3.59.43 \(\int (-4-2 x) \, dx\)

Optimal. Leaf size=24 \[ \left (-4+\frac {9}{x}+\frac {5}{\left (1+e^4\right ) x}-x\right ) x \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.38, number of steps used = 1, number of rules used = 0, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -x^2-4 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-4 - 2*x,x]

[Out]

-4*x - x^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-4 x-x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.38 \begin {gather*} -4 x-x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-4 - 2*x,x]

[Out]

-4*x - x^2

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fricas [A]  time = 0.82, size = 9, normalized size = 0.38 \begin {gather*} -x^{2} - 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*x-4,x, algorithm="fricas")

[Out]

-x^2 - 4*x

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giac [A]  time = 0.13, size = 9, normalized size = 0.38 \begin {gather*} -x^{2} - 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*x-4,x, algorithm="giac")

[Out]

-x^2 - 4*x

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maple [A]  time = 0.02, size = 7, normalized size = 0.29

method	result	size
gosper	\(-\left (4+x \right ) x\)	\(7\)
default	\(-x^{2}-4 x\)	\(10\)
norman	\(-x^{2}-4 x\)	\(10\)
risch	\(-x^{2}-4 x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2*x-4,x,method=_RETURNVERBOSE)

[Out]

-(4+x)*x

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maxima [A]  time = 0.36, size = 9, normalized size = 0.38 \begin {gather*} -x^{2} - 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*x-4,x, algorithm="maxima")

[Out]

-x^2 - 4*x

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mupad [B]  time = 0.03, size = 6, normalized size = 0.25 \begin {gather*} -x\,\left (x+4\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- 2*x - 4,x)

[Out]

-x*(x + 4)

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sympy [A]  time = 0.04, size = 7, normalized size = 0.29 \begin {gather*} - x^{2} - 4 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*x-4,x)

[Out]

-x**2 - 4*x

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