3.174 \(\int \left (2 x+\sqrt{2} x^2\right ) \, dx\)

Optimal. Leaf size=16 \[ \frac{\sqrt{2} x^3}{3}+x^2 \]

[Out]

x^2 + (Sqrt[2]*x^3)/3

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Rubi [A]  time = 0.00750072, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \frac{\sqrt{2} x^3}{3}+x^2 \]

Antiderivative was successfully verified.

[In]  Int[2*x + Sqrt[2]*x^2,x]

[Out]

x^2 + (Sqrt[2]*x^3)/3

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{\sqrt{2} x^{3}}{3} + 2 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

sqrt(2)*x**3/3 + 2*Integral(x, x)

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Mathematica [A]  time = 0.000056637, size = 16, normalized size = 1. \[ \frac{\sqrt{2} x^3}{3}+x^2 \]

Antiderivative was successfully verified.

[In]  Integrate[2*x + Sqrt[2]*x^2,x]

[Out]

x^2 + (Sqrt[2]*x^3)/3

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Maple [A]  time = 0.001, size = 13, normalized size = 0.8 \[{x}^{2}+{\frac{{x}^{3}\sqrt{2}}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(2*x+x^2*2^(1/2),x)

[Out]

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

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Maxima [A]  time = 1.54767, size = 16, normalized size = 1. \[ \frac{1}{3} \, \sqrt{2} x^{3} + x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(2)*x^2 + 2*x,x, algorithm="maxima")

[Out]

1/3*sqrt(2)*x^3 + x^2

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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(sqrt(2)*x^2 + 2*x,x, algorithm="fricas")

[Out]

Exception raised: SyntaxError

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Sympy [A]  time = 0.02803, size = 12, normalized size = 0.75 \[ \frac{\sqrt{2} x^{3}}{3} + x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(2*x+x**2*2**(1/2),x)

[Out]

sqrt(2)*x**3/3 + x**2

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GIAC/XCAS [A]  time = 0.198786, size = 16, normalized size = 1. \[ \frac{1}{3} \, \sqrt{2} x^{3} + x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(2)*x^2 + 2*x,x, algorithm="giac")

[Out]

1/3*sqrt(2)*x^3 + x^2