\(\int \frac {e^{e (c+d x)^3}}{a+b x} \, dx\) [395]

Optimal result

Integrand size = 19, antiderivative size = 19 \[ \int \frac {e^{e (c+d x)^3}}{a+b x} \, dx=\text {Int}\left (\frac {e^{e (c+d x)^3}}{a+b x},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {e^{e (c+d x)^3}}{a+b x} \, dx=\int \frac {e^{e (c+d x)^3}}{a+b x} \, dx \]

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

Mathematica [N/A]

Not integrable

Time = 0.50 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.11 \[ \int \frac {e^{e (c+d x)^3}}{a+b x} \, dx=\int \frac {e^{e (c+d x)^3}}{a+b x} \, dx \]

[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 [N/A]

Not integrable

Time = 0.03 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95

\[\int \frac {{\mathrm e}^{e \left (d x +c \right )^{3}}}{b x +a}d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.28 (sec) , antiderivative size = 43, normalized size of antiderivative = 2.26 \[ \int \frac {e^{e (c+d x)^3}}{a+b x} \, dx=\int { \frac {e^{\left ({\left (d x + c\right )}^{3} e\right )}}{b x + a} \,d x } \]

[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 [N/A]

Not integrable

Time = 54.79 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.53 \[ \int \frac {e^{e (c+d x)^3}}{a+b x} \, dx=e^{c^{3} e} \int \frac {e^{d^{3} e x^{3}} e^{3 c d^{2} e x^{2}} e^{3 c^{2} d e x}}{a + b x}\, dx \]

[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)

Maxima [N/A]

Not integrable

Time = 0.32 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{e (c+d x)^3}}{a+b x} \, dx=\int { \frac {e^{\left ({\left (d x + c\right )}^{3} e\right )}}{b x + a} \,d x } \]

[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)

Giac [N/A]

Not integrable

Time = 0.37 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{e (c+d x)^3}}{a+b x} \, dx=\int { \frac {e^{\left ({\left (d x + c\right )}^{3} e\right )}}{b x + a} \,d x } \]

[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)

Mupad [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{e (c+d x)^3}}{a+b x} \, dx=\int \frac {{\mathrm {e}}^{e\,{\left (c+d\,x\right )}^3}}{a+b\,x} \,d x \]

[In]

int(exp(e*(c + d*x)^3)/(a + b*x),x)

[Out]

int(exp(e*(c + d*x)^3)/(a + b*x), x)