3.1362 \(\int (1-2 x)^3 (3+5 x)^3 \, dx\)

Optimal. Leaf size=45 \[ \frac{125}{112} (1-2 x)^7-\frac{275}{32} (1-2 x)^6+\frac{363}{16} (1-2 x)^5-\frac{1331}{64} (1-2 x)^4 \]

[Out]

(-1331*(1 - 2*x)^4)/64 + (363*(1 - 2*x)^5)/16 - (275*(1 - 2*x)^6)/32 + (125*(1 -
2*x)^7)/112

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Rubi [A]  time = 0.041744, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{125}{112} (1-2 x)^7-\frac{275}{32} (1-2 x)^6+\frac{363}{16} (1-2 x)^5-\frac{1331}{64} (1-2 x)^4 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^3*(3 + 5*x)^3,x]

[Out]

(-1331*(1 - 2*x)^4)/64 + (363*(1 - 2*x)^5)/16 - (275*(1 - 2*x)^6)/32 + (125*(1 -
2*x)^7)/112

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{1000 x^{7}}{7} - 50 x^{6} + 174 x^{5} + \frac{179 x^{4}}{4} - 87 x^{3} + 27 x - 27 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1000*x**7/7 - 50*x**6 + 174*x**5 + 179*x**4/4 - 87*x**3 + 27*x - 27*Integral(x,
x)

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Mathematica [A]  time = 0.00223668, size = 40, normalized size = 0.89 \[ -\frac{1000 x^7}{7}-50 x^6+174 x^5+\frac{179 x^4}{4}-87 x^3-\frac{27 x^2}{2}+27 x \]

Antiderivative was successfully verified.

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

[Out]

27*x - (27*x^2)/2 - 87*x^3 + (179*x^4)/4 + 174*x^5 - 50*x^6 - (1000*x^7)/7

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Maple [A]  time = 0.001, size = 35, normalized size = 0.8 \[ -{\frac{1000\,{x}^{7}}{7}}-50\,{x}^{6}+174\,{x}^{5}+{\frac{179\,{x}^{4}}{4}}-87\,{x}^{3}-{\frac{27\,{x}^{2}}{2}}+27\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^3*(3+5*x)^3,x)

[Out]

-1000/7*x^7-50*x^6+174*x^5+179/4*x^4-87*x^3-27/2*x^2+27*x

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Maxima [A]  time = 1.32751, size = 46, normalized size = 1.02 \[ -\frac{1000}{7} \, x^{7} - 50 \, x^{6} + 174 \, x^{5} + \frac{179}{4} \, x^{4} - 87 \, x^{3} - \frac{27}{2} \, x^{2} + 27 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1000/7*x^7 - 50*x^6 + 174*x^5 + 179/4*x^4 - 87*x^3 - 27/2*x^2 + 27*x

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Fricas [A]  time = 0.187169, size = 1, normalized size = 0.02 \[ -\frac{1000}{7} x^{7} - 50 x^{6} + 174 x^{5} + \frac{179}{4} x^{4} - 87 x^{3} - \frac{27}{2} x^{2} + 27 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1000/7*x^7 - 50*x^6 + 174*x^5 + 179/4*x^4 - 87*x^3 - 27/2*x^2 + 27*x

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Sympy [A]  time = 0.083538, size = 37, normalized size = 0.82 \[ - \frac{1000 x^{7}}{7} - 50 x^{6} + 174 x^{5} + \frac{179 x^{4}}{4} - 87 x^{3} - \frac{27 x^{2}}{2} + 27 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1000*x**7/7 - 50*x**6 + 174*x**5 + 179*x**4/4 - 87*x**3 - 27*x**2/2 + 27*x

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GIAC/XCAS [A]  time = 0.20857, size = 46, normalized size = 1.02 \[ -\frac{1000}{7} \, x^{7} - 50 \, x^{6} + 174 \, x^{5} + \frac{179}{4} \, x^{4} - 87 \, x^{3} - \frac{27}{2} \, x^{2} + 27 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1000/7*x^7 - 50*x^6 + 174*x^5 + 179/4*x^4 - 87*x^3 - 27/2*x^2 + 27*x