3.1243 \(\int (1-2 x)^2 (2+3 x) (3+5 x)^2 \, dx\)

Optimal. Leaf size=45 \[ \frac{25}{32} (1-2 x)^6-\frac{101}{16} (1-2 x)^5+\frac{1133}{64} (1-2 x)^4-\frac{847}{48} (1-2 x)^3 \]

[Out]

(-847*(1 - 2*x)^3)/48 + (1133*(1 - 2*x)^4)/64 - (101*(1 - 2*x)^5)/16 + (25*(1 -
2*x)^6)/32

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Rubi [A]  time = 0.0599488, antiderivative size = 45, 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 \[ \frac{25}{32} (1-2 x)^6-\frac{101}{16} (1-2 x)^5+\frac{1133}{64} (1-2 x)^4-\frac{847}{48} (1-2 x)^3 \]

Antiderivative was successfully verified.

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

[Out]

(-847*(1 - 2*x)^3)/48 + (1133*(1 - 2*x)^4)/64 - (101*(1 - 2*x)^5)/16 + (25*(1 -
2*x)^6)/32

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ 50 x^{6} + 52 x^{5} - \frac{137 x^{4}}{4} - \frac{136 x^{3}}{3} + 18 x + 15 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

50*x**6 + 52*x**5 - 137*x**4/4 - 136*x**3/3 + 18*x + 15*Integral(x, x)

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Mathematica [A]  time = 0.00140921, size = 35, normalized size = 0.78 \[ 50 x^6+52 x^5-\frac{137 x^4}{4}-\frac{136 x^3}{3}+\frac{15 x^2}{2}+18 x \]

Antiderivative was successfully verified.

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

[Out]

18*x + (15*x^2)/2 - (136*x^3)/3 - (137*x^4)/4 + 52*x^5 + 50*x^6

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Maple [A]  time = 0.002, size = 30, normalized size = 0.7 \[ 50\,{x}^{6}+52\,{x}^{5}-{\frac{137\,{x}^{4}}{4}}-{\frac{136\,{x}^{3}}{3}}+{\frac{15\,{x}^{2}}{2}}+18\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

50*x^6+52*x^5-137/4*x^4-136/3*x^3+15/2*x^2+18*x

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Maxima [A]  time = 1.34131, size = 39, normalized size = 0.87 \[ 50 \, x^{6} + 52 \, x^{5} - \frac{137}{4} \, x^{4} - \frac{136}{3} \, x^{3} + \frac{15}{2} \, x^{2} + 18 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

50*x^6 + 52*x^5 - 137/4*x^4 - 136/3*x^3 + 15/2*x^2 + 18*x

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Fricas [A]  time = 0.18583, size = 1, normalized size = 0.02 \[ 50 x^{6} + 52 x^{5} - \frac{137}{4} x^{4} - \frac{136}{3} x^{3} + \frac{15}{2} x^{2} + 18 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

50*x^6 + 52*x^5 - 137/4*x^4 - 136/3*x^3 + 15/2*x^2 + 18*x

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Sympy [A]  time = 0.079979, size = 32, normalized size = 0.71 \[ 50 x^{6} + 52 x^{5} - \frac{137 x^{4}}{4} - \frac{136 x^{3}}{3} + \frac{15 x^{2}}{2} + 18 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

50*x**6 + 52*x**5 - 137*x**4/4 - 136*x**3/3 + 15*x**2/2 + 18*x

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GIAC/XCAS [A]  time = 0.211987, size = 39, normalized size = 0.87 \[ 50 \, x^{6} + 52 \, x^{5} - \frac{137}{4} \, x^{4} - \frac{136}{3} \, x^{3} + \frac{15}{2} \, x^{2} + 18 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

50*x^6 + 52*x^5 - 137/4*x^4 - 136/3*x^3 + 15/2*x^2 + 18*x