3.1227 \(\int (1-2 x)^2 (3+5 x) \, dx\)

Optimal. Leaf size=23 \[ \frac{5}{16} (1-2 x)^4-\frac{11}{12} (1-2 x)^3 \]

[Out]

(-11*(1 - 2*x)^3)/12 + (5*(1 - 2*x)^4)/16

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Rubi [A]  time = 0.0235108, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{5}{16} (1-2 x)^4-\frac{11}{12} (1-2 x)^3 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^2*(3 + 5*x),x]

[Out]

(-11*(1 - 2*x)^3)/12 + (5*(1 - 2*x)^4)/16

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ 5 x^{4} - \frac{8 x^{3}}{3} + 3 x - 7 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5*x**4 - 8*x**3/3 + 3*x - 7*Integral(x, x)

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Mathematica [A]  time = 0.000998347, size = 23, normalized size = 1. \[ 5 x^4-\frac{8 x^3}{3}-\frac{7 x^2}{2}+3 x \]

Antiderivative was successfully verified.

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

[Out]

3*x - (7*x^2)/2 - (8*x^3)/3 + 5*x^4

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Maple [A]  time = 0., size = 20, normalized size = 0.9 \[ 5\,{x}^{4}-{\frac{8\,{x}^{3}}{3}}-{\frac{7\,{x}^{2}}{2}}+3\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(3+5*x),x)

[Out]

5*x^4-8/3*x^3-7/2*x^2+3*x

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Maxima [A]  time = 1.34723, size = 26, normalized size = 1.13 \[ 5 \, x^{4} - \frac{8}{3} \, x^{3} - \frac{7}{2} \, x^{2} + 3 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5*x^4 - 8/3*x^3 - 7/2*x^2 + 3*x

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Fricas [A]  time = 0.18896, size = 1, normalized size = 0.04 \[ 5 x^{4} - \frac{8}{3} x^{3} - \frac{7}{2} x^{2} + 3 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5*x^4 - 8/3*x^3 - 7/2*x^2 + 3*x

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Sympy [A]  time = 0.06642, size = 20, normalized size = 0.87 \[ 5 x^{4} - \frac{8 x^{3}}{3} - \frac{7 x^{2}}{2} + 3 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2*(3+5*x),x)

[Out]

5*x**4 - 8*x**3/3 - 7*x**2/2 + 3*x

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GIAC/XCAS [A]  time = 0.205354, size = 26, normalized size = 1.13 \[ 5 \, x^{4} - \frac{8}{3} \, x^{3} - \frac{7}{2} \, x^{2} + 3 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5*x^4 - 8/3*x^3 - 7/2*x^2 + 3*x