3.1326 \(\int (1-2 x)^3 (2+3 x)^3 (3+5 x) \, dx\)

Optimal. Leaf size=56 \[ -\frac{135}{256} (1-2 x)^8+\frac{621}{112} (1-2 x)^7-\frac{357}{16} (1-2 x)^6+\frac{3283}{80} (1-2 x)^5-\frac{3773}{128} (1-2 x)^4 \]

[Out]

(-3773*(1 - 2*x)^4)/128 + (3283*(1 - 2*x)^5)/80 - (357*(1 - 2*x)^6)/16 + (621*(1
- 2*x)^7)/112 - (135*(1 - 2*x)^8)/256

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Rubi [A]  time = 0.0724064, 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 \[ -\frac{135}{256} (1-2 x)^8+\frac{621}{112} (1-2 x)^7-\frac{357}{16} (1-2 x)^6+\frac{3283}{80} (1-2 x)^5-\frac{3773}{128} (1-2 x)^4 \]

Antiderivative was successfully verified.

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

[Out]

(-3773*(1 - 2*x)^4)/128 + (3283*(1 - 2*x)^5)/80 - (357*(1 - 2*x)^6)/16 + (621*(1
- 2*x)^7)/112 - (135*(1 - 2*x)^8)/256

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - 135 x^{8} - \frac{1188 x^{7}}{7} + 111 x^{6} + \frac{949 x^{5}}{5} - \frac{117 x^{4}}{4} - 86 x^{3} + 24 x + 4 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135*x**8 - 1188*x**7/7 + 111*x**6 + 949*x**5/5 - 117*x**4/4 - 86*x**3 + 24*x +
4*Integral(x, x)

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Mathematica [A]  time = 0.0022562, size = 45, normalized size = 0.8 \[ -135 x^8-\frac{1188 x^7}{7}+111 x^6+\frac{949 x^5}{5}-\frac{117 x^4}{4}-86 x^3+2 x^2+24 x \]

Antiderivative was successfully verified.

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

[Out]

24*x + 2*x^2 - 86*x^3 - (117*x^4)/4 + (949*x^5)/5 + 111*x^6 - (1188*x^7)/7 - 135
*x^8

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Maple [A]  time = 0., size = 40, normalized size = 0.7 \[ -135\,{x}^{8}-{\frac{1188\,{x}^{7}}{7}}+111\,{x}^{6}+{\frac{949\,{x}^{5}}{5}}-{\frac{117\,{x}^{4}}{4}}-86\,{x}^{3}+2\,{x}^{2}+24\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135*x^8-1188/7*x^7+111*x^6+949/5*x^5-117/4*x^4-86*x^3+2*x^2+24*x

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Maxima [A]  time = 1.34806, size = 53, normalized size = 0.95 \[ -135 \, x^{8} - \frac{1188}{7} \, x^{7} + 111 \, x^{6} + \frac{949}{5} \, x^{5} - \frac{117}{4} \, x^{4} - 86 \, x^{3} + 2 \, x^{2} + 24 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135*x^8 - 1188/7*x^7 + 111*x^6 + 949/5*x^5 - 117/4*x^4 - 86*x^3 + 2*x^2 + 24*x

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Fricas [A]  time = 0.186375, size = 1, normalized size = 0.02 \[ -135 x^{8} - \frac{1188}{7} x^{7} + 111 x^{6} + \frac{949}{5} x^{5} - \frac{117}{4} x^{4} - 86 x^{3} + 2 x^{2} + 24 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135*x^8 - 1188/7*x^7 + 111*x^6 + 949/5*x^5 - 117/4*x^4 - 86*x^3 + 2*x^2 + 24*x

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Sympy [A]  time = 0.097196, size = 42, normalized size = 0.75 \[ - 135 x^{8} - \frac{1188 x^{7}}{7} + 111 x^{6} + \frac{949 x^{5}}{5} - \frac{117 x^{4}}{4} - 86 x^{3} + 2 x^{2} + 24 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135*x**8 - 1188*x**7/7 + 111*x**6 + 949*x**5/5 - 117*x**4/4 - 86*x**3 + 2*x**2
+ 24*x

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GIAC/XCAS [A]  time = 0.207941, size = 53, normalized size = 0.95 \[ -135 \, x^{8} - \frac{1188}{7} \, x^{7} + 111 \, x^{6} + \frac{949}{5} \, x^{5} - \frac{117}{4} \, x^{4} - 86 \, x^{3} + 2 \, x^{2} + 24 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135*x^8 - 1188/7*x^7 + 111*x^6 + 949/5*x^5 - 117/4*x^4 - 86*x^3 + 2*x^2 + 24*x