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

Optimal. Leaf size=20 \[ \text {Int}\left (\frac {e^{a+b x-c x^2}}{x},x\right ) \]

[Out]

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

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Rubi [A]
time = 0.02, 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 = {} \begin {gather*} \int \frac {e^{a+b x-c x^2}}{x} \, dx \end {gather*}

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*}

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Mathematica [A]
time = 0.19, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{a+b x-c x^2}}{x} \, dx \end {gather*}

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 = 0.01, size = 0, normalized size = 0.00 \[\int \frac {{\mathrm e}^{-c \,x^{2}+b x +a}}{x}\, dx\]

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} e^{a} \int \frac {e^{b x} e^{- c x^{2}}}{x}\, dx \end {gather*}

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {{\mathrm {e}}^{-c\,x^2+b\,x+a}}{x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(a + b*x - c*x^2)/x,x)

[Out]

int(exp(a + b*x - c*x^2)/x, x)

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