3.26.27 \(\int (7+e^{e^{18 x^2+24 x^3+8 x^4}+18 x^2+24 x^3+8 x^4} (36 x+72 x^2+32 x^3)) \, dx\)

Optimal. Leaf size=21 \[ 3+e^{e^{2 x^2 (3+2 x)^2}}+7 x \]

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Rubi [F]  time = 0.71, 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 \left (7+\exp \left (e^{18 x^2+24 x^3+8 x^4}+18 x^2+24 x^3+8 x^4\right ) \left (36 x+72 x^2+32 x^3\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[7 + E^(E^(18*x^2 + 24*x^3 + 8*x^4) + 18*x^2 + 24*x^3 + 8*x^4)*(36*x + 72*x^2 + 32*x^3),x]

[Out]

7*x + 36*Defer[Int][E^(E^(18*x^2 + 24*x^3 + 8*x^4) + 18*x^2 + 24*x^3 + 8*x^4)*x, x] + 72*Defer[Int][E^(E^(18*x
^2 + 24*x^3 + 8*x^4) + 18*x^2 + 24*x^3 + 8*x^4)*x^2, x] + 32*Defer[Int][E^(E^(18*x^2 + 24*x^3 + 8*x^4) + 18*x^
2 + 24*x^3 + 8*x^4)*x^3, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=7 x+\int \exp \left (e^{18 x^2+24 x^3+8 x^4}+18 x^2+24 x^3+8 x^4\right ) \left (36 x+72 x^2+32 x^3\right ) \, dx\\ &=7 x+\int \exp \left (e^{18 x^2+24 x^3+8 x^4}+18 x^2+24 x^3+8 x^4\right ) x \left (36+72 x+32 x^2\right ) \, dx\\ &=7 x+\int \left (36 \exp \left (e^{18 x^2+24 x^3+8 x^4}+18 x^2+24 x^3+8 x^4\right ) x+72 \exp \left (e^{18 x^2+24 x^3+8 x^4}+18 x^2+24 x^3+8 x^4\right ) x^2+32 \exp \left (e^{18 x^2+24 x^3+8 x^4}+18 x^2+24 x^3+8 x^4\right ) x^3\right ) \, dx\\ &=7 x+32 \int \exp \left (e^{18 x^2+24 x^3+8 x^4}+18 x^2+24 x^3+8 x^4\right ) x^3 \, dx+36 \int \exp \left (e^{18 x^2+24 x^3+8 x^4}+18 x^2+24 x^3+8 x^4\right ) x \, dx+72 \int \exp \left (e^{18 x^2+24 x^3+8 x^4}+18 x^2+24 x^3+8 x^4\right ) x^2 \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.26, size = 24, normalized size = 1.14 \begin {gather*} e^{e^{18 x^2+24 x^3+8 x^4}}+7 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[7 + E^(E^(18*x^2 + 24*x^3 + 8*x^4) + 18*x^2 + 24*x^3 + 8*x^4)*(36*x + 72*x^2 + 32*x^3),x]

[Out]

E^E^(18*x^2 + 24*x^3 + 8*x^4) + 7*x

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fricas [B]  time = 0.67, size = 73, normalized size = 3.48 \begin {gather*} {\left (7 \, x e^{\left (8 \, x^{4} + 24 \, x^{3} + 18 \, x^{2}\right )} + e^{\left (8 \, x^{4} + 24 \, x^{3} + 18 \, x^{2} + e^{\left (8 \, x^{4} + 24 \, x^{3} + 18 \, x^{2}\right )}\right )}\right )} e^{\left (-8 \, x^{4} - 24 \, x^{3} - 18 \, x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((32*x^3+72*x^2+36*x)*exp(4*x^4+12*x^3+9*x^2)^2*exp(exp(4*x^4+12*x^3+9*x^2)^2)+7,x, algorithm="fricas
")

[Out]

(7*x*e^(8*x^4 + 24*x^3 + 18*x^2) + e^(8*x^4 + 24*x^3 + 18*x^2 + e^(8*x^4 + 24*x^3 + 18*x^2)))*e^(-8*x^4 - 24*x
^3 - 18*x^2)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int 4 \, {\left (8 \, x^{3} + 18 \, x^{2} + 9 \, x\right )} e^{\left (8 \, x^{4} + 24 \, x^{3} + 18 \, x^{2} + e^{\left (8 \, x^{4} + 24 \, x^{3} + 18 \, x^{2}\right )}\right )} + 7\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((32*x^3+72*x^2+36*x)*exp(4*x^4+12*x^3+9*x^2)^2*exp(exp(4*x^4+12*x^3+9*x^2)^2)+7,x, algorithm="giac")

[Out]

integrate(4*(8*x^3 + 18*x^2 + 9*x)*e^(8*x^4 + 24*x^3 + 18*x^2 + e^(8*x^4 + 24*x^3 + 18*x^2)) + 7, x)

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maple [A]  time = 0.07, size = 19, normalized size = 0.90

method	result	size
risch	\(7 x +{\mathrm e}^{{\mathrm e}^{2 x^{2} \left (2 x +3\right )^{2}}}\)	\(19\)
default	\(7 x +{\mathrm e}^{{\mathrm e}^{8 x^{4}+24 x^{3}+18 x^{2}}}\)	\(25\)
norman	\(7 x +{\mathrm e}^{{\mathrm e}^{8 x^{4}+24 x^{3}+18 x^{2}}}\)	\(25\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((32*x^3+72*x^2+36*x)*exp(4*x^4+12*x^3+9*x^2)^2*exp(exp(4*x^4+12*x^3+9*x^2)^2)+7,x,method=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.56, size = 22, normalized size = 1.05 \begin {gather*} 7 \, x + e^{\left (e^{\left (8 \, x^{4} + 24 \, x^{3} + 18 \, x^{2}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((32*x^3+72*x^2+36*x)*exp(4*x^4+12*x^3+9*x^2)^2*exp(exp(4*x^4+12*x^3+9*x^2)^2)+7,x, algorithm="maxima
")

[Out]

7*x + e^(e^(8*x^4 + 24*x^3 + 18*x^2))

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mupad [B]  time = 1.50, size = 24, normalized size = 1.14 \begin {gather*} 7\,x+{\mathrm {e}}^{{\mathrm {e}}^{8\,x^4}\,{\mathrm {e}}^{18\,x^2}\,{\mathrm {e}}^{24\,x^3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(18*x^2 + 24*x^3 + 8*x^4)*exp(exp(18*x^2 + 24*x^3 + 8*x^4))*(36*x + 72*x^2 + 32*x^3) + 7,x)

[Out]

7*x + exp(exp(8*x^4)*exp(18*x^2)*exp(24*x^3))

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sympy [A]  time = 0.35, size = 20, normalized size = 0.95 \begin {gather*} 7 x + e^{e^{8 x^{4} + 24 x^{3} + 18 x^{2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((32*x**3+72*x**2+36*x)*exp(4*x**4+12*x**3+9*x**2)**2*exp(exp(4*x**4+12*x**3+9*x**2)**2)+7,x)

[Out]

7*x + exp(exp(8*x**4 + 24*x**3 + 18*x**2))

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