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

Optimal. Leaf size=16 \[ 2+\frac {1}{4} \left (2-729 e^2+x^4\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.44, 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} \begin {gather*} \frac {x^4}{4} \end {gather*}

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 {gather*} \begin {aligned} \text {integral} &=\frac {x^4}{4}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 0.44 \begin {gather*} \frac {x^4}{4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[x^3,x]

[Out]

x^4/4

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fricas [A]  time = 0.48, size = 5, normalized size = 0.31 \begin {gather*} \frac {1}{4} \, x^{4} \end {gather*}

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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giac [A]  time = 0.19, size = 5, normalized size = 0.31 \begin {gather*} \frac {1}{4} \, x^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^3,x, algorithm="giac")

[Out]

1/4*x^4

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maple [A]  time = 0.01, size = 6, normalized size = 0.38

method	result	size
gosper	\(\frac {x^{4}}{4}\)	\(6\)
default	\(\frac {x^{4}}{4}\)	\(6\)
norman	\(\frac {x^{4}}{4}\)	\(6\)
risch	\(\frac {x^{4}}{4}\)	\(6\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^3,x,method=_RETURNVERBOSE)

[Out]

1/4*x^4

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maxima [A]  time = 0.36, size = 5, normalized size = 0.31 \begin {gather*} \frac {1}{4} \, x^{4} \end {gather*}

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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mupad [B]  time = 0.04, size = 5, normalized size = 0.31 \begin {gather*} \frac {x^4}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^3,x)

[Out]

x^4/4

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sympy [A]  time = 0.05, size = 3, normalized size = 0.19 \begin {gather*} \frac {x^{4}}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**3,x)

[Out]

x**4/4

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