Optimal. Leaf size=37 \[ \frac{5 (5 x+3)^4}{12 (3 x+2)^4}+\frac{7 (5 x+3)^4}{15 (3 x+2)^5} \]
[Out]
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Rubi [A] time = 0.036063, 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 \[ \frac{5 (5 x+3)^4}{12 (3 x+2)^4}+\frac{7 (5 x+3)^4}{15 (3 x+2)^5} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^6,x]
[Out]
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Rubi in Sympy [A] time = 5.35374, size = 32, normalized size = 0.86 \[ \frac{5 \left (5 x + 3\right )^{4}}{12 \left (3 x + 2\right )^{4}} + \frac{7 \left (5 x + 3\right )^{4}}{15 \left (3 x + 2\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)*(3+5*x)**3/(2+3*x)**6,x)
[Out]
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Mathematica [A] time = 0.0157371, size = 31, normalized size = 0.84 \[ \frac{405000 x^4+803250 x^3+559800 x^2+153795 x+11758}{4860 (3 x+2)^5} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^6,x]
[Out]
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Maple [A] time = 0.009, size = 47, normalized size = 1.3 \[{\frac{7}{1215\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{250}{486+729\,x}}+{\frac{185}{243\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{107}{972\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{1025}{486\, \left ( 2+3\,x \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)*(3+5*x)^3/(2+3*x)^6,x)
[Out]
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Maxima [A] time = 1.35347, size = 66, normalized size = 1.78 \[ \frac{405000 \, x^{4} + 803250 \, x^{3} + 559800 \, x^{2} + 153795 \, x + 11758}{4860 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(2*x - 1)/(3*x + 2)^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208874, size = 66, normalized size = 1.78 \[ \frac{405000 \, x^{4} + 803250 \, x^{3} + 559800 \, x^{2} + 153795 \, x + 11758}{4860 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(2*x - 1)/(3*x + 2)^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.412406, size = 44, normalized size = 1.19 \[ \frac{405000 x^{4} + 803250 x^{3} + 559800 x^{2} + 153795 x + 11758}{1180980 x^{5} + 3936600 x^{4} + 5248800 x^{3} + 3499200 x^{2} + 1166400 x + 155520} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)*(3+5*x)**3/(2+3*x)**6,x)
[Out]
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GIAC/XCAS [A] time = 0.208729, size = 39, normalized size = 1.05 \[ \frac{405000 \, x^{4} + 803250 \, x^{3} + 559800 \, x^{2} + 153795 \, x + 11758}{4860 \,{\left (3 \, x + 2\right )}^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(2*x - 1)/(3*x + 2)^6,x, algorithm="giac")
[Out]