3.1897 \(\int (\frac{x^2}{2}+\frac{x^3}{3}) \, dx\)

Optimal. Leaf size=15 \[ \frac{x^4}{12}+\frac{x^3}{6} \]

[Out]

x^3/6 + x^4/12

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Rubi [A]  time = 0.0019564, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{x^4}{12}+\frac{x^3}{6} \]

Antiderivative was successfully verified.

[In]

Int[x^2/2 + x^3/3,x]

[Out]

x^3/6 + x^4/12

Rubi steps

\begin{align*} \int \left (\frac{x^2}{2}+\frac{x^3}{3}\right ) \, dx &=\frac{x^3}{6}+\frac{x^4}{12}\\ \end{align*}

Mathematica [A]  time = 0.0000454, size = 15, normalized size = 1. \[ \frac{x^4}{12}+\frac{x^3}{6} \]

Antiderivative was successfully verified.

[In]

Integrate[x^2/2 + x^3/3,x]

[Out]

x^3/6 + x^4/12

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Maple [A]  time = 0.001, size = 12, normalized size = 0.8 \begin{align*}{\frac{{x}^{3}}{6}}+{\frac{{x}^{4}}{12}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/6*x^3+1/12*x^4

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Maxima [A]  time = 0.974128, size = 15, normalized size = 1. \begin{align*} \frac{1}{12} \, x^{4} + \frac{1}{6} \, x^{3} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*x^2+1/3*x^3,x, algorithm="maxima")

[Out]

1/12*x^4 + 1/6*x^3

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Fricas [A]  time = 1.89879, size = 27, normalized size = 1.8 \begin{align*} \frac{1}{12} x^{4} + \frac{1}{6} x^{3} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*x^2+1/3*x^3,x, algorithm="fricas")

[Out]

1/12*x^4 + 1/6*x^3

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Sympy [A]  time = 0.050445, size = 8, normalized size = 0.53 \begin{align*} \frac{x^{4}}{12} + \frac{x^{3}}{6} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*x**2+1/3*x**3,x)

[Out]

x**4/12 + x**3/6

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Giac [A]  time = 1.09694, size = 15, normalized size = 1. \begin{align*} \frac{1}{12} \, x^{4} + \frac{1}{6} \, x^{3} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*x^2+1/3*x^3,x, algorithm="giac")

[Out]

1/12*x^4 + 1/6*x^3