3.54.41 \(\int (-1-3 x^2) \, dx\)

Optimal. Leaf size=23 \[ 2+e^4-x-x^2-x \left (-x+x^2\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.39, number of steps used = 1, number of rules used = 0, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -x^3-x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 - 3*x^2,x]

[Out]

-x - x^3

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.39 \begin {gather*} -x-x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 - 3*x^2,x]

[Out]

-x - x^3

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fricas [A]  time = 0.59, size = 9, normalized size = 0.39 \begin {gather*} -x^{3} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*x^2-1,x, algorithm="fricas")

[Out]

-x^3 - x

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giac [A]  time = 0.11, size = 9, normalized size = 0.39 \begin {gather*} -x^{3} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*x^2-1,x, algorithm="giac")

[Out]

-x^3 - x

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maple [A]  time = 0.01, size = 9, normalized size = 0.39

method	result	size
gosper	\(-x \left (x^{2}+1\right )\)	\(9\)
default	\(-x^{3}-x\)	\(10\)
norman	\(-x^{3}-x\)	\(10\)
risch	\(-x^{3}-x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-3*x^2-1,x,method=_RETURNVERBOSE)

[Out]

-x*(x^2+1)

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maxima [A]  time = 0.36, size = 9, normalized size = 0.39 \begin {gather*} -x^{3} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*x^2-1,x, algorithm="maxima")

[Out]

-x^3 - x

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mupad [B]  time = 0.02, size = 9, normalized size = 0.39 \begin {gather*} -x^3-x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- 3*x^2 - 1,x)

[Out]

- x - x^3

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sympy [A]  time = 0.04, size = 5, normalized size = 0.22 \begin {gather*} - x^{3} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*x**2-1,x)

[Out]

-x**3 - x

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