Optimal. Leaf size=19 \[ \text{Unintegrable}\left (\frac{1}{x^2 \left (a+b e^{c+d x}\right )^3},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0436581, 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 = {} \[ \int \frac{1}{\left (a+b e^{c+d x}\right )^3 x^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{1}{\left (a+b e^{c+d x}\right )^3 x^2} \, dx &=\int \frac{1}{\left (a+b e^{c+d x}\right )^3 x^2} \, dx\\ \end{align*}
Mathematica [A] time = 0.744828, size = 0, normalized size = 0. \[ \int \frac{1}{\left (a+b e^{c+d x}\right )^3 x^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.123, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( a+b{{\rm e}^{dx+c}} \right ) ^{3}{x}^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \frac{3 \, a d x + 2 \,{\left (b d x e^{c} + b e^{c}\right )} e^{\left (d x\right )} + 2 \, a}{2 \,{\left (a^{2} b^{2} d^{2} x^{3} e^{\left (2 \, d x + 2 \, c\right )} + 2 \, a^{3} b d^{2} x^{3} e^{\left (d x + c\right )} + a^{4} d^{2} x^{3}\right )}} + \int \frac{d^{2} x^{2} + 3 \, d x + 3}{a^{2} b d^{2} x^{4} e^{\left (d x + c\right )} + a^{3} d^{2} x^{4}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{b^{3} x^{2} e^{\left (3 \, d x + 3 \, c\right )} + 3 \, a b^{2} x^{2} e^{\left (2 \, d x + 2 \, c\right )} + 3 \, a^{2} b x^{2} e^{\left (d x + c\right )} + a^{3} x^{2}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \frac{3 a d x + 2 a + \left (2 b d x + 2 b\right ) e^{c + d x}}{2 a^{4} d^{2} x^{3} + 4 a^{3} b d^{2} x^{3} e^{c + d x} + 2 a^{2} b^{2} d^{2} x^{3} e^{2 c + 2 d x}} + \frac{\int \frac{3 d x}{a x^{4} + b x^{4} e^{c} e^{d x}}\, dx + \int \frac{d^{2} x^{2}}{a x^{4} + b x^{4} e^{c} e^{d x}}\, dx + \int \frac{3}{a x^{4} + b x^{4} e^{c} e^{d x}}\, dx}{a^{2} d^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b e^{\left (d x + c\right )} + a\right )}^{3} x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]