3.2.74 \(\int (2 x+\sqrt {2} x^2) \, dx\) [174]

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

[Out]

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

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Rubi [A]
time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {\sqrt {2} x^3}{3}+x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2*x + Sqrt[2]*x^2,x]

[Out]

x^2 + (Sqrt[2]*x^3)/3

Rubi steps

\begin {align*} \int \left (2 x+\sqrt {2} x^2\right ) \, dx &=x^2+\frac {\sqrt {2} x^3}{3}\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} x^2+\frac {\sqrt {2} x^3}{3} \end {gather*}

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 = 0.02, size = 19, normalized size = 1.19

method	result	size
norman	\(x^{2}+\frac {x^{3} \sqrt {2}}{3}\)	\(13\)
risch	\(x^{2}+\frac {x^{3} \sqrt {2}}{3}\)	\(13\)
default	\(\sqrt {2}\, \left (\frac {x^{3}}{3}+\frac {x^{2} \sqrt {2}}{2}\right )\)	\(19\)
gosper	\(\frac {x^{2} \left (2 x +3 \sqrt {2}\right ) \left (x \sqrt {2}+2\right )}{6 x +6 \sqrt {2}}\)	\(29\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x+x^2*2^(1/2),x,method=_RETURNVERBOSE)

[Out]

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

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Maxima [A]
time = 2.94, size = 12, normalized size = 0.75 \begin {gather*} \frac {1}{3} \, \sqrt {2} x^{3} + x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x+x^2*2^(1/2),x, algorithm="maxima")

[Out]

1/3*sqrt(2)*x^3 + x^2

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Fricas [A]
time = 0.45, size = 12, normalized size = 0.75 \begin {gather*} \frac {1}{3} \, \sqrt {2} x^{3} + x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x+x^2*2^(1/2),x, algorithm="fricas")

[Out]

1/3*sqrt(2)*x^3 + x^2

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Sympy [A]
time = 0.01, size = 12, normalized size = 0.75 \begin {gather*} \frac {\sqrt {2} x^{3}}{3} + x^{2} \end {gather*}

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 [A]
time = 0.53, size = 12, normalized size = 0.75 \begin {gather*} \frac {1}{3} \, \sqrt {2} x^{3} + x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x+x^2*2^(1/2),x, algorithm="giac")

[Out]

1/3*sqrt(2)*x^3 + x^2

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Mupad [B]
time = 0.03, size = 12, normalized size = 0.75 \begin {gather*} \frac {x^2\,\left (\sqrt {2}\,x+3\right )}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + 2^(1/2)*x^2,x)

[Out]

(x^2*(2^(1/2)*x + 3))/3

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