3.57.74 \(\int 2 x \, dx\)

Optimal. Leaf size=6 \[ x^2+\log (3) \]

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Rubi [A]  time = 0.00, antiderivative size = 3, 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*} x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2*x,x]

[Out]

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

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Mathematica [A]  time = 0.00, size = 3, normalized size = 0.50 \begin {gather*} x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2*x,x]

[Out]

x^2

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fricas [A]  time = 0.56, size = 3, normalized size = 0.50 \begin {gather*} x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x,x, algorithm="fricas")

[Out]

x^2

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giac [A]  time = 0.15, size = 3, normalized size = 0.50 \begin {gather*} x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x,x, algorithm="giac")

[Out]

x^2

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maple [A]  time = 0.01, size = 4, normalized size = 0.67

method	result	size
gosper	\(x^{2}\)	\(4\)
default	\(x^{2}\)	\(4\)
norman	\(x^{2}\)	\(4\)
risch	\(x^{2}\)	\(4\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x,x,method=_RETURNVERBOSE)

[Out]

x^2

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maxima [A]  time = 0.35, size = 3, normalized size = 0.50 \begin {gather*} x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x,x, algorithm="maxima")

[Out]

x^2

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mupad [B]  time = 0.01, size = 3, normalized size = 0.50 \begin {gather*} x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x,x)

[Out]

x^2

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sympy [A]  time = 0.01, size = 2, normalized size = 0.33 \begin {gather*} x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x,x)

[Out]

x**2

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