\(\int (3+3 e^{x^2} x) \, dx\) [6497]

Optimal result

Integrand size = 10, antiderivative size = 13 \[ \int \left (3+3 e^{x^2} x\right ) \, dx=3 \left (\frac {e^{x^2}}{2}+x\right ) \]

[Out]

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

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2240} \[ \int \left (3+3 e^{x^2} x\right ) \, dx=\frac {3 e^{x^2}}{2}+3 x \]

[In]

Int[3 + 3*E^x^2*x,x]

[Out]

(3*E^x^2)/2 + 3*x

Rule 2240

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{align*} \text {integral}& = 3 x+3 \int e^{x^2} x \, dx \\ & = \frac {3 e^{x^2}}{2}+3 x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \left (3+3 e^{x^2} x\right ) \, dx=\frac {3 e^{x^2}}{2}+3 x \]

[In]

Integrate[3 + 3*E^x^2*x,x]

[Out]

(3*E^x^2)/2 + 3*x

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 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	\(\frac {3 \,{\mathrm e}^{x^{2}}}{2}+3 x\)	\(11\)
parallelrisch	\(\frac {3 \,{\mathrm e}^{x^{2}}}{2}+3 x\)	\(11\)
parts	\(\frac {3 \,{\mathrm e}^{x^{2}}}{2}+3 x\)	\(11\)

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \left (3+3 e^{x^2} x\right ) \, dx=3 \, x + \frac {3}{2} \, e^{\left (x^{2}\right )} \]

[In]

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

[Out]

3*x + 3/2*e^(x^2)

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \left (3+3 e^{x^2} x\right ) \, dx=3 x + \frac {3 e^{x^{2}}}{2} \]

[In]

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

[Out]

3*x + 3*exp(x**2)/2

Maxima [A] (verification not implemented)

none

Time = 0.17 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \left (3+3 e^{x^2} x\right ) \, dx=3 \, x + \frac {3}{2} \, e^{\left (x^{2}\right )} \]

[In]

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

[Out]

3*x + 3/2*e^(x^2)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \left (3+3 e^{x^2} x\right ) \, dx=3 \, x + \frac {3}{2} \, e^{\left (x^{2}\right )} \]

[In]

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

[Out]

3*x + 3/2*e^(x^2)

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \left (3+3 e^{x^2} x\right ) \, dx=3\,x+\frac {3\,{\mathrm {e}}^{x^2}}{2} \]

[In]

int(3*x*exp(x^2) + 3,x)

[Out]

3*x + (3*exp(x^2))/2