Optimal. Leaf size=37 \[ \frac{(1-2 x)^4}{105 (3 x+2)^5}-\frac{173 (1-2 x)^4}{2940 (3 x+2)^4} \]
[Out]
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Rubi [A] time = 0.0368793, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{(1-2 x)^4}{105 (3 x+2)^5}-\frac{173 (1-2 x)^4}{2940 (3 x+2)^4} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^6,x]
[Out]
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Rubi in Sympy [A] time = 5.29486, size = 31, normalized size = 0.84 \[ - \frac{173 \left (- 2 x + 1\right )^{4}}{2940 \left (3 x + 2\right )^{4}} + \frac{\left (- 2 x + 1\right )^{4}}{105 \left (3 x + 2\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(3+5*x)/(2+3*x)**6,x)
[Out]
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Mathematica [A] time = 0.0183453, size = 31, normalized size = 0.84 \[ \frac{64800 x^4+57240 x^3+34920 x^2+16905 x+1282}{4860 (3 x+2)^5} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^6,x]
[Out]
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Maple [A] time = 0.008, size = 47, normalized size = 1.3 \[{\frac{343}{1215\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{40}{486+729\,x}}+{\frac{518}{243\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{2009}{972\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{214}{243\, \left ( 2+3\,x \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(3+5*x)/(2+3*x)^6,x)
[Out]
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Maxima [A] time = 1.35065, size = 66, normalized size = 1.78 \[ \frac{64800 \, x^{4} + 57240 \, x^{3} + 34920 \, x^{2} + 16905 \, x + 1282}{4860 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)*(2*x - 1)^3/(3*x + 2)^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21043, size = 66, normalized size = 1.78 \[ \frac{64800 \, x^{4} + 57240 \, x^{3} + 34920 \, x^{2} + 16905 \, x + 1282}{4860 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)*(2*x - 1)^3/(3*x + 2)^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.387362, size = 44, normalized size = 1.19 \[ \frac{64800 x^{4} + 57240 x^{3} + 34920 x^{2} + 16905 x + 1282}{1180980 x^{5} + 3936600 x^{4} + 5248800 x^{3} + 3499200 x^{2} + 1166400 x + 155520} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(3+5*x)/(2+3*x)**6,x)
[Out]
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GIAC/XCAS [A] time = 0.211088, size = 39, normalized size = 1.05 \[ \frac{64800 \, x^{4} + 57240 \, x^{3} + 34920 \, x^{2} + 16905 \, x + 1282}{4860 \,{\left (3 \, x + 2\right )}^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)*(2*x - 1)^3/(3*x + 2)^6,x, algorithm="giac")
[Out]