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

Optimal. Leaf size=17 \[ 3 e^{e^{x+x \left (x+4 x^2\right )}} \]

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Rubi [F]  time = 0.41, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int e^{e^{x+x^2+4 x^3}+x+x^2+4 x^3} \left (3+6 x+36 x^2\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[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 {gather*} \begin {aligned} \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 {aligned} \end {gather*}

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Mathematica [A]  time = 0.25, size = 16, normalized size = 0.94 \begin {gather*} 3 e^{e^{x+x^2+4 x^3}} \end {gather*}

Antiderivative was successfully verified.

[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)

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fricas [A]  time = 0.61, size = 14, normalized size = 0.82 \begin {gather*} 3 \, e^{\left (e^{\left (4 \, x^{3} + x^{2} + x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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maple [A]  time = 0.02, size = 15, normalized size = 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	\(3 \,{\mathrm e}^{{\mathrm e}^{x \left (4 x^{2}+x +1\right )}}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[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))

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maxima [A]  time = 0.59, size = 14, normalized size = 0.82 \begin {gather*} 3 \, e^{\left (e^{\left (4 \, x^{3} + x^{2} + x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))

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mupad [B]  time = 4.60, size = 14, normalized size = 0.82 \begin {gather*} 3\,{\mathrm {e}}^{{\mathrm {e}}^{4\,x^3+x^2+x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))

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sympy [A]  time = 0.30, size = 14, normalized size = 0.82 \begin {gather*} 3 e^{e^{4 x^{3} + x^{2} + x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))

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