3.483 \(\int \left (\frac{1}{2} \left (3-\sqrt{37}\right )+x\right ) \left (\frac{1}{2} \left (3+\sqrt{37}\right )+x\right ) \, dx\)

Optimal. Leaf size=18 \[ \frac{x^3}{3}+\frac{3 x^2}{2}-7 x \]

[Out]

-7*x + (3*x^2)/2 + x^3/3

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Rubi [A]  time = 0.0308022, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 29, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.034 \[ \frac{x^3}{3}+\frac{3 x^2}{2}-7 x \]

Antiderivative was successfully verified.

[In]  Int[((3 - Sqrt[37])/2 + x)*((3 + Sqrt[37])/2 + x),x]

[Out]

-7*x + (3*x^2)/2 + x^3/3

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((x+3/2-1/2*37**(1/2))*(x+3/2+1/2*37**(1/2)),x)

[Out]

x**3/3 - 7*x + 3*Integral(x, x)

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Mathematica [A]  time = 0.000988747, size = 18, normalized size = 1. \[ \frac{x^3}{3}+\frac{3 x^2}{2}-7 x \]

Antiderivative was successfully verified.

[In]  Integrate[((3 - Sqrt[37])/2 + x)*((3 + Sqrt[37])/2 + x),x]

[Out]

-7*x + (3*x^2)/2 + x^3/3

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Maple [A]  time = 0.001, size = 28, normalized size = 1.6 \[{\frac{{x}^{3}}{3}}+{\frac{3\,{x}^{2}}{2}}+ \left ({\frac{3}{2}}-{\frac{\sqrt{37}}{2}} \right ) \left ({\frac{3}{2}}+{\frac{\sqrt{37}}{2}} \right ) x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x+3/2-1/2*37^(1/2))*(x+3/2+1/2*37^(1/2)),x)

[Out]

1/3*x^3+3/2*x^2+(3/2-1/2*37^(1/2))*(3/2+1/2*37^(1/2))*x

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Maxima [A]  time = 0.869247, size = 19, normalized size = 1.06 \[ \frac{1}{3} \, x^{3} + \frac{3}{2} \, x^{2} - 7 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/4*(2*x + sqrt(37) + 3)*(2*x - sqrt(37) + 3),x, algorithm="maxima")

[Out]

1/3*x^3 + 3/2*x^2 - 7*x

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Fricas [F(-2)]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: SyntaxError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/4*(2*x + sqrt(37) + 3)*(2*x - sqrt(37) + 3),x, algorithm="fricas")

[Out]

Exception raised: SyntaxError

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Sympy [A]  time = 0.066213, size = 14, normalized size = 0.78 \[ \frac{x^{3}}{3} + \frac{3 x^{2}}{2} - 7 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x+3/2-1/2*37**(1/2))*(x+3/2+1/2*37**(1/2)),x)

[Out]

x**3/3 + 3*x**2/2 - 7*x

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GIAC/XCAS [A]  time = 0.25815, size = 19, normalized size = 1.06 \[ \frac{1}{3} \, x^{3} + \frac{3}{2} \, x^{2} - 7 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/4*(2*x + sqrt(37) + 3)*(2*x - sqrt(37) + 3),x, algorithm="giac")

[Out]

1/3*x^3 + 3/2*x^2 - 7*x