3.63.32 \(\int \frac {-2 e-3 x^2}{e} \, dx\)

Optimal. Leaf size=12 \[ x \left (-2-\frac {x^2}{e}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12} \begin {gather*} -\frac {x^3}{e}-2 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-2*E - 3*x^2)/E,x]

[Out]

-2*x - x^3/E

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (-2 e-3 x^2\right ) \, dx}{e}\\ &=-2 x-\frac {x^3}{e}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} -2 x-\frac {x^3}{e} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2*E - 3*x^2)/E,x]

[Out]

-2*x - x^3/E

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fricas [A]  time = 0.60, size = 13, normalized size = 1.08 \begin {gather*} -{\left (x^{3} + 2 \, x e\right )} e^{\left (-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(x^3 + 2*x*e)*e^(-1)

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giac [A]  time = 0.12, size = 13, normalized size = 1.08 \begin {gather*} -{\left (x^{3} + 2 \, x e\right )} e^{\left (-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(x^3 + 2*x*e)*e^(-1)

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maple [A]  time = 0.05, size = 12, normalized size = 1.00

method	result	size
risch	\(-2 x -{\mathrm e}^{-1} x^{3}\)	\(12\)
norman	\(-2 x -{\mathrm e}^{-1} x^{3}\)	\(14\)
gosper	\(-x \left (x^{2}+2 \,{\mathrm e}\right ) {\mathrm e}^{-1}\)	\(16\)
default	\({\mathrm e}^{-1} \left (-2 x \,{\mathrm e}-x^{3}\right )\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2*x-exp(-1)*x^3

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maxima [A]  time = 0.44, size = 13, normalized size = 1.08 \begin {gather*} -{\left (x^{3} + 2 \, x e\right )} e^{\left (-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(x^3 + 2*x*e)*e^(-1)

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mupad [B]  time = 4.11, size = 11, normalized size = 0.92 \begin {gather*} -{\mathrm {e}}^{-1}\,x^3-2\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(-1)*(2*exp(1) + 3*x^2),x)

[Out]

- 2*x - x^3*exp(-1)

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sympy [A]  time = 0.05, size = 10, normalized size = 0.83 \begin {gather*} - \frac {x^{3}}{e} - 2 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x**3*exp(-1) - 2*x

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