3.1221 \(\int (1-2 x)^2 (2+3 x)^6 (3+5 x) \, dx\)

Optimal. Leaf size=45 \[ \frac{2}{81} (3 x+2)^{10}-\frac{16}{81} (3 x+2)^9+\frac{91}{216} (3 x+2)^8-\frac{7}{81} (3 x+2)^7 \]

[Out]

(-7*(2 + 3*x)^7)/81 + (91*(2 + 3*x)^8)/216 - (16*(2 + 3*x)^9)/81 + (2*(2 + 3*x)^
10)/81

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Rubi [A]  time = 0.0788134, 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 \[ \frac{2}{81} (3 x+2)^{10}-\frac{16}{81} (3 x+2)^9+\frac{91}{216} (3 x+2)^8-\frac{7}{81} (3 x+2)^7 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x),x]

[Out]

(-7*(2 + 3*x)^7)/81 + (91*(2 + 3*x)^8)/216 - (16*(2 + 3*x)^9)/81 + (2*(2 + 3*x)^
10)/81

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Rubi in Sympy [A]  time = 10.7444, size = 39, normalized size = 0.87 \[ \frac{2 \left (3 x + 2\right )^{10}}{81} - \frac{16 \left (3 x + 2\right )^{9}}{81} + \frac{91 \left (3 x + 2\right )^{8}}{216} - \frac{7 \left (3 x + 2\right )^{7}}{81} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2*(2+3*x)**6*(3+5*x),x)

[Out]

2*(3*x + 2)**10/81 - 16*(3*x + 2)**9/81 + 91*(3*x + 2)**8/216 - 7*(3*x + 2)**7/8
1

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Mathematica [A]  time = 0.00313935, size = 53, normalized size = 1.18 \[ 1458 x^{10}+5832 x^9+\frac{68769 x^8}{8}+4185 x^7-2772 x^6-4284 x^5-1372 x^4+\frac{1936 x^3}{3}+640 x^2+192 x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x),x]

[Out]

192*x + 640*x^2 + (1936*x^3)/3 - 1372*x^4 - 4284*x^5 - 2772*x^6 + 4185*x^7 + (68
769*x^8)/8 + 5832*x^9 + 1458*x^10

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Maple [A]  time = 0.001, size = 50, normalized size = 1.1 \[ 1458\,{x}^{10}+5832\,{x}^{9}+{\frac{68769\,{x}^{8}}{8}}+4185\,{x}^{7}-2772\,{x}^{6}-4284\,{x}^{5}-1372\,{x}^{4}+{\frac{1936\,{x}^{3}}{3}}+640\,{x}^{2}+192\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(2+3*x)^6*(3+5*x),x)

[Out]

1458*x^10+5832*x^9+68769/8*x^8+4185*x^7-2772*x^6-4284*x^5-1372*x^4+1936/3*x^3+64
0*x^2+192*x

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Maxima [A]  time = 1.34286, size = 66, normalized size = 1.47 \[ 1458 \, x^{10} + 5832 \, x^{9} + \frac{68769}{8} \, x^{8} + 4185 \, x^{7} - 2772 \, x^{6} - 4284 \, x^{5} - 1372 \, x^{4} + \frac{1936}{3} \, x^{3} + 640 \, x^{2} + 192 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(3*x + 2)^6*(2*x - 1)^2,x, algorithm="maxima")

[Out]

1458*x^10 + 5832*x^9 + 68769/8*x^8 + 4185*x^7 - 2772*x^6 - 4284*x^5 - 1372*x^4 +
1936/3*x^3 + 640*x^2 + 192*x

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Fricas [A]  time = 0.183838, size = 1, normalized size = 0.02 \[ 1458 x^{10} + 5832 x^{9} + \frac{68769}{8} x^{8} + 4185 x^{7} - 2772 x^{6} - 4284 x^{5} - 1372 x^{4} + \frac{1936}{3} x^{3} + 640 x^{2} + 192 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(3*x + 2)^6*(2*x - 1)^2,x, algorithm="fricas")

[Out]

1458*x^10 + 5832*x^9 + 68769/8*x^8 + 4185*x^7 - 2772*x^6 - 4284*x^5 - 1372*x^4 +
1936/3*x^3 + 640*x^2 + 192*x

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Sympy [A]  time = 0.097719, size = 51, normalized size = 1.13 \[ 1458 x^{10} + 5832 x^{9} + \frac{68769 x^{8}}{8} + 4185 x^{7} - 2772 x^{6} - 4284 x^{5} - 1372 x^{4} + \frac{1936 x^{3}}{3} + 640 x^{2} + 192 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2*(2+3*x)**6*(3+5*x),x)

[Out]

1458*x**10 + 5832*x**9 + 68769*x**8/8 + 4185*x**7 - 2772*x**6 - 4284*x**5 - 1372
*x**4 + 1936*x**3/3 + 640*x**2 + 192*x

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GIAC/XCAS [A]  time = 0.202319, size = 66, normalized size = 1.47 \[ 1458 \, x^{10} + 5832 \, x^{9} + \frac{68769}{8} \, x^{8} + 4185 \, x^{7} - 2772 \, x^{6} - 4284 \, x^{5} - 1372 \, x^{4} + \frac{1936}{3} \, x^{3} + 640 \, x^{2} + 192 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(3*x + 2)^6*(2*x - 1)^2,x, algorithm="giac")

[Out]

1458*x^10 + 5832*x^9 + 68769/8*x^8 + 4185*x^7 - 2772*x^6 - 4284*x^5 - 1372*x^4 +
1936/3*x^3 + 640*x^2 + 192*x