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

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

[Out]

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

________________________________________________________________________________________

Rubi [A]
time = 0.04, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {e^{\frac {e}{(c+d x)^2}}}{(a+b x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[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*} \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\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]
time = 0.16, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{\frac {e}{(c+d x)^2}}}{(a+b x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[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 [A]
time = 0.03, size = 0, normalized size = 0.00 \[\int \frac {{\mathrm e}^{\frac {e}{\left (d x +c \right )^{2}}}}{\left (b x +a \right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[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)

________________________________________________________________________________________

Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

________________________________________________________________________________________

Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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 [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{\frac {e}{c^{2} + 2 c d x + d^{2} x^{2}}}}{\left (a + b x\right )^{2}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

________________________________________________________________________________________

Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

undef

________________________________________________________________________________________

Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {{\mathrm {e}}^{\frac {e}{{\left (c+d\,x\right )}^2}}}{{\left (a+b\,x\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

________________________________________________________________________________________