3.70.60 \(\int (-1+e^{6 e^{3 x+3 x^2}+3 x+3 x^2} (18+36 x)) \, dx\)

Optimal. Leaf size=18 \[ 4+e^{6 e^{x (3+3 x)}}-x \]

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Rubi [F]  time = 0.48, 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 (-1+e^{6 e^{3 x+3 x^2}+3 x+3 x^2} (18+36 x)\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[-1 + E^(6*E^(3*x + 3*x^2) + 3*x + 3*x^2)*(18 + 36*x),x]

[Out]

-x + 18*Defer[Int][E^(3*(2*E^(3*x*(1 + x)) + x + x^2)), x] + 36*Defer[Int][E^(3*(2*E^(3*x*(1 + x)) + x + x^2))
*x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-x+\int e^{6 e^{3 x+3 x^2}+3 x+3 x^2} (18+36 x) \, dx\\ &=-x+\int e^{3 \left (2 e^{3 x (1+x)}+x+x^2\right )} (18+36 x) \, dx\\ &=-x+\int \left (18 e^{3 \left (2 e^{3 x (1+x)}+x+x^2\right )}+36 e^{3 \left (2 e^{3 x (1+x)}+x+x^2\right )} x\right ) \, dx\\ &=-x+18 \int e^{3 \left (2 e^{3 x (1+x)}+x+x^2\right )} \, dx+36 \int e^{3 \left (2 e^{3 x (1+x)}+x+x^2\right )} x \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.12, size = 19, normalized size = 1.06 \begin {gather*} e^{6 e^{3 x+3 x^2}}-x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 + E^(6*E^(3*x + 3*x^2) + 3*x + 3*x^2)*(18 + 36*x),x]

[Out]

E^(6*E^(3*x + 3*x^2)) - x

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fricas [B]  time = 0.66, size = 49, normalized size = 2.72 \begin {gather*} -{\left (x e^{\left (3 \, x^{2} + 3 \, x\right )} - e^{\left (3 \, x^{2} + 3 \, x + 6 \, e^{\left (3 \, x^{2} + 3 \, x\right )}\right )}\right )} e^{\left (-3 \, x^{2} - 3 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((36*x+18)*exp(3*x^2+3*x)*exp(6*exp(3*x^2+3*x))-1,x, algorithm="fricas")

[Out]

-(x*e^(3*x^2 + 3*x) - e^(3*x^2 + 3*x + 6*e^(3*x^2 + 3*x)))*e^(-3*x^2 - 3*x)

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giac [A]  time = 0.22, size = 17, normalized size = 0.94 \begin {gather*} -x + e^{\left (6 \, e^{\left (3 \, x^{2} + 3 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((36*x+18)*exp(3*x^2+3*x)*exp(6*exp(3*x^2+3*x))-1,x, algorithm="giac")

[Out]

-x + e^(6*e^(3*x^2 + 3*x))

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maple [A]  time = 0.04, size = 15, normalized size = 0.83

method	result	size
risch	\(-x +{\mathrm e}^{6 \,{\mathrm e}^{3 \left (x +1\right ) x}}\)	\(15\)
default	\(-x +{\mathrm e}^{6 \,{\mathrm e}^{3 x^{2}+3 x}}\)	\(18\)
norman	\(-x +{\mathrm e}^{6 \,{\mathrm e}^{3 x^{2}+3 x}}\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((36*x+18)*exp(3*x^2+3*x)*exp(6*exp(3*x^2+3*x))-1,x,method=_RETURNVERBOSE)

[Out]

-x+exp(6*exp(3*(x+1)*x))

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maxima [A]  time = 0.57, size = 17, normalized size = 0.94 \begin {gather*} -x + e^{\left (6 \, e^{\left (3 \, x^{2} + 3 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((36*x+18)*exp(3*x^2+3*x)*exp(6*exp(3*x^2+3*x))-1,x, algorithm="maxima")

[Out]

-x + e^(6*e^(3*x^2 + 3*x))

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mupad [B]  time = 0.10, size = 17, normalized size = 0.94 \begin {gather*} {\mathrm {e}}^{6\,{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{3\,x^2}}-x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(6*exp(3*x + 3*x^2))*exp(3*x + 3*x^2)*(36*x + 18) - 1,x)

[Out]

exp(6*exp(3*x)*exp(3*x^2)) - x

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sympy [A]  time = 0.27, size = 14, normalized size = 0.78 \begin {gather*} - x + e^{6 e^{3 x^{2} + 3 x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((36*x+18)*exp(3*x**2+3*x)*exp(6*exp(3*x**2+3*x))-1,x)

[Out]

-x + exp(6*exp(3*x**2 + 3*x))

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