3.97.30 \(\int (-3-10 x-6 x^2-4 x^3) \, dx\)

Optimal. Leaf size=17 \[ -e^{17}+x-\left (2+x+x^2\right )^2 \]

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Rubi [A]  time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.12, number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -x^4-2 x^3-5 x^2-3 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-3 - 10*x - 6*x^2 - 4*x^3,x]

[Out]

-3*x - 5*x^2 - 2*x^3 - x^4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-3 x-5 x^2-2 x^3-x^4\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 19, normalized size = 1.12 \begin {gather*} -3 x-5 x^2-2 x^3-x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-3 - 10*x - 6*x^2 - 4*x^3,x]

[Out]

-3*x - 5*x^2 - 2*x^3 - x^4

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fricas [A]  time = 0.61, size = 19, normalized size = 1.12 \begin {gather*} -x^{4} - 2 \, x^{3} - 5 \, x^{2} - 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x^3-6*x^2-10*x-3,x, algorithm="fricas")

[Out]

-x^4 - 2*x^3 - 5*x^2 - 3*x

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giac [A]  time = 0.18, size = 19, normalized size = 1.12 \begin {gather*} -x^{4} - 2 \, x^{3} - 5 \, x^{2} - 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x^3-6*x^2-10*x-3,x, algorithm="giac")

[Out]

-x^4 - 2*x^3 - 5*x^2 - 3*x

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maple [A]  time = 0.01, size = 17, normalized size = 1.00

method	result	size
gosper	\(-x \left (x^{3}+2 x^{2}+5 x +3\right )\)	\(17\)
default	\(-x^{4}-2 x^{3}-5 x^{2}-3 x\)	\(20\)
norman	\(-x^{4}-2 x^{3}-5 x^{2}-3 x\)	\(20\)
risch	\(-x^{4}-2 x^{3}-5 x^{2}-3 x\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-4*x^3-6*x^2-10*x-3,x,method=_RETURNVERBOSE)

[Out]

-x*(x^3+2*x^2+5*x+3)

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maxima [A]  time = 0.35, size = 19, normalized size = 1.12 \begin {gather*} -x^{4} - 2 \, x^{3} - 5 \, x^{2} - 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x^3-6*x^2-10*x-3,x, algorithm="maxima")

[Out]

-x^4 - 2*x^3 - 5*x^2 - 3*x

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mupad [B]  time = 0.03, size = 19, normalized size = 1.12 \begin {gather*} -x^4-2\,x^3-5\,x^2-3\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- 10*x - 6*x^2 - 4*x^3 - 3,x)

[Out]

- 3*x - 5*x^2 - 2*x^3 - x^4

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sympy [A]  time = 0.05, size = 17, normalized size = 1.00 \begin {gather*} - x^{4} - 2 x^{3} - 5 x^{2} - 3 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x**3-6*x**2-10*x-3,x)

[Out]

-x**4 - 2*x**3 - 5*x**2 - 3*x

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