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

Optimal. Leaf size=19 \[ \text{Unintegrable}\left (\frac{e^{a+b x-c x^2}}{x},x\right ) \]

[Out]

Unintegrable[E^(a + b*x - c*x^2)/x, x]

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Rubi [A]  time = 0.0276418, 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., Rules used = {} \[ \int \frac{e^{a+b x-c x^2}}{x} \, dx \]

Verification is Not applicable to the result.

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

Mathematica [A]  time = 0.120651, size = 0, normalized size = 0. \[ \int \frac{e^{a+b x-c x^2}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[E^(a + b*x - c*x^2)/x,x]

[Out]

Integrate[E^(a + b*x - c*x^2)/x, x]

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Maple [A]  time = 0.012, size = 0, normalized size = 0. \begin{align*} \int{\frac{{{\rm e}^{-c{x}^{2}+bx+a}}}{x}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(e^(-c*x^2 + b*x + a)/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(e^(-c*x^2 + b*x + a)/x, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} e^{a} \int \frac{e^{b x} e^{- c x^{2}}}{x}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{e^{\left (-c x^{2} + b x + a\right )}}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(e^(-c*x^2 + b*x + a)/x, x)