\(\int \frac {e^{a+b x-c x^2}}{x} \, dx\) [436]

Optimal result

Integrand size = 17, antiderivative size = 17 \[ \int \frac {e^{a+b x-c x^2}}{x} \, dx=\text {Int}\left (\frac {e^{a+b x-c x^2}}{x},x\right ) \]

[Out]

Unintegrable(exp(-c*x^2+b*x+a)/x,x)

Rubi [N/A]

Not integrable

Time = 0.02 (sec) , antiderivative size = 17, 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 = {} \[ \int \frac {e^{a+b x-c x^2}}{x} \, dx=\int \frac {e^{a+b x-c x^2}}{x} \, dx \]

[In]

Int[E^(a + b*x - c*x^2)/x,x]

[Out]

Defer[Int][E^(a + b*x - c*x^2)/x, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{a+b x-c x^2}}{x} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.17 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.12 \[ \int \frac {e^{a+b x-c x^2}}{x} \, dx=\int \frac {e^{a+b x-c x^2}}{x} \, dx \]

[In]

Integrate[E^(a + b*x - c*x^2)/x,x]

[Out]

Integrate[E^(a + b*x - c*x^2)/x, x]

Maple [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.94

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.31 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int \frac {e^{a+b x-c x^2}}{x} \, dx=\int { \frac {e^{\left (-c x^{2} + b x + a\right )}}{x} \,d x } \]

[In]

integrate(exp(-c*x^2+b*x+a)/x,x, algorithm="fricas")

[Out]

integral(e^(-c*x^2 + b*x + a)/x, x)

Sympy [N/A]

Not integrable

Time = 2.41 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \frac {e^{a+b x-c x^2}}{x} \, dx=e^{a} \int \frac {e^{b x} e^{- c x^{2}}}{x}\, dx \]

[In]

integrate(exp(-c*x**2+b*x+a)/x,x)

[Out]

exp(a)*Integral(exp(b*x)*exp(-c*x**2)/x, x)

Maxima [N/A]

Not integrable

Time = 0.29 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int \frac {e^{a+b x-c x^2}}{x} \, dx=\int { \frac {e^{\left (-c x^{2} + b x + a\right )}}{x} \,d x } \]

[In]

integrate(exp(-c*x^2+b*x+a)/x,x, algorithm="maxima")

[Out]

integrate(e^(-c*x^2 + b*x + a)/x, x)

Giac [N/A]

Not integrable

Time = 0.31 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int \frac {e^{a+b x-c x^2}}{x} \, dx=\int { \frac {e^{\left (-c x^{2} + b x + a\right )}}{x} \,d x } \]

[In]

integrate(exp(-c*x^2+b*x+a)/x,x, algorithm="giac")

[Out]

integrate(e^(-c*x^2 + b*x + a)/x, x)

Mupad [N/A]

Not integrable

Time = 0.22 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int \frac {e^{a+b x-c x^2}}{x} \, dx=\int \frac {{\mathrm {e}}^{-c\,x^2+b\,x+a}}{x} \,d x \]

[In]

int(exp(a + b*x - c*x^2)/x,x)

[Out]

int(exp(a + b*x - c*x^2)/x, x)