3.5.13 \(\int \frac {e^{\frac {e}{(c+d x)^2}}}{a+b x} \, dx\) [413]

Optimal. Leaf size=22 \[ \text {Int}\left (\frac {e^{\frac {e}{(c+d x)^2}}}{a+b x},x\right ) \]

[Out]

Unintegrable(exp(e/(d*x+c)^2)/(b*x+a),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^{\frac {e}{(c+d x)^2}}}{a+b x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(e/(c + d*x)^2)/(a + b*x),x]

[Out]

Defer[Int][E^(e/(c + d*x)^2)/(a + b*x), x]

Rubi steps

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

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Mathematica [A]
time = 0.03, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{\frac {e}{(c+d x)^2}}}{a+b x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[E^(e/(c + d*x)^2)/(a + b*x),x]

[Out]

Integrate[E^(e/(c + d*x)^2)/(a + b*x), x]

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Maple [A]
time = 0.03, size = 0, normalized size = 0.00 \[\int \frac {{\mathrm e}^{\frac {e}{\left (d x +c \right )^{2}}}}{b x +a}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(exp(e/(d*x+c)^2)/(b*x+a),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(e/(d*x+c)^2)/(b*x+a),x, algorithm="maxima")

[Out]

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

[Out]

integral(e^(e/(d^2*x^2 + 2*c*d*x + c^2))/(b*x + a), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(exp(e/(c**2 + 2*c*d*x + d**2*x**2))/(a + b*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(e/(d*x+c)^2)/(b*x+a),x, algorithm="giac")

[Out]

integrate(e^(e/(d*x + c)^2)/(b*x + a), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(e/(c + d*x)^2)/(a + b*x),x)

[Out]

int(exp(e/(c + d*x)^2)/(a + b*x), x)

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