\(\int \frac {e^{\frac {e}{(c+d x)^2}}}{(a+b x)^2} \, dx\) [414]

Optimal result

Integrand size = 19, antiderivative size = 19 \[ \int \frac {e^{\frac {e}{(c+d x)^2}}}{(a+b x)^2} \, dx=\text {Int}\left (\frac {e^{\frac {e}{(c+d x)^2}}}{(a+b x)^2},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.04 (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 = {} \[ \int \frac {e^{\frac {e}{(c+d x)^2}}}{(a+b x)^2} \, dx=\int \frac {e^{\frac {e}{(c+d x)^2}}}{(a+b x)^2} \, dx \]

[In]

Int[E^(e/(c + d*x)^2)/(a + b*x)^2,x]

[Out]

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

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

Mathematica [N/A]

Not integrable

Time = 0.16 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.11 \[ \int \frac {e^{\frac {e}{(c+d x)^2}}}{(a+b x)^2} \, dx=\int \frac {e^{\frac {e}{(c+d x)^2}}}{(a+b x)^2} \, dx \]

[In]

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

[Out]

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

Maple [N/A]

Not integrable

Time = 0.04 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95

\[\int \frac {{\mathrm e}^{\frac {e}{\left (d x +c \right )^{2}}}}{\left (b x +a \right )^{2}}d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.29 (sec) , antiderivative size = 42, normalized size of antiderivative = 2.21 \[ \int \frac {e^{\frac {e}{(c+d x)^2}}}{(a+b x)^2} \, dx=\int { \frac {e^{\left (\frac {e}{{\left (d x + c\right )}^{2}}\right )}}{{\left (b x + a\right )}^{2}} \,d x } \]

[In]

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

[Out]

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

Sympy [N/A]

Not integrable

Time = 16.22 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.42 \[ \int \frac {e^{\frac {e}{(c+d x)^2}}}{(a+b x)^2} \, dx=\int \frac {e^{\frac {e}{c^{2} + 2 c d x + d^{2} x^{2}}}}{\left (a + b x\right )^{2}}\, dx \]

[In]

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

[Out]

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

Maxima [N/A]

Not integrable

Time = 0.29 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{\frac {e}{(c+d x)^2}}}{(a+b x)^2} \, dx=\int { \frac {e^{\left (\frac {e}{{\left (d x + c\right )}^{2}}\right )}}{{\left (b x + a\right )}^{2}} \,d x } \]

[In]

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

[Out]

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

Giac [N/A]

Not integrable

Time = 0.35 (sec) , antiderivative size = 1, normalized size of antiderivative = 0.05 \[ \int \frac {e^{\frac {e}{(c+d x)^2}}}{(a+b x)^2} \, dx=\int { \frac {e^{\left (\frac {e}{{\left (d x + c\right )}^{2}}\right )}}{{\left (b x + a\right )}^{2}} \,d x } \]

[In]

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

[Out]

undef

Mupad [N/A]

Not integrable

Time = 0.83 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{\frac {e}{(c+d x)^2}}}{(a+b x)^2} \, dx=\int \frac {{\mathrm {e}}^{\frac {e}{{\left (c+d\,x\right )}^2}}}{{\left (a+b\,x\right )}^2} \,d x \]

[In]

int(exp(e/(c + d*x)^2)/(a + b*x)^2,x)

[Out]

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