3.77.89 \(\int -2 x \, dx\)

Optimal. Leaf size=16 \[ 2-i \pi -x^2-\log (15) \]

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Rubi [A]  time = 0.00, antiderivative size = 5, normalized size of antiderivative = 0.31, 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 = 5, normalized size = 0.31 \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 = 0.75, size = 5, normalized size = 0.31 \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 = 0.13, size = 5, normalized size = 0.31 \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 = 6, normalized size = 0.38

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

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 = 0.36, size = 5, normalized size = 0.31 \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 = 0.03, size = 5, normalized size = 0.31 \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 = 3, normalized size = 0.19 \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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