\(\int (3 x^2+3 e^{3-x^3} x^2) \, dx\) [7342]

Optimal result

Integrand size = 20, antiderivative size = 21 \[ \int \left (3 x^2+3 e^{3-x^3} x^2\right ) \, dx=-3+e^6-e^{3-x^3}+x^3+\log (5) \]

[Out]

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

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.71, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {2240} \[ \int \left (3 x^2+3 e^{3-x^3} x^2\right ) \, dx=x^3-e^{3-x^3} \]

[In]

Int[3*x^2 + 3*E^(3 - x^3)*x^2,x]

[Out]

-E^(3 - x^3) + x^3

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

Mathematica [A] (verified)

Time = 0.04 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.33 \[ \int \left (3 x^2+3 e^{3-x^3} x^2\right ) \, dx=3 \left (-\frac {1}{3} e^{3-x^3}-\frac {1}{3} \log \left (e^{-x^3}\right )\right ) \]

[In]

Integrate[3*x^2 + 3*E^(3 - x^3)*x^2,x]

[Out]

3*(-1/3*E^(3 - x^3) - Log[E^(-x^3)]/3)

Maple [A] (verified)

Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.71

method	result	size
default	\(x^{3}-{\mathrm e}^{-x^{3}+3}\)	\(15\)
norman	\(x^{3}-{\mathrm e}^{-x^{3}+3}\)	\(15\)
risch	\(x^{3}-{\mathrm e}^{-x^{3}+3}\)	\(15\)
parallelrisch	\(x^{3}-{\mathrm e}^{-x^{3}+3}\)	\(15\)
parts	\(x^{3}-{\mathrm e}^{-x^{3}+3}\)	\(15\)

[In]

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

[Out]

x^3-exp(-x^3+3)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.67 \[ \int \left (3 x^2+3 e^{3-x^3} x^2\right ) \, dx=x^{3} - e^{\left (-x^{3} + 3\right )} \]

[In]

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

[Out]

x^3 - e^(-x^3 + 3)

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.38 \[ \int \left (3 x^2+3 e^{3-x^3} x^2\right ) \, dx=x^{3} - e^{3 - x^{3}} \]

[In]

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

[Out]

x**3 - exp(3 - x**3)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.67 \[ \int \left (3 x^2+3 e^{3-x^3} x^2\right ) \, dx=x^{3} - e^{\left (-x^{3} + 3\right )} \]

[In]

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

[Out]

x^3 - e^(-x^3 + 3)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.67 \[ \int \left (3 x^2+3 e^{3-x^3} x^2\right ) \, dx=x^{3} - e^{\left (-x^{3} + 3\right )} \]

[In]

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

[Out]

x^3 - e^(-x^3 + 3)

Mupad [B] (verification not implemented)

Time = 14.31 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.67 \[ \int \left (3 x^2+3 e^{3-x^3} x^2\right ) \, dx=x^3-{\mathrm {e}}^{3-x^3} \]

[In]

int(3*x^2*exp(3 - x^3) + 3*x^2,x)

[Out]

x^3 - exp(3 - x^3)