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

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

[Out]

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

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Rubi [A]  time = 0.05, 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 = {} \[ \int \frac {e^{\frac {e}{(c+d x)^2}}}{(a+b x)^3} \, dx \]

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*}

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Mathematica [A]  time = 0.09, size = 0, normalized size = 0.00 \[ \int \frac {e^{\frac {e}{(c+d x)^2}}}{(a+b x)^3} \, dx \]

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

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

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)

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maple [A]  time = 0.20, size = 0, normalized size = 0.00 \[ \int \frac {{\mathrm e}^{\frac {e}{\left (d x +c \right )^{2}}}}{\left (b x +a \right )^{3}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(e/(c + d*x)^2)/(a + b*x)^3,x)

[Out]

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

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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)**2)/(b*x+a)**3,x)

[Out]

Timed out

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