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

Optimal. Leaf size=21 \[ \text{CannotIntegrate}\left (\frac{e^{\frac{e}{(c+d x)^2}}}{(a+b x)^3},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0530332, 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 = {} \[ \int \frac{e^{\frac{e}{(c+d x)^2}}}{(a+b x)^3} \, dx \]

Verification is Not applicable to the result.

[In]

Int[E^(e/(c + d*x)^2)/(a + b*x)^3,x]

[Out]

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

Rubi steps

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

Mathematica [A]  time = 0.0831338, size = 0, normalized size = 0. \[ \int \frac{e^{\frac{e}{(c+d x)^2}}}{(a+b x)^3} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.14, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( bx+a \right ) ^{3}}{{\rm e}^{{\frac{e}{ \left ( dx+c \right ) ^{2}}}}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{e^{\left (\frac{e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right )}}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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