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

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

[Out]

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

________________________________________________________________________________________

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 = {} \[ \frac {\sqrt {2} x^3}{3}+x^2 \]

Antiderivative was successfully verified.

[In]

Int[2*x + Sqrt[2]*x^2,x]

[Out]

x^2 + (Sqrt[2]*x^3)/3

Rubi steps

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

________________________________________________________________________________________

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

Antiderivative was successfully verified.

[In]

Integrate[2*x + Sqrt[2]*x^2,x]

[Out]

x^2 + (Sqrt[2]*x^3)/3

________________________________________________________________________________________

fricas [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: SyntaxError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: SyntaxError >> Malformed expression

________________________________________________________________________________________

giac [A]  time = 1.07, size = 12, normalized size = 0.75 \[ \frac {1}{3} \, \sqrt {2} x^{3} + x^{2} \]

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

________________________________________________________________________________________

maple [A]  time = 0.00, size = 13, normalized size = 0.81 \[ \frac {\sqrt {2}\, x^{3}}{3}+x^{2} \]

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)

________________________________________________________________________________________

maxima [A]  time = 0.95, size = 12, normalized size = 0.75 \[ \frac {1}{3} \, \sqrt {2} x^{3} + x^{2} \]

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

________________________________________________________________________________________

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

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

________________________________________________________________________________________

sympy [A]  time = 0.06, 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

________________________________________________________________________________________