3.1220 \(\int (1-2 x)^2 (2+3 x)^7 (3+5 x) \, dx\)

Optimal. Leaf size=45 \[ \frac{20}{891} (3 x+2)^{11}-\frac{8}{45} (3 x+2)^{10}+\frac{91}{243} (3 x+2)^9-\frac{49}{648} (3 x+2)^8 \]

[Out]

(-49*(2 + 3*x)^8)/648 + (91*(2 + 3*x)^9)/243 - (8*(2 + 3*x)^10)/45 + (20*(2 + 3*
x)^11)/891

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Rubi [A]  time = 0.0811739, 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 \[ \frac{20}{891} (3 x+2)^{11}-\frac{8}{45} (3 x+2)^{10}+\frac{91}{243} (3 x+2)^9-\frac{49}{648} (3 x+2)^8 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x),x]

[Out]

(-49*(2 + 3*x)^8)/648 + (91*(2 + 3*x)^9)/243 - (8*(2 + 3*x)^10)/45 + (20*(2 + 3*
x)^11)/891

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Rubi in Sympy [A]  time = 11.4616, size = 39, normalized size = 0.87 \[ \frac{20 \left (3 x + 2\right )^{11}}{891} - \frac{8 \left (3 x + 2\right )^{10}}{45} + \frac{91 \left (3 x + 2\right )^{9}}{243} - \frac{49 \left (3 x + 2\right )^{8}}{648} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2*(2+3*x)**7*(3+5*x),x)

[Out]

20*(3*x + 2)**11/891 - 8*(3*x + 2)**10/45 + 91*(3*x + 2)**9/243 - 49*(3*x + 2)**
8/648

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Mathematica [A]  time = 0.00346702, size = 64, normalized size = 1.42 \[ \frac{43740 x^{11}}{11}+\frac{93312 x^{10}}{5}+34587 x^9+\frac{225423 x^8}{8}+1242 x^7-16254 x^6-\frac{59304 x^5}{5}-1292 x^4+\frac{7712 x^3}{3}+1568 x^2+384 x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x),x]

[Out]

384*x + 1568*x^2 + (7712*x^3)/3 - 1292*x^4 - (59304*x^5)/5 - 16254*x^6 + 1242*x^
7 + (225423*x^8)/8 + 34587*x^9 + (93312*x^10)/5 + (43740*x^11)/11

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Maple [A]  time = 0.002, size = 55, normalized size = 1.2 \[{\frac{43740\,{x}^{11}}{11}}+{\frac{93312\,{x}^{10}}{5}}+34587\,{x}^{9}+{\frac{225423\,{x}^{8}}{8}}+1242\,{x}^{7}-16254\,{x}^{6}-{\frac{59304\,{x}^{5}}{5}}-1292\,{x}^{4}+{\frac{7712\,{x}^{3}}{3}}+1568\,{x}^{2}+384\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(2+3*x)^7*(3+5*x),x)

[Out]

43740/11*x^11+93312/5*x^10+34587*x^9+225423/8*x^8+1242*x^7-16254*x^6-59304/5*x^5
-1292*x^4+7712/3*x^3+1568*x^2+384*x

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Maxima [A]  time = 1.34082, size = 73, normalized size = 1.62 \[ \frac{43740}{11} \, x^{11} + \frac{93312}{5} \, x^{10} + 34587 \, x^{9} + \frac{225423}{8} \, x^{8} + 1242 \, x^{7} - 16254 \, x^{6} - \frac{59304}{5} \, x^{5} - 1292 \, x^{4} + \frac{7712}{3} \, x^{3} + 1568 \, x^{2} + 384 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(3*x + 2)^7*(2*x - 1)^2,x, algorithm="maxima")

[Out]

43740/11*x^11 + 93312/5*x^10 + 34587*x^9 + 225423/8*x^8 + 1242*x^7 - 16254*x^6 -
59304/5*x^5 - 1292*x^4 + 7712/3*x^3 + 1568*x^2 + 384*x

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Fricas [A]  time = 0.183767, size = 1, normalized size = 0.02 \[ \frac{43740}{11} x^{11} + \frac{93312}{5} x^{10} + 34587 x^{9} + \frac{225423}{8} x^{8} + 1242 x^{7} - 16254 x^{6} - \frac{59304}{5} x^{5} - 1292 x^{4} + \frac{7712}{3} x^{3} + 1568 x^{2} + 384 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(3*x + 2)^7*(2*x - 1)^2,x, algorithm="fricas")

[Out]

43740/11*x^11 + 93312/5*x^10 + 34587*x^9 + 225423/8*x^8 + 1242*x^7 - 16254*x^6 -
59304/5*x^5 - 1292*x^4 + 7712/3*x^3 + 1568*x^2 + 384*x

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Sympy [A]  time = 0.110728, size = 61, normalized size = 1.36 \[ \frac{43740 x^{11}}{11} + \frac{93312 x^{10}}{5} + 34587 x^{9} + \frac{225423 x^{8}}{8} + 1242 x^{7} - 16254 x^{6} - \frac{59304 x^{5}}{5} - 1292 x^{4} + \frac{7712 x^{3}}{3} + 1568 x^{2} + 384 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2*(2+3*x)**7*(3+5*x),x)

[Out]

43740*x**11/11 + 93312*x**10/5 + 34587*x**9 + 225423*x**8/8 + 1242*x**7 - 16254*
x**6 - 59304*x**5/5 - 1292*x**4 + 7712*x**3/3 + 1568*x**2 + 384*x

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GIAC/XCAS [A]  time = 0.207467, size = 73, normalized size = 1.62 \[ \frac{43740}{11} \, x^{11} + \frac{93312}{5} \, x^{10} + 34587 \, x^{9} + \frac{225423}{8} \, x^{8} + 1242 \, x^{7} - 16254 \, x^{6} - \frac{59304}{5} \, x^{5} - 1292 \, x^{4} + \frac{7712}{3} \, x^{3} + 1568 \, x^{2} + 384 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(3*x + 2)^7*(2*x - 1)^2,x, algorithm="giac")

[Out]

43740/11*x^11 + 93312/5*x^10 + 34587*x^9 + 225423/8*x^8 + 1242*x^7 - 16254*x^6 -
59304/5*x^5 - 1292*x^4 + 7712/3*x^3 + 1568*x^2 + 384*x