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(exp(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)/x,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 = {} \[ \int \frac {e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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]

Rubi steps

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

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Mathematica [A]  time = 0.24, size = 0, normalized size = 0.00 \[ \int \frac {e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3}}{x} \, dx \]

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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fricas [A]  time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {e^{\left (b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right )}}{x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(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)

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maple [A]  time = 0.03, size = 0, normalized size = 0.00 \[ \int \frac {{\mathrm e}^{b^{3} x^{3}+3 a \,b^{2} x^{2}+3 a^{2} b x +a^{3}}}{x}\, dx \]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ e^{a^{3}} \int \frac {e^{b^{3} x^{3}} e^{3 a b^{2} x^{2}} e^{3 a^{2} b x}}{x}\, dx \]

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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