3.1361 \(\int (1-2 x)^3 (2+3 x) (3+5 x)^3 \, dx\)

Optimal. Leaf size=56 \[ -\frac{375}{256} (1-2 x)^8+\frac{1675}{112} (1-2 x)^7-\frac{935}{16} (1-2 x)^6+\frac{8349}{80} (1-2 x)^5-\frac{9317}{128} (1-2 x)^4 \]

[Out]

(-9317*(1 - 2*x)^4)/128 + (8349*(1 - 2*x)^5)/80 - (935*(1 - 2*x)^6)/16 + (1675*(
1 - 2*x)^7)/112 - (375*(1 - 2*x)^8)/256

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Rubi [A]  time = 0.0719335, 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 \[ -\frac{375}{256} (1-2 x)^8+\frac{1675}{112} (1-2 x)^7-\frac{935}{16} (1-2 x)^6+\frac{8349}{80} (1-2 x)^5-\frac{9317}{128} (1-2 x)^4 \]

Antiderivative was successfully verified.

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

[Out]

(-9317*(1 - 2*x)^4)/128 + (8349*(1 - 2*x)^5)/80 - (935*(1 - 2*x)^6)/16 + (1675*(
1 - 2*x)^7)/112 - (375*(1 - 2*x)^8)/256

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - 375 x^{8} - \frac{2900 x^{7}}{7} + 335 x^{6} + \frac{2277 x^{5}}{5} - \frac{425 x^{4}}{4} - 201 x^{3} + 54 x + 27 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375*x**8 - 2900*x**7/7 + 335*x**6 + 2277*x**5/5 - 425*x**4/4 - 201*x**3 + 54*x
+ 27*Integral(x, x)

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Mathematica [A]  time = 0.00161015, size = 47, normalized size = 0.84 \[ -375 x^8-\frac{2900 x^7}{7}+335 x^6+\frac{2277 x^5}{5}-\frac{425 x^4}{4}-201 x^3+\frac{27 x^2}{2}+54 x \]

Antiderivative was successfully verified.

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

[Out]

54*x + (27*x^2)/2 - 201*x^3 - (425*x^4)/4 + (2277*x^5)/5 + 335*x^6 - (2900*x^7)/
7 - 375*x^8

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Maple [A]  time = 0.002, size = 40, normalized size = 0.7 \[ -375\,{x}^{8}-{\frac{2900\,{x}^{7}}{7}}+335\,{x}^{6}+{\frac{2277\,{x}^{5}}{5}}-{\frac{425\,{x}^{4}}{4}}-201\,{x}^{3}+{\frac{27\,{x}^{2}}{2}}+54\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375*x^8-2900/7*x^7+335*x^6+2277/5*x^5-425/4*x^4-201*x^3+27/2*x^2+54*x

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Maxima [A]  time = 1.37146, size = 53, normalized size = 0.95 \[ -375 \, x^{8} - \frac{2900}{7} \, x^{7} + 335 \, x^{6} + \frac{2277}{5} \, x^{5} - \frac{425}{4} \, x^{4} - 201 \, x^{3} + \frac{27}{2} \, x^{2} + 54 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375*x^8 - 2900/7*x^7 + 335*x^6 + 2277/5*x^5 - 425/4*x^4 - 201*x^3 + 27/2*x^2 +
54*x

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Fricas [A]  time = 0.177677, size = 1, normalized size = 0.02 \[ -375 x^{8} - \frac{2900}{7} x^{7} + 335 x^{6} + \frac{2277}{5} x^{5} - \frac{425}{4} x^{4} - 201 x^{3} + \frac{27}{2} x^{2} + 54 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375*x^8 - 2900/7*x^7 + 335*x^6 + 2277/5*x^5 - 425/4*x^4 - 201*x^3 + 27/2*x^2 +
54*x

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Sympy [A]  time = 0.088389, size = 44, normalized size = 0.79 \[ - 375 x^{8} - \frac{2900 x^{7}}{7} + 335 x^{6} + \frac{2277 x^{5}}{5} - \frac{425 x^{4}}{4} - 201 x^{3} + \frac{27 x^{2}}{2} + 54 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375*x**8 - 2900*x**7/7 + 335*x**6 + 2277*x**5/5 - 425*x**4/4 - 201*x**3 + 27*x*
*2/2 + 54*x

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GIAC/XCAS [A]  time = 0.206301, size = 53, normalized size = 0.95 \[ -375 \, x^{8} - \frac{2900}{7} \, x^{7} + 335 \, x^{6} + \frac{2277}{5} \, x^{5} - \frac{425}{4} \, x^{4} - 201 \, x^{3} + \frac{27}{2} \, x^{2} + 54 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375*x^8 - 2900/7*x^7 + 335*x^6 + 2277/5*x^5 - 425/4*x^4 - 201*x^3 + 27/2*x^2 +
54*x