3.1329 \(\int (1-2 x)^3 (3+5 x) \, dx\)

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

[Out]

(-11*(1 - 2*x)^4)/16 + (1 - 2*x)^5/4

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Rubi [A]  time = 0.0203887, 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 \[ \frac{1}{4} (1-2 x)^5-\frac{11}{16} (1-2 x)^4 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^3*(3 + 5*x),x]

[Out]

(-11*(1 - 2*x)^4)/16 + (1 - 2*x)^5/4

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - 8 x^{5} + 9 x^{4} + 2 x^{3} + 3 x - 13 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8*x**5 + 9*x**4 + 2*x**3 + 3*x - 13*Integral(x, x)

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Mathematica [A]  time = 0.0014588, size = 26, normalized size = 1.13 \[ -8 x^5+9 x^4+2 x^3-\frac{13 x^2}{2}+3 x \]

Antiderivative was successfully verified.

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

[Out]

3*x - (13*x^2)/2 + 2*x^3 + 9*x^4 - 8*x^5

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Maple [A]  time = 0.001, size = 25, normalized size = 1.1 \[ -8\,{x}^{5}+9\,{x}^{4}+2\,{x}^{3}-{\frac{13\,{x}^{2}}{2}}+3\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^3*(3+5*x),x)

[Out]

-8*x^5+9*x^4+2*x^3-13/2*x^2+3*x

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Maxima [A]  time = 1.34143, size = 32, normalized size = 1.39 \[ -8 \, x^{5} + 9 \, x^{4} + 2 \, x^{3} - \frac{13}{2} \, x^{2} + 3 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8*x^5 + 9*x^4 + 2*x^3 - 13/2*x^2 + 3*x

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Fricas [A]  time = 0.183383, size = 1, normalized size = 0.04 \[ -8 x^{5} + 9 x^{4} + 2 x^{3} - \frac{13}{2} x^{2} + 3 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8*x^5 + 9*x^4 + 2*x^3 - 13/2*x^2 + 3*x

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Sympy [A]  time = 0.076498, size = 24, normalized size = 1.04 \[ - 8 x^{5} + 9 x^{4} + 2 x^{3} - \frac{13 x^{2}}{2} + 3 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**3*(3+5*x),x)

[Out]

-8*x**5 + 9*x**4 + 2*x**3 - 13*x**2/2 + 3*x

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GIAC/XCAS [A]  time = 0.207287, size = 32, normalized size = 1.39 \[ -8 \, x^{5} + 9 \, x^{4} + 2 \, x^{3} - \frac{13}{2} \, x^{2} + 3 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8*x^5 + 9*x^4 + 2*x^3 - 13/2*x^2 + 3*x