3.214 \(\int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx\)

Optimal. Leaf size=36 \[ \text {Int}\left (x^m e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3},x\right ) \]

[Out]

CannotIntegrate(exp(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)*x^m,x)

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Rubi [A]  time = 0.09, 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 = {} \[ \int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx \]

Verification is Not applicable to the result.

[In]

Int[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)*x^m,x]

[Out]

Defer[Int][E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)*x^m, x]

Rubi steps

\begin {align*} \int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx &=\int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx\\ \end {align*}

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Mathematica [A]  time = 0.19, size = 0, normalized size = 0.00 \[ \int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)*x^m,x]

[Out]

Integrate[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)*x^m, x]

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fricas [A]  time = 0.42, size = 0, normalized size = 0.00 \[ {\rm integral}\left (x^{m} e^{\left (b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right )}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)*x^m,x, algorithm="fricas")

[Out]

integral(x^m*e^(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3), x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int x^{m} e^{\left (b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right )}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)*x^m,x, algorithm="giac")

[Out]

integrate(x^m*e^(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3), x)

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maple [A]  time = 0.05, size = 0, normalized size = 0.00 \[ \int x^{m} {\mathrm e}^{b^{3} x^{3}+3 a \,b^{2} x^{2}+3 a^{2} b x +a^{3}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)*x^m,x)

[Out]

int(exp(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)*x^m,x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int x^{m} e^{\left (b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right )}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)*x^m,x, algorithm="maxima")

[Out]

integrate(x^m*e^(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.03 \[ \int x^m\,{\mathrm {e}}^{a^3+3\,a^2\,b\,x+3\,a\,b^2\,x^2+b^3\,x^3} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^m*exp(a^3 + b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x),x)

[Out]

int(x^m*exp(a^3 + b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x), x)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(b**3*x**3+3*a*b**2*x**2+3*a**2*b*x+a**3)*x**m,x)

[Out]

Timed out

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