\(\int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx\) [214]

Optimal result

Integrand size = 33, antiderivative size = 33 \[ \int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx=\text {Int}\left (e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m,x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.06 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx=\int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx \]

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

Mathematica [N/A]

Not integrable

Time = 0.12 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.06 \[ \int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx=\int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx \]

[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]

Maple [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.97

\[\int {\mathrm e}^{b^{3} x^{3}+3 a \,b^{2} x^{2}+3 a^{2} b x +a^{3}} x^{m}d x\]

[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)

Fricas [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.03 \[ \int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx=\int { x^{m} e^{\left (b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right )} \,d x } \]

[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)

Sympy [N/A]

Not integrable

Time = 92.00 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.18 \[ \int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx=e^{a^{3}} \int x^{m} e^{b^{3} x^{3}} e^{3 a b^{2} x^{2}} e^{3 a^{2} b x}\, dx \]

[In]

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

[Out]

exp(a**3)*Integral(x**m*exp(b**3*x**3)*exp(3*a*b**2*x**2)*exp(3*a**2*b*x), x)

Maxima [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.03 \[ \int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx=\int { x^{m} e^{\left (b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right )} \,d x } \]

[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)

Giac [N/A]

Not integrable

Time = 0.33 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.03 \[ \int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx=\int { x^{m} e^{\left (b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right )} \,d x } \]

[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)

Mupad [N/A]

Not integrable

Time = 0.16 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.03 \[ \int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx=\int x^m\,{\mathrm {e}}^{a^3+3\,a^2\,b\,x+3\,a\,b^2\,x^2+b^3\,x^3} \,d x \]

[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)