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

Optimal. Leaf size=21 \[ \text{Unintegrable}\left (\frac{e^{e (c+d x)^3}}{a+b x},x\right ) \]

[Out]

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

________________________________________________________________________________________

Rubi [A]  time = 0.0226154, 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 = {} \[ \int \frac{e^{e (c+d x)^3}}{a+b x} \, dx \]

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 steps

\begin{align*} \int \frac{e^{e (c+d x)^3}}{a+b x} \, dx &=\int \frac{e^{e (c+d x)^3}}{a+b x} \, dx\\ \end{align*}

Mathematica [A]  time = 0.384807, 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 = 0.044, size = 0, normalized size = 0. \begin{align*} \int{\frac{{{\rm e}^{e \left ( dx+c \right ) ^{3}}}}{bx+a}}\, dx \end{align*}

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. \begin{align*} \int \frac{e^{\left ({\left (d x + c\right )}^{3} e\right )}}{b x + a}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(e*(d*x+c)^3)/(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. \begin{align*}{\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 ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(e*(d*x+c)^3)/(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 [A]  time = 0., size = 0, normalized size = 0. \begin{align*} e^{c^{3} e} \int \frac{e^{d^{3} e x^{3}} e^{3 c d^{2} e x^{2}} e^{3 c^{2} d e x}}{a + b x}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(c**3*e)*Integral(exp(d**3*e*x**3)*exp(3*c*d**2*e*x**2)*exp(3*c**2*d*e*x)/(a + b*x), x)

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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