3.13.21 \(\int (-2 x-6 x^2-4 x^3) \, dx\)

Optimal. Leaf size=23 \[ 1-\left (x+x^2\right )^2+4 \left (-4+\frac {\log ^2(3)}{4}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 16, normalized size of antiderivative = 0.70, number of steps used = 1, number of rules used = 0, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -x^4-2 x^3-x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-2*x - 6*x^2 - 4*x^3,x]

[Out]

-x^2 - 2*x^3 - x^4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-x^2-2 x^3-x^4\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 16, normalized size = 0.70 \begin {gather*} -x^2-2 x^3-x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-2*x - 6*x^2 - 4*x^3,x]

[Out]

-x^2 - 2*x^3 - x^4

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fricas [A]  time = 1.11, size = 16, normalized size = 0.70 \begin {gather*} -x^{4} - 2 \, x^{3} - x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x^3-6*x^2-2*x,x, algorithm="fricas")

[Out]

-x^4 - 2*x^3 - x^2

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giac [A]  time = 0.29, size = 16, normalized size = 0.70 \begin {gather*} -x^{4} - 2 \, x^{3} - x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x^3-6*x^2-2*x,x, algorithm="giac")

[Out]

-x^4 - 2*x^3 - x^2

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maple [A]  time = 0.01, size = 11, normalized size = 0.48

method	result	size
gosper	\(-x^{2} \left (x +1\right )^{2}\)	\(11\)
default	\(-x^{4}-2 x^{3}-x^{2}\)	\(17\)
norman	\(-x^{4}-2 x^{3}-x^{2}\)	\(17\)
risch	\(-x^{4}-2 x^{3}-x^{2}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-4*x^3-6*x^2-2*x,x,method=_RETURNVERBOSE)

[Out]

-x^2*(x+1)^2

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maxima [A]  time = 0.54, size = 16, normalized size = 0.70 \begin {gather*} -x^{4} - 2 \, x^{3} - x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x^3-6*x^2-2*x,x, algorithm="maxima")

[Out]

-x^4 - 2*x^3 - x^2

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mupad [B]  time = 0.03, size = 10, normalized size = 0.43 \begin {gather*} -x^2\,{\left (x+1\right )}^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- 2*x - 6*x^2 - 4*x^3,x)

[Out]

-x^2*(x + 1)^2

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sympy [A]  time = 0.05, size = 12, normalized size = 0.52 \begin {gather*} - x^{4} - 2 x^{3} - x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x**3-6*x**2-2*x,x)

[Out]

-x**4 - 2*x**3 - x**2

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