3.1134 \(\int (1-2 x) (3+5 x) \, dx\)

Optimal. Leaf size=18 \[ -\frac{10 x^3}{3}-\frac{x^2}{2}+3 x \]

[Out]

3*x - x^2/2 - (10*x^3)/3

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Rubi [A]  time = 0.0166218, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{10 x^3}{3}-\frac{x^2}{2}+3 x \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)*(3 + 5*x),x]

[Out]

3*x - x^2/2 - (10*x^3)/3

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{10 x^{3}}{3} + 3 x - \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-10*x**3/3 + 3*x - Integral(x, x)

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Mathematica [A]  time = 0.00122489, size = 18, normalized size = 1. \[ -\frac{10 x^3}{3}-\frac{x^2}{2}+3 x \]

Antiderivative was successfully verified.

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

[Out]

3*x - x^2/2 - (10*x^3)/3

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Maple [A]  time = 0.002, size = 15, normalized size = 0.8 \[ 3\,x-{\frac{{x}^{2}}{2}}-{\frac{10\,{x}^{3}}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(3+5*x),x)

[Out]

3*x-1/2*x^2-10/3*x^3

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Maxima [A]  time = 1.84457, size = 19, normalized size = 1.06 \[ -\frac{10}{3} \, x^{3} - \frac{1}{2} \, x^{2} + 3 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-10/3*x^3 - 1/2*x^2 + 3*x

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Fricas [A]  time = 0.181323, size = 1, normalized size = 0.06 \[ -\frac{10}{3} x^{3} - \frac{1}{2} x^{2} + 3 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-10/3*x^3 - 1/2*x^2 + 3*x

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Sympy [A]  time = 0.058662, size = 14, normalized size = 0.78 \[ - \frac{10 x^{3}}{3} - \frac{x^{2}}{2} + 3 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)*(3+5*x),x)

[Out]

-10*x**3/3 - x**2/2 + 3*x

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GIAC/XCAS [A]  time = 0.231775, size = 19, normalized size = 1.06 \[ -\frac{10}{3} \, x^{3} - \frac{1}{2} \, x^{2} + 3 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-10/3*x^3 - 1/2*x^2 + 3*x