3.11 \(\int x^3 \, dx\)

Optimal. Leaf size=7 \[ \frac{x^4}{4} \]

[Out]

x^4/4

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Rubi [A]  time = 0.0003908, antiderivative size = 7, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 3, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {30} \[ \frac{x^4}{4} \]

Antiderivative was successfully verified.

[In]

Int[x^3,x]

[Out]

x^4/4

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin{align*} \int x^3 \, dx &=\frac{x^4}{4}\\ \end{align*}

Mathematica [A]  time = 0.0001082, size = 7, normalized size = 1. \[ \frac{x^4}{4} \]

Antiderivative was successfully verified.

[In]

Integrate[x^3,x]

[Out]

x^4/4

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Maple [A]  time = 0., size = 6, normalized size = 0.9 \begin{align*}{\frac{{x}^{4}}{4}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^3,x)

[Out]

1/4*x^4

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Maxima [A]  time = 0.948067, size = 7, normalized size = 1. \begin{align*} \frac{1}{4} \, x^{4} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^3,x, algorithm="maxima")

[Out]

1/4*x^4

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Fricas [A]  time = 1.2617, size = 12, normalized size = 1.71 \begin{align*} \frac{1}{4} x^{4} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^3,x, algorithm="fricas")

[Out]

1/4*x^4

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Sympy [A]  time = 0.04775, size = 3, normalized size = 0.43 \begin{align*} \frac{x^{4}}{4} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**3,x)

[Out]

x**4/4

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Giac [A]  time = 1.08909, size = 7, normalized size = 1. \begin{align*} \frac{1}{4} \, x^{4} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^3,x, algorithm="giac")

[Out]

1/4*x^4