3.24.22 \(\int (-3 e^2 x^2-3 e^{10} x^2) \, dx\)

Optimal. Leaf size=18 \[ 6-x^2 \left (e^2 x+e^{10} x\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.72, number of steps used = 3, number of rules used = 3, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.176, Rules used = {6, 12, 30} \begin {gather*} -e^2 \left (1+e^8\right ) x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-3*E^2*x^2 - 3*E^10*x^2,x]

[Out]

-(E^2*(1 + E^8)*x^3)

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rule 12

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

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int -3 \left (e^2+e^{10}\right ) x^2 \, dx\\ &=-\left (\left (3 e^2 \left (1+e^8\right )\right ) \int x^2 \, dx\right )\\ &=-e^2 \left (1+e^8\right ) x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 17, normalized size = 0.94 \begin {gather*} -e^2 x^3-e^{10} x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-3*E^2*x^2 - 3*E^10*x^2,x]

[Out]

-(E^2*x^3) - E^10*x^3

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fricas [A]  time = 0.73, size = 15, normalized size = 0.83 \begin {gather*} -x^{3} e^{10} - x^{3} e^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*x^2*exp(5)^2-3*x^2*exp(2),x, algorithm="fricas")

[Out]

-x^3*e^10 - x^3*e^2

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giac [A]  time = 0.25, size = 15, normalized size = 0.83 \begin {gather*} -x^{3} e^{10} - x^{3} e^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*x^2*exp(5)^2-3*x^2*exp(2),x, algorithm="giac")

[Out]

-x^3*e^10 - x^3*e^2

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maple [A]  time = 0.06, size = 13, normalized size = 0.72

method	result	size
gosper	\(-x^{3} \left ({\mathrm e}^{10}+{\mathrm e}^{2}\right )\)	\(13\)
norman	\(\left (-{\mathrm e}^{10}-{\mathrm e}^{2}\right ) x^{3}\)	\(16\)
risch	\(-x^{3} {\mathrm e}^{10}-x^{3} {\mathrm e}^{2}\)	\(16\)
default	\(-x^{3} {\mathrm e}^{10}-x^{3} {\mathrm e}^{2}\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-3*x^2*exp(5)^2-3*x^2*exp(2),x,method=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.34, size = 15, normalized size = 0.83 \begin {gather*} -x^{3} e^{10} - x^{3} e^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*x^2*exp(5)^2-3*x^2*exp(2),x, algorithm="maxima")

[Out]

-x^3*e^10 - x^3*e^2

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mupad [B]  time = 1.41, size = 11, normalized size = 0.61 \begin {gather*} -x^3\,{\mathrm {e}}^2\,\left ({\mathrm {e}}^8+1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- 3*x^2*exp(2) - 3*x^2*exp(10),x)

[Out]

-x^3*exp(2)*(exp(8) + 1)

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sympy [A]  time = 0.06, size = 10, normalized size = 0.56 \begin {gather*} x^{3} \left (- e^{10} - e^{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*x**2*exp(5)**2-3*x**2*exp(2),x)

[Out]

x**3*(-exp(10) - exp(2))

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