3.1.11 \(\int x^3 \, dx\) [11]

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

[Out]

1/4*x^4

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Rubi [A]
time = 0.00, antiderivative size = 7, normalized size of antiderivative = 1.00, 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 {align*} \int x^3 \, dx &=\frac {x^4}{4}\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 7, normalized size = 1.00 \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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Maple [A]
time = 0.00, size = 6, normalized size = 0.86

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 = 0.29, size = 5, normalized size = 0.71 \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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Fricas [A]
time = 1.88, size = 5, normalized size = 0.71 \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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Sympy [A]
time = 0.02, size = 3, normalized size = 0.43 \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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Giac [A]
time = 1.47, size = 5, normalized size = 0.71 \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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Mupad [B]
time = 0.02, size = 5, normalized size = 0.71 \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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