3.19.97 \(\int (\frac {x^2}{2}+\frac {x^3}{3}) \, dx\) [1897]

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

[Out]

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

________________________________________________________________________________________

Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {x^4}{12}+\frac {x^3}{6} \end {gather*}

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 = 0.00, size = 15, normalized size = 1.00 \begin {gather*} \frac {x^3}{6}+\frac {x^4}{12} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[x^2/2 + x^3/3,x]

[Out]

x^3/6 + x^4/12

________________________________________________________________________________________

Maple [A]
time = 0.01, size = 12, normalized size = 0.80

method	result	size
gosper	\(\frac {x^{3} \left (2+x \right )}{12}\)	\(9\)
default	\(\frac {1}{6} x^{3}+\frac {1}{12} x^{4}\)	\(12\)
norman	\(\frac {1}{6} x^{3}+\frac {1}{12} x^{4}\)	\(12\)
risch	\(\frac {1}{6} x^{3}+\frac {1}{12} x^{4}\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

Maxima [A]
time = 0.27, size = 11, normalized size = 0.73 \begin {gather*} \frac {1}{12} \, x^{4} + \frac {1}{6} \, x^{3} \end {gather*}

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

________________________________________________________________________________________

Fricas [A]
time = 0.84, size = 11, normalized size = 0.73 \begin {gather*} \frac {1}{12} \, x^{4} + \frac {1}{6} \, x^{3} \end {gather*}

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

________________________________________________________________________________________

Sympy [A]
time = 0.01, size = 8, normalized size = 0.53 \begin {gather*} \frac {x^{4}}{12} + \frac {x^{3}}{6} \end {gather*}

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

________________________________________________________________________________________

Giac [A]
time = 1.01, size = 11, normalized size = 0.73 \begin {gather*} \frac {1}{12} \, x^{4} + \frac {1}{6} \, x^{3} \end {gather*}

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

________________________________________________________________________________________

Mupad [B]
time = 0.02, size = 8, normalized size = 0.53 \begin {gather*} \frac {x^3\,\left (x+2\right )}{12} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^2/2 + x^3/3,x)

[Out]

(x^3*(x + 2))/12

________________________________________________________________________________________