3.1239 \(\int (1-2 x)^2 (2+3 x)^5 (3+5 x)^2 \, dx\)

Optimal. Leaf size=56 \[ \frac{10}{243} (3 x+2)^{10}-\frac{740 (3 x+2)^9}{2187}+\frac{503}{648} (3 x+2)^8-\frac{74}{243} (3 x+2)^7+\frac{49 (3 x+2)^6}{1458} \]

[Out]

(49*(2 + 3*x)^6)/1458 - (74*(2 + 3*x)^7)/243 + (503*(2 + 3*x)^8)/648 - (740*(2 +
3*x)^9)/2187 + (10*(2 + 3*x)^10)/243

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Rubi [A]  time = 0.0947406, antiderivative size = 56, 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 \[ \frac{10}{243} (3 x+2)^{10}-\frac{740 (3 x+2)^9}{2187}+\frac{503}{648} (3 x+2)^8-\frac{74}{243} (3 x+2)^7+\frac{49 (3 x+2)^6}{1458} \]

Antiderivative was successfully verified.

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

[Out]

(49*(2 + 3*x)^6)/1458 - (74*(2 + 3*x)^7)/243 + (503*(2 + 3*x)^8)/648 - (740*(2 +
3*x)^9)/2187 + (10*(2 + 3*x)^10)/243

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ 2430 x^{10} + 9540 x^{9} + \frac{109863 x^{8}}{8} + 6336 x^{7} - \frac{9331 x^{6}}{2} - 6734 x^{5} - 2030 x^{4} + \frac{3152 x^{3}}{3} + 288 x + 1968 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2430*x**10 + 9540*x**9 + 109863*x**8/8 + 6336*x**7 - 9331*x**6/2 - 6734*x**5 - 2
030*x**4 + 3152*x**3/3 + 288*x + 1968*Integral(x, x)

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Mathematica [A]  time = 0.00353453, size = 55, normalized size = 0.98 \[ 2430 x^{10}+9540 x^9+\frac{109863 x^8}{8}+6336 x^7-\frac{9331 x^6}{2}-6734 x^5-2030 x^4+\frac{3152 x^3}{3}+984 x^2+288 x \]

Antiderivative was successfully verified.

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

[Out]

288*x + 984*x^2 + (3152*x^3)/3 - 2030*x^4 - 6734*x^5 - (9331*x^6)/2 + 6336*x^7 +
(109863*x^8)/8 + 9540*x^9 + 2430*x^10

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Maple [A]  time = 0.001, size = 50, normalized size = 0.9 \[ 2430\,{x}^{10}+9540\,{x}^{9}+{\frac{109863\,{x}^{8}}{8}}+6336\,{x}^{7}-{\frac{9331\,{x}^{6}}{2}}-6734\,{x}^{5}-2030\,{x}^{4}+{\frac{3152\,{x}^{3}}{3}}+984\,{x}^{2}+288\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2430*x^10+9540*x^9+109863/8*x^8+6336*x^7-9331/2*x^6-6734*x^5-2030*x^4+3152/3*x^3
+984*x^2+288*x

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Maxima [A]  time = 1.34176, size = 66, normalized size = 1.18 \[ 2430 \, x^{10} + 9540 \, x^{9} + \frac{109863}{8} \, x^{8} + 6336 \, x^{7} - \frac{9331}{2} \, x^{6} - 6734 \, x^{5} - 2030 \, x^{4} + \frac{3152}{3} \, x^{3} + 984 \, x^{2} + 288 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2430*x^10 + 9540*x^9 + 109863/8*x^8 + 6336*x^7 - 9331/2*x^6 - 6734*x^5 - 2030*x^
4 + 3152/3*x^3 + 984*x^2 + 288*x

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Fricas [A]  time = 0.18873, size = 1, normalized size = 0.02 \[ 2430 x^{10} + 9540 x^{9} + \frac{109863}{8} x^{8} + 6336 x^{7} - \frac{9331}{2} x^{6} - 6734 x^{5} - 2030 x^{4} + \frac{3152}{3} x^{3} + 984 x^{2} + 288 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2430*x^10 + 9540*x^9 + 109863/8*x^8 + 6336*x^7 - 9331/2*x^6 - 6734*x^5 - 2030*x^
4 + 3152/3*x^3 + 984*x^2 + 288*x

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Sympy [A]  time = 0.107269, size = 53, normalized size = 0.95 \[ 2430 x^{10} + 9540 x^{9} + \frac{109863 x^{8}}{8} + 6336 x^{7} - \frac{9331 x^{6}}{2} - 6734 x^{5} - 2030 x^{4} + \frac{3152 x^{3}}{3} + 984 x^{2} + 288 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2430*x**10 + 9540*x**9 + 109863*x**8/8 + 6336*x**7 - 9331*x**6/2 - 6734*x**5 - 2
030*x**4 + 3152*x**3/3 + 984*x**2 + 288*x

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GIAC/XCAS [A]  time = 0.205254, size = 66, normalized size = 1.18 \[ 2430 \, x^{10} + 9540 \, x^{9} + \frac{109863}{8} \, x^{8} + 6336 \, x^{7} - \frac{9331}{2} \, x^{6} - 6734 \, x^{5} - 2030 \, x^{4} + \frac{3152}{3} \, x^{3} + 984 \, x^{2} + 288 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2430*x^10 + 9540*x^9 + 109863/8*x^8 + 6336*x^7 - 9331/2*x^6 - 6734*x^5 - 2030*x^
4 + 3152/3*x^3 + 984*x^2 + 288*x