3.65.97 \(\int (3+3 e^{x^2} x) \, dx\)

Optimal. Leaf size=13 \[ 3 \left (\frac {e^{x^2}}{2}+x\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2209} \begin {gather*} \frac {3 e^{x^2}}{2}+3 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[3 + 3*E^x^2*x,x]

[Out]

(3*E^x^2)/2 + 3*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} &=3 x+3 \int e^{x^2} x \, dx\\ &=\frac {3 e^{x^2}}{2}+3 x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {3 e^{x^2}}{2}+3 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3 + 3*E^x^2*x,x]

[Out]

(3*E^x^2)/2 + 3*x

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fricas [A]  time = 0.46, size = 10, normalized size = 0.77 \begin {gather*} 3 \, x + \frac {3}{2} \, e^{\left (x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3*x + 3/2*e^(x^2)

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giac [A]  time = 0.12, size = 10, normalized size = 0.77 \begin {gather*} 3 \, x + \frac {3}{2} \, e^{\left (x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3*x + 3/2*e^(x^2)

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maple [A]  time = 0.01, size = 11, normalized size = 0.85

method	result	size
default	\(\frac {3 \,{\mathrm e}^{x^{2}}}{2}+3 x\)	\(11\)
norman	\(\frac {3 \,{\mathrm e}^{x^{2}}}{2}+3 x\)	\(11\)
risch	\(\frac {3 \,{\mathrm e}^{x^{2}}}{2}+3 x\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3/2*exp(x^2)+3*x

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maxima [A]  time = 0.36, size = 10, normalized size = 0.77 \begin {gather*} 3 \, x + \frac {3}{2} \, e^{\left (x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3*x + 3/2*e^(x^2)

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mupad [B]  time = 0.04, size = 10, normalized size = 0.77 \begin {gather*} 3\,x+\frac {3\,{\mathrm {e}}^{x^2}}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*x*exp(x^2) + 3,x)

[Out]

3*x + (3*exp(x^2))/2

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sympy [A]  time = 0.07, size = 10, normalized size = 0.77 \begin {gather*} 3 x + \frac {3 e^{x^{2}}}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*exp(x**2)*x+3,x)

[Out]

3*x + 3*exp(x**2)/2

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