Optimal. Leaf size=45 \[ \frac{5}{243} (3 x+2)^{12}-\frac{16}{99} (3 x+2)^{11}+\frac{91}{270} (3 x+2)^{10}-\frac{49}{729} (3 x+2)^9 \]
[Out]
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Rubi [A] time = 0.0858559, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{5}{243} (3 x+2)^{12}-\frac{16}{99} (3 x+2)^{11}+\frac{91}{270} (3 x+2)^{10}-\frac{49}{729} (3 x+2)^9 \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x),x]
[Out]
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Rubi in Sympy [A] time = 12.1375, size = 39, normalized size = 0.87 \[ \frac{5 \left (3 x + 2\right )^{12}}{243} - \frac{16 \left (3 x + 2\right )^{11}}{99} + \frac{91 \left (3 x + 2\right )^{10}}{270} - \frac{49 \left (3 x + 2\right )^{9}}{729} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(2+3*x)**8*(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0042225, size = 67, normalized size = 1.49 \[ 10935 x^{12}+\frac{647352 x^{11}}{11}+\frac{1307097 x^{10}}{10}+144315 x^9+59616 x^8-39312 x^7-62160 x^6-\frac{134112 x^5}{5}+3200 x^4+\frac{24832 x^3}{3}+3712 x^2+768 x \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x),x]
[Out]
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Maple [A] time = 0.001, size = 60, normalized size = 1.3 \[ 10935\,{x}^{12}+{\frac{647352\,{x}^{11}}{11}}+{\frac{1307097\,{x}^{10}}{10}}+144315\,{x}^{9}+59616\,{x}^{8}-39312\,{x}^{7}-62160\,{x}^{6}-{\frac{134112\,{x}^{5}}{5}}+3200\,{x}^{4}+{\frac{24832\,{x}^{3}}{3}}+3712\,{x}^{2}+768\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(2+3*x)^8*(3+5*x),x)
[Out]
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Maxima [A] time = 1.32532, size = 80, normalized size = 1.78 \[ 10935 \, x^{12} + \frac{647352}{11} \, x^{11} + \frac{1307097}{10} \, x^{10} + 144315 \, x^{9} + 59616 \, x^{8} - 39312 \, x^{7} - 62160 \, x^{6} - \frac{134112}{5} \, x^{5} + 3200 \, x^{4} + \frac{24832}{3} \, x^{3} + 3712 \, x^{2} + 768 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^8*(2*x - 1)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.191651, size = 1, normalized size = 0.02 \[ 10935 x^{12} + \frac{647352}{11} x^{11} + \frac{1307097}{10} x^{10} + 144315 x^{9} + 59616 x^{8} - 39312 x^{7} - 62160 x^{6} - \frac{134112}{5} x^{5} + 3200 x^{4} + \frac{24832}{3} x^{3} + 3712 x^{2} + 768 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^8*(2*x - 1)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.116835, size = 65, normalized size = 1.44 \[ 10935 x^{12} + \frac{647352 x^{11}}{11} + \frac{1307097 x^{10}}{10} + 144315 x^{9} + 59616 x^{8} - 39312 x^{7} - 62160 x^{6} - \frac{134112 x^{5}}{5} + 3200 x^{4} + \frac{24832 x^{3}}{3} + 3712 x^{2} + 768 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(2+3*x)**8*(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.203871, size = 80, normalized size = 1.78 \[ 10935 \, x^{12} + \frac{647352}{11} \, x^{11} + \frac{1307097}{10} \, x^{10} + 144315 \, x^{9} + 59616 \, x^{8} - 39312 \, x^{7} - 62160 \, x^{6} - \frac{134112}{5} \, x^{5} + 3200 \, x^{4} + \frac{24832}{3} \, x^{3} + 3712 \, x^{2} + 768 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^8*(2*x - 1)^2,x, algorithm="giac")
[Out]