3.2.80 \(\int 4 x \, dx\)

Optimal. Leaf size=10 \[ 2+22 e+2 x^2 \]

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Rubi [A]  time = 0.00, antiderivative size = 5, normalized size of antiderivative = 0.50, number of steps used = 2, number of rules used = 2, integrand size = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.667, Rules used = {12, 30} \begin {gather*} 2 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[4*x,x]

[Out]

2*x^2

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

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} &=4 \int x \, dx\\ &=2 x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 5, normalized size = 0.50 \begin {gather*} 2 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[4*x,x]

[Out]

2*x^2

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fricas [A]  time = 0.90, size = 5, normalized size = 0.50 \begin {gather*} 2 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x,x, algorithm="fricas")

[Out]

2*x^2

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giac [A]  time = 0.23, size = 5, normalized size = 0.50 \begin {gather*} 2 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x,x, algorithm="giac")

[Out]

2*x^2

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maple [A]  time = 0.01, size = 6, normalized size = 0.60

method	result	size
gosper	\(2 x^{2}\)	\(6\)
default	\(2 x^{2}\)	\(6\)
norman	\(2 x^{2}\)	\(6\)
risch	\(2 x^{2}\)	\(6\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*x,x,method=_RETURNVERBOSE)

[Out]

2*x^2

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maxima [A]  time = 0.37, size = 5, normalized size = 0.50 \begin {gather*} 2 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x,x, algorithm="maxima")

[Out]

2*x^2

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mupad [B]  time = 0.02, size = 5, normalized size = 0.50 \begin {gather*} 2\,x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*x,x)

[Out]

2*x^2

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sympy [A]  time = 0.01, size = 3, normalized size = 0.30 \begin {gather*} 2 x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x,x)

[Out]

2*x**2

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