\(\int \frac {e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3}}{x} \, dx\) [213]

Optimal result

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

[Out]

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

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 = {} \[ \int \frac {e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3}}{x} \, dx=\int \frac {e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3}}{x} \, dx \]

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

Mathematica [N/A]

Not integrable

Time = 0.38 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.06 \[ \int \frac {e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3}}{x} \, dx=\int \frac {e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3}}{x} \, dx \]

[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]

Maple [N/A]

Not integrable

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

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

[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)

Fricas [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.03 \[ \int \frac {e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3}}{x} \, dx=\int { \frac {e^{\left (b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right )}}{x} \,d x } \]

[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)

Sympy [N/A]

Not integrable

Time = 9.14 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.12 \[ \int \frac {e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3}}{x} \, dx=e^{a^{3}} \int \frac {e^{b^{3} x^{3}} e^{3 a b^{2} x^{2}} e^{3 a^{2} b x}}{x}\, dx \]

[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)

Maxima [N/A]

Not integrable

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

[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)

Giac [N/A]

Not integrable

Time = 0.34 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.03 \[ \int \frac {e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3}}{x} \, dx=\int { \frac {e^{\left (b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right )}}{x} \,d x } \]

[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)

Mupad [N/A]

Not integrable

Time = 0.13 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.03 \[ \int \frac {e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3}}{x} \, dx=\int \frac {{\mathrm {e}}^{a^3+3\,a^2\,b\,x+3\,a\,b^2\,x^2+b^3\,x^3}}{x} \,d x \]

[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)