\(\int e^{e^{x+x^2+4 x^3}+x+x^2+4 x^3} (3+6 x+36 x^2) \, dx\) [7575]

Optimal result

Integrand size = 35, antiderivative size = 17 \[ \int e^{e^{x+x^2+4 x^3}+x+x^2+4 x^3} \left (3+6 x+36 x^2\right ) \, dx=3 e^{e^{x+x \left (x+4 x^2\right )}} \]

[Out]

3*exp(exp(x+x*(4*x^2+x)))

Rubi [F]

\[ \int e^{e^{x+x^2+4 x^3}+x+x^2+4 x^3} \left (3+6 x+36 x^2\right ) \, dx=\int e^{e^{x+x^2+4 x^3}+x+x^2+4 x^3} \left (3+6 x+36 x^2\right ) \, dx \]

[In]

Int[E^(E^(x + x^2 + 4*x^3) + x + x^2 + 4*x^3)*(3 + 6*x + 36*x^2),x]

[Out]

3*Defer[Int][E^(E^(x + x^2 + 4*x^3) + x + x^2 + 4*x^3), x] + 6*Defer[Int][E^(E^(x + x^2 + 4*x^3) + x + x^2 + 4
*x^3)*x, x] + 36*Defer[Int][E^(E^(x + x^2 + 4*x^3) + x + x^2 + 4*x^3)*x^2, x]

Rubi steps \begin{align*} \text {integral}& = \int \left (3 e^{e^{x+x^2+4 x^3}+x+x^2+4 x^3}+6 e^{e^{x+x^2+4 x^3}+x+x^2+4 x^3} x+36 e^{e^{x+x^2+4 x^3}+x+x^2+4 x^3} x^2\right ) \, dx \\ & = 3 \int e^{e^{x+x^2+4 x^3}+x+x^2+4 x^3} \, dx+6 \int e^{e^{x+x^2+4 x^3}+x+x^2+4 x^3} x \, dx+36 \int e^{e^{x+x^2+4 x^3}+x+x^2+4 x^3} x^2 \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.59 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.94 \[ \int e^{e^{x+x^2+4 x^3}+x+x^2+4 x^3} \left (3+6 x+36 x^2\right ) \, dx=3 e^{e^{x+x^2+4 x^3}} \]

[In]

Integrate[E^(E^(x + x^2 + 4*x^3) + x + x^2 + 4*x^3)*(3 + 6*x + 36*x^2),x]

[Out]

3*E^E^(x + x^2 + 4*x^3)

Maple [A] (verified)

Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88

method	result	size
default	\(3 \,{\mathrm e}^{{\mathrm e}^{4 x^{3}+x^{2}+x}}\)	\(15\)
norman	\(3 \,{\mathrm e}^{{\mathrm e}^{4 x^{3}+x^{2}+x}}\)	\(15\)
risch	\(3 \,{\mathrm e}^{{\mathrm e}^{x \left (4 x^{2}+x +1\right )}}\)	\(15\)
parallelrisch	\(3 \,{\mathrm e}^{{\mathrm e}^{4 x^{3}+x^{2}+x}}\)	\(15\)

[In]

int((36*x^2+6*x+3)*exp(4*x^3+x^2+x)*exp(exp(4*x^3+x^2+x)),x,method=_RETURNVERBOSE)

[Out]

3*exp(exp(4*x^3+x^2+x))

Fricas [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int e^{e^{x+x^2+4 x^3}+x+x^2+4 x^3} \left (3+6 x+36 x^2\right ) \, dx=3 \, e^{\left (e^{\left (4 \, x^{3} + x^{2} + x\right )}\right )} \]

[In]

integrate((36*x^2+6*x+3)*exp(4*x^3+x^2+x)*exp(exp(4*x^3+x^2+x)),x, algorithm="fricas")

[Out]

3*e^(e^(4*x^3 + x^2 + x))

Sympy [A] (verification not implemented)

Time = 0.09 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int e^{e^{x+x^2+4 x^3}+x+x^2+4 x^3} \left (3+6 x+36 x^2\right ) \, dx=3 e^{e^{4 x^{3} + x^{2} + x}} \]

[In]

integrate((36*x**2+6*x+3)*exp(4*x**3+x**2+x)*exp(exp(4*x**3+x**2+x)),x)

[Out]

3*exp(exp(4*x**3 + x**2 + x))

Maxima [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int e^{e^{x+x^2+4 x^3}+x+x^2+4 x^3} \left (3+6 x+36 x^2\right ) \, dx=3 \, e^{\left (e^{\left (4 \, x^{3} + x^{2} + x\right )}\right )} \]

[In]

integrate((36*x^2+6*x+3)*exp(4*x^3+x^2+x)*exp(exp(4*x^3+x^2+x)),x, algorithm="maxima")

[Out]

3*e^(e^(4*x^3 + x^2 + x))

Giac [F]

\[ \int e^{e^{x+x^2+4 x^3}+x+x^2+4 x^3} \left (3+6 x+36 x^2\right ) \, dx=\int { 3 \, {\left (12 \, x^{2} + 2 \, x + 1\right )} e^{\left (4 \, x^{3} + x^{2} + x + e^{\left (4 \, x^{3} + x^{2} + x\right )}\right )} \,d x } \]

[In]

integrate((36*x^2+6*x+3)*exp(4*x^3+x^2+x)*exp(exp(4*x^3+x^2+x)),x, algorithm="giac")

[Out]

integrate(3*(12*x^2 + 2*x + 1)*e^(4*x^3 + x^2 + x + e^(4*x^3 + x^2 + x)), x)

Mupad [B] (verification not implemented)

Time = 13.14 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int e^{e^{x+x^2+4 x^3}+x+x^2+4 x^3} \left (3+6 x+36 x^2\right ) \, dx=3\,{\mathrm {e}}^{{\mathrm {e}}^{4\,x^3+x^2+x}} \]

[In]

int(exp(x + x^2 + 4*x^3)*exp(exp(x + x^2 + 4*x^3))*(6*x + 36*x^2 + 3),x)

[Out]

3*exp(exp(x + x^2 + 4*x^3))