3.3.37 \(\int 2 e^{x^2} x \, dx\)

Optimal. Leaf size=7 \[ 10+e^{x^2} \]

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Rubi [A]  time = 0.01, antiderivative size = 5, normalized size of antiderivative = 0.71, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 2209} \begin {gather*} e^{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2*E^x^2*x,x]

[Out]

E^x^2

Rule 12

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

Rule 2209

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[((e + f*x)^n*
F^(a + b*(c + d*x)^n))/(b*f*n*(c + d*x)^n*Log[F]), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=2 \int e^{x^2} x \, dx\\ &=e^{x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 5, normalized size = 0.71 \begin {gather*} e^{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2*E^x^2*x,x]

[Out]

E^x^2

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fricas [A]  time = 0.61, size = 4, normalized size = 0.57 \begin {gather*} e^{\left (x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

e^(x^2)

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giac [A]  time = 0.25, size = 4, normalized size = 0.57 \begin {gather*} e^{\left (x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

e^(x^2)

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maple [A]  time = 0.06, size = 5, normalized size = 0.71

method	result	size
gosper	\({\mathrm e}^{x^{2}}\)	\(5\)
derivativedivides	\({\mathrm e}^{x^{2}}\)	\(5\)
default	\({\mathrm e}^{x^{2}}\)	\(5\)
norman	\({\mathrm e}^{x^{2}}\)	\(5\)
risch	\({\mathrm e}^{x^{2}}\)	\(5\)
meijerg	\({\mathrm e}^{x^{2}}-1\)	\(7\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(x^2)

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maxima [A]  time = 0.51, size = 4, normalized size = 0.57 \begin {gather*} e^{\left (x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

e^(x^2)

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mupad [B]  time = 0.02, size = 4, normalized size = 0.57 \begin {gather*} {\mathrm {e}}^{x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x*exp(x^2),x)

[Out]

exp(x^2)

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sympy [A]  time = 0.08, size = 3, normalized size = 0.43 \begin {gather*} e^{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(x**2)*x,x)

[Out]

exp(x**2)

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