3.395 \(\int \frac{e^{e (c+d x)^3}}{a+b x} \, dx\)

Optimal. Leaf size=22 \[ \text{Int}\left (\frac{e^{e (c+d x)^3}}{a+b x},x\right ) \]

[Out]

Unintegrable[E^(e*(c + d*x)^3)/(a + b*x), x]

_______________________________________________________________________________________

Rubi [A]  time = 0.0350013, 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. \[ \text{Int}\left (\frac{e^{e (c+d x)^3}}{a+b x},x\right ) \]

Verification is Not applicable to the result.

[In]  Int[E^(e*(c + d*x)^3)/(a + b*x),x]

[Out]

Defer[Int][E^(e*(c + d*x)^3)/(a + b*x), x]

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{e \left (c + d x\right )^{3}}}{a + b x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(e*(d*x+c)**3)/(b*x+a),x)

[Out]

Integral(exp(e*(c + d*x)**3)/(a + b*x), x)

_______________________________________________________________________________________

Mathematica [A]  time = 0.583459, size = 0, normalized size = 0. \[ \int \frac{e^{e (c+d x)^3}}{a+b x} \, dx \]

Verification is Not applicable to the result.

[In]  Integrate[E^(e*(c + d*x)^3)/(a + b*x),x]

[Out]

Integrate[E^(e*(c + d*x)^3)/(a + b*x), x]

_______________________________________________________________________________________

Maple [A]  time = 0.052, size = 0, normalized size = 0. \[ \int{\frac{{{\rm e}^{e \left ( dx+c \right ) ^{3}}}}{bx+a}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(e*(d*x+c)^3)/(b*x+a),x)

[Out]

int(exp(e*(d*x+c)^3)/(b*x+a),x)

_______________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{\left ({\left (d x + c\right )}^{3} e\right )}}{b x + a}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^((d*x + c)^3*e)/(b*x + a),x, algorithm="maxima")

[Out]

integrate(e^((d*x + c)^3*e)/(b*x + a), x)

_______________________________________________________________________________________

Fricas [A]  time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{e^{\left (d^{3} e x^{3} + 3 \, c d^{2} e x^{2} + 3 \, c^{2} d e x + c^{3} e\right )}}{b x + a}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^((d*x + c)^3*e)/(b*x + a),x, algorithm="fricas")

[Out]

integral(e^(d^3*e*x^3 + 3*c*d^2*e*x^2 + 3*c^2*d*e*x + c^3*e)/(b*x + a), x)

_______________________________________________________________________________________

Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(e*(d*x+c)**3)/(b*x+a),x)

[Out]

Timed out

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{\left ({\left (d x + c\right )}^{3} e\right )}}{b x + a}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^((d*x + c)^3*e)/(b*x + a),x, algorithm="giac")

[Out]

integrate(e^((d*x + c)^3*e)/(b*x + a), x)