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

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

[Out]

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

_______________________________________________________________________________________

Rubi [A]  time = 0.0372409, 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. \[ \text{Int}\left (\frac{e^{\frac{e}{(c+d x)^2}}}{a+b x},x\right ) \]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(e/(d*x+c)**2)/(b*x+a),x)

[Out]

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

_______________________________________________________________________________________

Mathematica [A]  time = 0.0335861, size = 0, normalized size = 0. \[ \int \frac{e^{\frac{e}{(c+d x)^2}}}{a+b x} \, dx \]

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]

_______________________________________________________________________________________

Maple [A]  time = 0.072, size = 0, normalized size = 0. \[ \int{\frac{1}{bx+a}{{\rm e}^{{\frac{e}{ \left ( dx+c \right ) ^{2}}}}}}\, dx \]

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)

_______________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^(e/(d*x + c)^2)/(b*x + a),x, algorithm="maxima")

[Out]

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

_______________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^(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)

_______________________________________________________________________________________

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

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)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{\left (\frac{e}{{\left (d x + c\right )}^{2}}\right )}}{b x + a}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^(e/(d*x + c)^2)/(b*x + a),x, algorithm="giac")

[Out]

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