3.421 \(\int \frac {e^{\frac {e}{(c+d x)^3}}}{(a+b x)^2} \, dx\)

Optimal. Leaf size=22 \[ \text {Int}\left (\frac {e^{\frac {e}{(c+d x)^3}}}{(a+b x)^2},x\right ) \]

[Out]

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

________________________________________________________________________________________

Rubi [A]  time = 0.06, 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 = {} \[ \int \frac {e^{\frac {e}{(c+d x)^3}}}{(a+b x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[E^(e/(c + d*x)^3)/(a + b*x)^2,x]

[Out]

Defer[Int][E^(e/(c + d*x)^3)/(a + b*x)^2, x]

Rubi steps

\begin {align*} \int \frac {e^{\frac {e}{(c+d x)^3}}}{(a+b x)^2} \, dx &=\int \frac {e^{\frac {e}{(c+d x)^3}}}{(a+b x)^2} \, dx\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 0.36, size = 0, normalized size = 0.00 \[ \int \frac {e^{\frac {e}{(c+d x)^3}}}{(a+b x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[E^(e/(c + d*x)^3)/(a + b*x)^2,x]

[Out]

Integrate[E^(e/(c + d*x)^3)/(a + b*x)^2, x]

________________________________________________________________________________________

fricas [A]  time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {e^{\left (\frac {e}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right )}}{b^{2} x^{2} + 2 \, a b x + a^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(e/(d*x+c)^3)/(b*x+a)^2,x, algorithm="fricas")

[Out]

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

________________________________________________________________________________________

giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \mathit {undef} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(e/(d*x+c)^3)/(b*x+a)^2,x, algorithm="giac")

[Out]

undef

________________________________________________________________________________________

maple [A]  time = 0.12, size = 0, normalized size = 0.00 \[ \int \frac {{\mathrm e}^{\frac {e}{\left (d x +c \right )^{3}}}}{\left (b x +a \right )^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(1/(d*x+c)^3*e)/(b*x+a)^2,x)

[Out]

int(exp(1/(d*x+c)^3*e)/(b*x+a)^2,x)

________________________________________________________________________________________

maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {e^{\left (\frac {e}{{\left (d x + c\right )}^{3}}\right )}}{{\left (b x + a\right )}^{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(e/(d*x+c)^3)/(b*x+a)^2,x, algorithm="maxima")

[Out]

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

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {{\mathrm {e}}^{\frac {e}{{\left (c+d\,x\right )}^3}}}{{\left (a+b\,x\right )}^2} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(e/(c + d*x)^3)/(a + b*x)^2,x)

[Out]

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

________________________________________________________________________________________

sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

________________________________________________________________________________________