3.29.72 \(\int 12 e^{2/5} x^2 \, dx\)

Optimal. Leaf size=12 \[ -1+4 e^{2/5} x^3 \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.83, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 30} \begin {gather*} 4 e^{2/5} x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[12*E^(2/5)*x^2,x]

[Out]

4*E^(2/5)*x^3

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} &=\left (12 e^{2/5}\right ) \int x^2 \, dx\\ &=4 e^{2/5} x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.83 \begin {gather*} 4 e^{2/5} x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[12*E^(2/5)*x^2,x]

[Out]

4*E^(2/5)*x^3

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fricas [A]  time = 0.71, size = 7, normalized size = 0.58 \begin {gather*} 4 \, x^{3} e^{\frac {2}{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(12*x^2*exp(2/5),x, algorithm="fricas")

[Out]

4*x^3*e^(2/5)

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giac [A]  time = 0.24, size = 7, normalized size = 0.58 \begin {gather*} 4 \, x^{3} e^{\frac {2}{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(12*x^2*exp(2/5),x, algorithm="giac")

[Out]

4*x^3*e^(2/5)

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maple [A]  time = 0.02, size = 8, normalized size = 0.67

method	result	size
gosper	\(4 x^{3} {\mathrm e}^{\frac {2}{5}}\)	\(8\)
default	\(4 x^{3} {\mathrm e}^{\frac {2}{5}}\)	\(8\)
norman	\(4 x^{3} {\mathrm e}^{\frac {2}{5}}\)	\(8\)
risch	\(4 x^{3} {\mathrm e}^{\frac {2}{5}}\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(12*x^2*exp(2/5),x,method=_RETURNVERBOSE)

[Out]

4*x^3*exp(2/5)

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maxima [A]  time = 0.42, size = 7, normalized size = 0.58 \begin {gather*} 4 \, x^{3} e^{\frac {2}{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(12*x^2*exp(2/5),x, algorithm="maxima")

[Out]

4*x^3*e^(2/5)

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mupad [B]  time = 0.02, size = 7, normalized size = 0.58 \begin {gather*} 4\,x^3\,{\mathrm {e}}^{2/5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(12*x^2*exp(2/5),x)

[Out]

4*x^3*exp(2/5)

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sympy [A]  time = 0.05, size = 8, normalized size = 0.67 \begin {gather*} 4 x^{3} e^{\frac {2}{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(12*x**2*exp(2/5),x)

[Out]

4*x**3*exp(2/5)

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