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

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

[Out]

CannotIntegrate[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)/x, x]

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Rubi [A]  time = 0.141259, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \text{Int}\left (\frac{e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3}}{x},x\right ) \]

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,x]

[Out]

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

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Rubi in Sympy [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(b**3*x**3+3*a*b**2*x**2+3*a**2*b*x+a**3)/x,x)

[Out]

Integral(exp(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3)/x, x)

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Mathematica [A]  time = 0.326581, size = 0, normalized size = 0. \[ \int \frac{e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3}}{x} \, dx \]

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,x]

[Out]

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

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Maple [A]  time = 0.021, size = 0, normalized size = 0. \[ \int{\frac{{{\rm e}^{{b}^{3}{x}^{3}+3\,a{b}^{2}{x}^{2}+3\,{a}^{2}bx+{a}^{3}}}}{x}}\, dx \]

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,x)

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)/x,x, algorithm="maxima")

[Out]

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

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Fricas [A]  time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{e^{\left (b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right )}}{x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)/x,x, algorithm="fricas")

[Out]

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

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Sympy [A]  time = 0., size = 0, normalized size = 0. \[ e^{a^{3}} \int \frac{e^{b^{3} x^{3}} e^{3 a b^{2} x^{2}} e^{3 a^{2} b x}}{x}\, dx \]

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,x)

[Out]

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

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GIAC/XCAS [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{\left (b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right )}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)/x,x, algorithm="giac")

[Out]

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