3.1322 \(\int (1-2 x)^3 (2+3 x)^7 (3+5 x) \, dx\)

Optimal. Leaf size=56 \[ -\frac{10}{729} (3 x+2)^{12}+\frac{428 (3 x+2)^{11}}{2673}-\frac{259}{405} (3 x+2)^{10}+\frac{2009 (3 x+2)^9}{2187}-\frac{343 (3 x+2)^8}{1944} \]

[Out]

(-343*(2 + 3*x)^8)/1944 + (2009*(2 + 3*x)^9)/2187 - (259*(2 + 3*x)^10)/405 + (42
8*(2 + 3*x)^11)/2673 - (10*(2 + 3*x)^12)/729

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Rubi [A]  time = 0.091518, antiderivative size = 56, 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 \[ -\frac{10}{729} (3 x+2)^{12}+\frac{428 (3 x+2)^{11}}{2673}-\frac{259}{405} (3 x+2)^{10}+\frac{2009 (3 x+2)^9}{2187}-\frac{343 (3 x+2)^8}{1944} \]

Antiderivative was successfully verified.

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

[Out]

(-343*(2 + 3*x)^8)/1944 + (2009*(2 + 3*x)^9)/2187 - (259*(2 + 3*x)^10)/405 + (42
8*(2 + 3*x)^11)/2673 - (10*(2 + 3*x)^12)/729

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Rubi in Sympy [A]  time = 13.2014, size = 49, normalized size = 0.88 \[ - \frac{10 \left (3 x + 2\right )^{12}}{729} + \frac{428 \left (3 x + 2\right )^{11}}{2673} - \frac{259 \left (3 x + 2\right )^{10}}{405} + \frac{2009 \left (3 x + 2\right )^{9}}{2187} - \frac{343 \left (3 x + 2\right )^{8}}{1944} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-10*(3*x + 2)**12/729 + 428*(3*x + 2)**11/2673 - 259*(3*x + 2)**10/405 + 2009*(3
*x + 2)**9/2187 - 343*(3*x + 2)**8/1944

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Mathematica [A]  time = 0.00343694, size = 67, normalized size = 1.2 \[ -7290 x^{12}-\frac{329508 x^{11}}{11}-\frac{217971 x^{10}}{5}-15507 x^9+\frac{208035 x^8}{8}+29106 x^7+3514 x^6-\frac{48968 x^5}{5}-5148 x^4+480 x^3+1184 x^2+384 x \]

Antiderivative was successfully verified.

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

[Out]

384*x + 1184*x^2 + 480*x^3 - 5148*x^4 - (48968*x^5)/5 + 3514*x^6 + 29106*x^7 + (
208035*x^8)/8 - 15507*x^9 - (217971*x^10)/5 - (329508*x^11)/11 - 7290*x^12

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Maple [A]  time = 0.002, size = 60, normalized size = 1.1 \[ -7290\,{x}^{12}-{\frac{329508\,{x}^{11}}{11}}-{\frac{217971\,{x}^{10}}{5}}-15507\,{x}^{9}+{\frac{208035\,{x}^{8}}{8}}+29106\,{x}^{7}+3514\,{x}^{6}-{\frac{48968\,{x}^{5}}{5}}-5148\,{x}^{4}+480\,{x}^{3}+1184\,{x}^{2}+384\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-7290*x^12-329508/11*x^11-217971/5*x^10-15507*x^9+208035/8*x^8+29106*x^7+3514*x^
6-48968/5*x^5-5148*x^4+480*x^3+1184*x^2+384*x

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Maxima [A]  time = 1.33903, size = 80, normalized size = 1.43 \[ -7290 \, x^{12} - \frac{329508}{11} \, x^{11} - \frac{217971}{5} \, x^{10} - 15507 \, x^{9} + \frac{208035}{8} \, x^{8} + 29106 \, x^{7} + 3514 \, x^{6} - \frac{48968}{5} \, x^{5} - 5148 \, x^{4} + 480 \, x^{3} + 1184 \, x^{2} + 384 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-7290*x^12 - 329508/11*x^11 - 217971/5*x^10 - 15507*x^9 + 208035/8*x^8 + 29106*x
^7 + 3514*x^6 - 48968/5*x^5 - 5148*x^4 + 480*x^3 + 1184*x^2 + 384*x

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Fricas [A]  time = 0.186946, size = 1, normalized size = 0.02 \[ -7290 x^{12} - \frac{329508}{11} x^{11} - \frac{217971}{5} x^{10} - 15507 x^{9} + \frac{208035}{8} x^{8} + 29106 x^{7} + 3514 x^{6} - \frac{48968}{5} x^{5} - 5148 x^{4} + 480 x^{3} + 1184 x^{2} + 384 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-7290*x^12 - 329508/11*x^11 - 217971/5*x^10 - 15507*x^9 + 208035/8*x^8 + 29106*x
^7 + 3514*x^6 - 48968/5*x^5 - 5148*x^4 + 480*x^3 + 1184*x^2 + 384*x

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Sympy [A]  time = 0.124132, size = 65, normalized size = 1.16 \[ - 7290 x^{12} - \frac{329508 x^{11}}{11} - \frac{217971 x^{10}}{5} - 15507 x^{9} + \frac{208035 x^{8}}{8} + 29106 x^{7} + 3514 x^{6} - \frac{48968 x^{5}}{5} - 5148 x^{4} + 480 x^{3} + 1184 x^{2} + 384 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-7290*x**12 - 329508*x**11/11 - 217971*x**10/5 - 15507*x**9 + 208035*x**8/8 + 29
106*x**7 + 3514*x**6 - 48968*x**5/5 - 5148*x**4 + 480*x**3 + 1184*x**2 + 384*x

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GIAC/XCAS [A]  time = 0.21262, size = 80, normalized size = 1.43 \[ -7290 \, x^{12} - \frac{329508}{11} \, x^{11} - \frac{217971}{5} \, x^{10} - 15507 \, x^{9} + \frac{208035}{8} \, x^{8} + 29106 \, x^{7} + 3514 \, x^{6} - \frac{48968}{5} \, x^{5} - 5148 \, x^{4} + 480 \, x^{3} + 1184 \, x^{2} + 384 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-7290*x^12 - 329508/11*x^11 - 217971/5*x^10 - 15507*x^9 + 208035/8*x^8 + 29106*x
^7 + 3514*x^6 - 48968/5*x^5 - 5148*x^4 + 480*x^3 + 1184*x^2 + 384*x