Optimal. Leaf size=67 \[ \frac{125 (3 x+2)^{16}}{2916}-\frac{760 (3 x+2)^{15}}{2187}+\frac{8285 (3 x+2)^{14}}{10206}-\frac{4099 (3 x+2)^{13}}{9477}+\frac{763 (3 x+2)^{12}}{8748}-\frac{49 (3 x+2)^{11}}{8019} \]
[Out]
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Rubi [A] time = 0.132019, 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 \[ \frac{125 (3 x+2)^{16}}{2916}-\frac{760 (3 x+2)^{15}}{2187}+\frac{8285 (3 x+2)^{14}}{10206}-\frac{4099 (3 x+2)^{13}}{9477}+\frac{763 (3 x+2)^{12}}{8748}-\frac{49 (3 x+2)^{11}}{8019} \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2*(2 + 3*x)^10*(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 18.2327, size = 60, normalized size = 0.9 \[ \frac{125 \left (3 x + 2\right )^{16}}{2916} - \frac{760 \left (3 x + 2\right )^{15}}{2187} + \frac{8285 \left (3 x + 2\right )^{14}}{10206} - \frac{4099 \left (3 x + 2\right )^{13}}{9477} + \frac{763 \left (3 x + 2\right )^{12}}{8748} - \frac{49 \left (3 x + 2\right )^{11}}{8019} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(2+3*x)**10*(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.00545795, size = 93, normalized size = 1.39 \[ \frac{7381125 x^{16}}{4}+14696640 x^{15}+\frac{734077485 x^{14}}{14}+\frac{1417418757 x^{13}}{13}+\frac{569034801 x^{12}}{4}+\frac{1233925083 x^{11}}{11}+36043704 x^{10}-26237700 x^9-40113468 x^8-\frac{154612896 x^7}{7}-\frac{10627328 x^6}{3}+3185792 x^5+2644160 x^4+1000704 x^3+221184 x^2+27648 x \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2*(2 + 3*x)^10*(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.003, size = 80, normalized size = 1.2 \[{\frac{7381125\,{x}^{16}}{4}}+14696640\,{x}^{15}+{\frac{734077485\,{x}^{14}}{14}}+{\frac{1417418757\,{x}^{13}}{13}}+{\frac{569034801\,{x}^{12}}{4}}+{\frac{1233925083\,{x}^{11}}{11}}+36043704\,{x}^{10}-26237700\,{x}^{9}-40113468\,{x}^{8}-{\frac{154612896\,{x}^{7}}{7}}-{\frac{10627328\,{x}^{6}}{3}}+3185792\,{x}^{5}+2644160\,{x}^{4}+1000704\,{x}^{3}+221184\,{x}^{2}+27648\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(2+3*x)^10*(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.3576, size = 107, normalized size = 1.6 \[ \frac{7381125}{4} \, x^{16} + 14696640 \, x^{15} + \frac{734077485}{14} \, x^{14} + \frac{1417418757}{13} \, x^{13} + \frac{569034801}{4} \, x^{12} + \frac{1233925083}{11} \, x^{11} + 36043704 \, x^{10} - 26237700 \, x^{9} - 40113468 \, x^{8} - \frac{154612896}{7} \, x^{7} - \frac{10627328}{3} \, x^{6} + 3185792 \, x^{5} + 2644160 \, x^{4} + 1000704 \, x^{3} + 221184 \, x^{2} + 27648 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^10*(2*x - 1)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.173927, size = 1, normalized size = 0.01 \[ \frac{7381125}{4} x^{16} + 14696640 x^{15} + \frac{734077485}{14} x^{14} + \frac{1417418757}{13} x^{13} + \frac{569034801}{4} x^{12} + \frac{1233925083}{11} x^{11} + 36043704 x^{10} - 26237700 x^{9} - 40113468 x^{8} - \frac{154612896}{7} x^{7} - \frac{10627328}{3} x^{6} + 3185792 x^{5} + 2644160 x^{4} + 1000704 x^{3} + 221184 x^{2} + 27648 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^10*(2*x - 1)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.146713, size = 90, normalized size = 1.34 \[ \frac{7381125 x^{16}}{4} + 14696640 x^{15} + \frac{734077485 x^{14}}{14} + \frac{1417418757 x^{13}}{13} + \frac{569034801 x^{12}}{4} + \frac{1233925083 x^{11}}{11} + 36043704 x^{10} - 26237700 x^{9} - 40113468 x^{8} - \frac{154612896 x^{7}}{7} - \frac{10627328 x^{6}}{3} + 3185792 x^{5} + 2644160 x^{4} + 1000704 x^{3} + 221184 x^{2} + 27648 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(2+3*x)**10*(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.221629, size = 107, normalized size = 1.6 \[ \frac{7381125}{4} \, x^{16} + 14696640 \, x^{15} + \frac{734077485}{14} \, x^{14} + \frac{1417418757}{13} \, x^{13} + \frac{569034801}{4} \, x^{12} + \frac{1233925083}{11} \, x^{11} + 36043704 \, x^{10} - 26237700 \, x^{9} - 40113468 \, x^{8} - \frac{154612896}{7} \, x^{7} - \frac{10627328}{3} \, x^{6} + 3185792 \, x^{5} + 2644160 \, x^{4} + 1000704 \, x^{3} + 221184 \, x^{2} + 27648 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^10*(2*x - 1)^2,x, algorithm="giac")
[Out]