3.1128 \(\int (1-2 x) (2+3 x)^6 (3+5 x) \, dx\)

Optimal. Leaf size=34 \[ -\frac{10}{243} (3 x+2)^9+\frac{37}{216} (3 x+2)^8-\frac{1}{27} (3 x+2)^7 \]

[Out]

-(2 + 3*x)^7/27 + (37*(2 + 3*x)^8)/216 - (10*(2 + 3*x)^9)/243

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Rubi [A]  time = 0.0593568, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ -\frac{10}{243} (3 x+2)^9+\frac{37}{216} (3 x+2)^8-\frac{1}{27} (3 x+2)^7 \]

Antiderivative was successfully verified.

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

[Out]

-(2 + 3*x)^7/27 + (37*(2 + 3*x)^8)/216 - (10*(2 + 3*x)^9)/243

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Rubi in Sympy [A]  time = 8.87429, size = 27, normalized size = 0.79 \[ - \frac{10 \left (3 x + 2\right )^{9}}{243} + \frac{37 \left (3 x + 2\right )^{8}}{216} - \frac{\left (3 x + 2\right )^{7}}{27} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-10*(3*x + 2)**9/243 + 37*(3*x + 2)**8/216 - (3*x + 2)**7/27

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Mathematica [A]  time = 0.00332494, size = 48, normalized size = 1.41 \[ -810 x^9-\frac{29889 x^8}{8}-7047 x^7-6552 x^6-2268 x^5+1260 x^4+\frac{5264 x^3}{3}+832 x^2+192 x \]

Antiderivative was successfully verified.

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

[Out]

192*x + 832*x^2 + (5264*x^3)/3 + 1260*x^4 - 2268*x^5 - 6552*x^6 - 7047*x^7 - (29
889*x^8)/8 - 810*x^9

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Maple [A]  time = 0.001, size = 45, normalized size = 1.3 \[ -810\,{x}^{9}-{\frac{29889\,{x}^{8}}{8}}-7047\,{x}^{7}-6552\,{x}^{6}-2268\,{x}^{5}+1260\,{x}^{4}+{\frac{5264\,{x}^{3}}{3}}+832\,{x}^{2}+192\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-810*x^9-29889/8*x^8-7047*x^7-6552*x^6-2268*x^5+1260*x^4+5264/3*x^3+832*x^2+192*
x

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Maxima [A]  time = 1.33723, size = 59, normalized size = 1.74 \[ -810 \, x^{9} - \frac{29889}{8} \, x^{8} - 7047 \, x^{7} - 6552 \, x^{6} - 2268 \, x^{5} + 1260 \, x^{4} + \frac{5264}{3} \, x^{3} + 832 \, x^{2} + 192 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-810*x^9 - 29889/8*x^8 - 7047*x^7 - 6552*x^6 - 2268*x^5 + 1260*x^4 + 5264/3*x^3
+ 832*x^2 + 192*x

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Fricas [A]  time = 0.181758, size = 1, normalized size = 0.03 \[ -810 x^{9} - \frac{29889}{8} x^{8} - 7047 x^{7} - 6552 x^{6} - 2268 x^{5} + 1260 x^{4} + \frac{5264}{3} x^{3} + 832 x^{2} + 192 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-810*x^9 - 29889/8*x^8 - 7047*x^7 - 6552*x^6 - 2268*x^5 + 1260*x^4 + 5264/3*x^3
+ 832*x^2 + 192*x

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Sympy [A]  time = 0.09381, size = 46, normalized size = 1.35 \[ - 810 x^{9} - \frac{29889 x^{8}}{8} - 7047 x^{7} - 6552 x^{6} - 2268 x^{5} + 1260 x^{4} + \frac{5264 x^{3}}{3} + 832 x^{2} + 192 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-810*x**9 - 29889*x**8/8 - 7047*x**7 - 6552*x**6 - 2268*x**5 + 1260*x**4 + 5264*
x**3/3 + 832*x**2 + 192*x

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GIAC/XCAS [A]  time = 0.210433, size = 59, normalized size = 1.74 \[ -810 \, x^{9} - \frac{29889}{8} \, x^{8} - 7047 \, x^{7} - 6552 \, x^{6} - 2268 \, x^{5} + 1260 \, x^{4} + \frac{5264}{3} \, x^{3} + 832 \, x^{2} + 192 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-810*x^9 - 29889/8*x^8 - 7047*x^7 - 6552*x^6 - 2268*x^5 + 1260*x^4 + 5264/3*x^3
+ 832*x^2 + 192*x