3.1149 \(\int (1-2 x) (3+5 x)^2 \, dx\)

Optimal. Leaf size=23 \[ \frac{11}{75} (5 x+3)^3-\frac{1}{50} (5 x+3)^4 \]

[Out]

(11*(3 + 5*x)^3)/75 - (3 + 5*x)^4/50

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Rubi [A]  time = 0.0243657, 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 \[ \frac{11}{75} (5 x+3)^3-\frac{1}{50} (5 x+3)^4 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)*(3 + 5*x)^2,x]

[Out]

(11*(3 + 5*x)^3)/75 - (3 + 5*x)^4/50

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{25 x^{4}}{2} - \frac{35 x^{3}}{3} + 9 x + 12 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25*x**4/2 - 35*x**3/3 + 9*x + 12*Integral(x, x)

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Mathematica [A]  time = 0.00109018, size = 23, normalized size = 1. \[ -\frac{25 x^4}{2}-\frac{35 x^3}{3}+6 x^2+9 x \]

Antiderivative was successfully verified.

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

[Out]

9*x + 6*x^2 - (35*x^3)/3 - (25*x^4)/2

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Maple [A]  time = 0.001, size = 20, normalized size = 0.9 \[ -{\frac{25\,{x}^{4}}{2}}-{\frac{35\,{x}^{3}}{3}}+6\,{x}^{2}+9\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(3+5*x)^2,x)

[Out]

-25/2*x^4-35/3*x^3+6*x^2+9*x

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Maxima [A]  time = 1.3502, size = 26, normalized size = 1.13 \[ -\frac{25}{2} \, x^{4} - \frac{35}{3} \, x^{3} + 6 \, x^{2} + 9 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/2*x^4 - 35/3*x^3 + 6*x^2 + 9*x

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Fricas [A]  time = 0.181636, size = 1, normalized size = 0.04 \[ -\frac{25}{2} x^{4} - \frac{35}{3} x^{3} + 6 x^{2} + 9 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/2*x^4 - 35/3*x^3 + 6*x^2 + 9*x

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Sympy [A]  time = 0.074889, size = 20, normalized size = 0.87 \[ - \frac{25 x^{4}}{2} - \frac{35 x^{3}}{3} + 6 x^{2} + 9 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)*(3+5*x)**2,x)

[Out]

-25*x**4/2 - 35*x**3/3 + 6*x**2 + 9*x

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GIAC/XCAS [A]  time = 0.209147, size = 26, normalized size = 1.13 \[ -\frac{25}{2} \, x^{4} - \frac{35}{3} \, x^{3} + 6 \, x^{2} + 9 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/2*x^4 - 35/3*x^3 + 6*x^2 + 9*x