 2\right )^{3}} - \frac{1813}{2916 \left (3 x + 2\right )^{4}} + \frac{343}{10935 \left (3 x + 2\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(3+5*x)**3/(2+3*x)**6,x)
[Out]
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Mathematica [A] time = 0.0350394, size = 56, normalized size = 0.79 \[ \frac{-14580000 x^6-58320000 x^5-27264600 x^4+82222290 x^3+109363320 x^2+49872855 x+222000 (3 x+2)^5 \log (3 x+2)+7991782}{43740 (3 x+2)^5} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^6,x]
[Out]
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Maple [A] time = 0.012, size = 58, normalized size = 0.8 \[ -{\frac{1000\,x}{729}}+{\frac{343}{10935\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{1813}{2916\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{10073}{2187\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{66193}{4374\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{14390}{1458+2187\,x}}+{\frac{3700\,\ln \left ( 2+3\,x \right ) }{729}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(3+5*x)^3/(2+3*x)^6,x)
[Out]
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Maxima [A] time = 1.34435, size = 82, normalized size = 1.15 \[ -\frac{1000}{729} \, x + \frac{23311800 \, x^{4} + 56207430 \, x^{3} + 50854440 \, x^{2} + 20464285 \, x + 3090594}{14580 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac{3700}{729} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(2*x - 1)^3/(3*x + 2)^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215409, size = 124, normalized size = 1.75 \[ -\frac{4860000 \, x^{6} + 16200000 \, x^{5} - 1711800 \, x^{4} - 41807430 \, x^{3} - 46054440 \, x^{2} - 74000 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) - 19824285 \, x - 3090594}{14580 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(2*x - 1)^3/(3*x + 2)^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.462737, size = 60, normalized size = 0.85 \[ - \frac{1000 x}{729} + \frac{23311800 x^{4} + 56207430 x^{3} + 50854440 x^{2} + 20464285 x + 3090594}{3542940 x^{5} + 11809800 x^{4} + 15746400 x^{3} + 10497600 x^{2} + 3499200 x + 466560} + \frac{3700 \log{\left (3 x + 2 \right )}}{729} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(3+5*x)**3/(2+3*x)**6,x)
[Out]
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GIAC/XCAS [A] time = 0.210268, size = 57, normalized size = 0.8 \[ -\frac{1000}{729} \, x + \frac{23311800 \, x^{4} + 56207430 \, x^{3} + 50854440 \, x^{2} + 20464285 \, x + 3090594}{14580 \,{\left (3 \, x + 2\right )}^{5}} + \frac{3700}{729} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(2*x - 1)^3/(3*x + 2)^6,x, algorithm="giac")
[Out]