3.1339 \(\int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx\)

Optimal. Leaf size=67 \[ -\frac{200 (3 x+2)^{13}}{9477}+\frac{545 (3 x+2)^{12}}{2187}-\frac{8198 (3 x+2)^{11}}{8019}+\frac{11599 (3 x+2)^{10}}{7290}-\frac{3724 (3 x+2)^9}{6561}+\frac{343 (3 x+2)^8}{5832} \]

[Out]

(343*(2 + 3*x)^8)/5832 - (3724*(2 + 3*x)^9)/6561 + (11599*(2 + 3*x)^10)/7290 - (
8198*(2 + 3*x)^11)/8019 + (545*(2 + 3*x)^12)/2187 - (200*(2 + 3*x)^13)/9477

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Rubi [A]  time = 0.109149, 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 \[ -\frac{200 (3 x+2)^{13}}{9477}+\frac{545 (3 x+2)^{12}}{2187}-\frac{8198 (3 x+2)^{11}}{8019}+\frac{11599 (3 x+2)^{10}}{7290}-\frac{3724 (3 x+2)^9}{6561}+\frac{343 (3 x+2)^8}{5832} \]

Antiderivative was successfully verified.

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

[Out]

(343*(2 + 3*x)^8)/5832 - (3724*(2 + 3*x)^9)/6561 + (11599*(2 + 3*x)^10)/7290 - (
8198*(2 + 3*x)^11)/8019 + (545*(2 + 3*x)^12)/2187 - (200*(2 + 3*x)^13)/9477

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Rubi in Sympy [A]  time = 15.5245, size = 60, normalized size = 0.9 \[ - \frac{200 \left (3 x + 2\right )^{13}}{9477} + \frac{545 \left (3 x + 2\right )^{12}}{2187} - \frac{8198 \left (3 x + 2\right )^{11}}{8019} + \frac{11599 \left (3 x + 2\right )^{10}}{7290} - \frac{3724 \left (3 x + 2\right )^{9}}{6561} + \frac{343 \left (3 x + 2\right )^{8}}{5832} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-200*(3*x + 2)**13/9477 + 545*(3*x + 2)**12/2187 - 8198*(3*x + 2)**11/8019 + 115
99*(3*x + 2)**10/7290 - 3724*(3*x + 2)**9/6561 + 343*(3*x + 2)**8/5832

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Mathematica [A]  time = 0.00402635, size = 78, normalized size = 1.16 \[ -\frac{437400 x^{13}}{13}-159165 x^{12}-\frac{3168234 x^{11}}{11}-\frac{2005641 x^{10}}{10}+69054 x^9+\frac{1642815 x^8}{8}+102378 x^7-\frac{90794 x^6}{3}-\frac{249864 x^5}{5}-13644 x^4+\frac{16160 x^3}{3}+4512 x^2+1152 x \]

Antiderivative was successfully verified.

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

[Out]

1152*x + 4512*x^2 + (16160*x^3)/3 - 13644*x^4 - (249864*x^5)/5 - (90794*x^6)/3 +
102378*x^7 + (1642815*x^8)/8 + 69054*x^9 - (2005641*x^10)/10 - (3168234*x^11)/1
1 - 159165*x^12 - (437400*x^13)/13

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Maple [A]  time = 0.003, size = 65, normalized size = 1. \[ -{\frac{437400\,{x}^{13}}{13}}-159165\,{x}^{12}-{\frac{3168234\,{x}^{11}}{11}}-{\frac{2005641\,{x}^{10}}{10}}+69054\,{x}^{9}+{\frac{1642815\,{x}^{8}}{8}}+102378\,{x}^{7}-{\frac{90794\,{x}^{6}}{3}}-{\frac{249864\,{x}^{5}}{5}}-13644\,{x}^{4}+{\frac{16160\,{x}^{3}}{3}}+4512\,{x}^{2}+1152\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-437400/13*x^13-159165*x^12-3168234/11*x^11-2005641/10*x^10+69054*x^9+1642815/8*
x^8+102378*x^7-90794/3*x^6-249864/5*x^5-13644*x^4+16160/3*x^3+4512*x^2+1152*x

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Maxima [A]  time = 1.3391, size = 86, normalized size = 1.28 \[ -\frac{437400}{13} \, x^{13} - 159165 \, x^{12} - \frac{3168234}{11} \, x^{11} - \frac{2005641}{10} \, x^{10} + 69054 \, x^{9} + \frac{1642815}{8} \, x^{8} + 102378 \, x^{7} - \frac{90794}{3} \, x^{6} - \frac{249864}{5} \, x^{5} - 13644 \, x^{4} + \frac{16160}{3} \, x^{3} + 4512 \, x^{2} + 1152 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-437400/13*x^13 - 159165*x^12 - 3168234/11*x^11 - 2005641/10*x^10 + 69054*x^9 +
1642815/8*x^8 + 102378*x^7 - 90794/3*x^6 - 249864/5*x^5 - 13644*x^4 + 16160/3*x^
3 + 4512*x^2 + 1152*x

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Fricas [A]  time = 0.188974, size = 1, normalized size = 0.01 \[ -\frac{437400}{13} x^{13} - 159165 x^{12} - \frac{3168234}{11} x^{11} - \frac{2005641}{10} x^{10} + 69054 x^{9} + \frac{1642815}{8} x^{8} + 102378 x^{7} - \frac{90794}{3} x^{6} - \frac{249864}{5} x^{5} - 13644 x^{4} + \frac{16160}{3} x^{3} + 4512 x^{2} + 1152 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-437400/13*x^13 - 159165*x^12 - 3168234/11*x^11 - 2005641/10*x^10 + 69054*x^9 +
1642815/8*x^8 + 102378*x^7 - 90794/3*x^6 - 249864/5*x^5 - 13644*x^4 + 16160/3*x^
3 + 4512*x^2 + 1152*x

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Sympy [A]  time = 0.122211, size = 75, normalized size = 1.12 \[ - \frac{437400 x^{13}}{13} - 159165 x^{12} - \frac{3168234 x^{11}}{11} - \frac{2005641 x^{10}}{10} + 69054 x^{9} + \frac{1642815 x^{8}}{8} + 102378 x^{7} - \frac{90794 x^{6}}{3} - \frac{249864 x^{5}}{5} - 13644 x^{4} + \frac{16160 x^{3}}{3} + 4512 x^{2} + 1152 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-437400*x**13/13 - 159165*x**12 - 3168234*x**11/11 - 2005641*x**10/10 + 69054*x*
*9 + 1642815*x**8/8 + 102378*x**7 - 90794*x**6/3 - 249864*x**5/5 - 13644*x**4 +
16160*x**3/3 + 4512*x**2 + 1152*x

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GIAC/XCAS [A]  time = 0.204378, size = 86, normalized size = 1.28 \[ -\frac{437400}{13} \, x^{13} - 159165 \, x^{12} - \frac{3168234}{11} \, x^{11} - \frac{2005641}{10} \, x^{10} + 69054 \, x^{9} + \frac{1642815}{8} \, x^{8} + 102378 \, x^{7} - \frac{90794}{3} \, x^{6} - \frac{249864}{5} \, x^{5} - 13644 \, x^{4} + \frac{16160}{3} \, x^{3} + 4512 \, x^{2} + 1152 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-437400/13*x^13 - 159165*x^12 - 3168234/11*x^11 - 2005641/10*x^10 + 69054*x^9 +
1642815/8*x^8 + 102378*x^7 - 90794/3*x^6 - 249864/5*x^5 - 13644*x^4 + 16160/3*x^
3 + 4512*x^2 + 1152*x