Integrand size = 17, antiderivative size = 17 \[ \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x^2} \, dx=\text {Int}\left (\frac {1}{\left (a+b e^{c+d x}\right )^3 x^2},x\right ) \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x^2} \, dx=\int \frac {1}{\left (a+b e^{c+d x}\right )^3 x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x^2} \, dx \\ \end{align*}
Not integrable
Time = 1.17 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.12 \[ \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x^2} \, dx=\int \frac {1}{\left (a+b e^{c+d x}\right )^3 x^2} \, dx \]
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Not integrable
Time = 0.16 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.94
\[\int \frac {1}{\left (a +b \,{\mathrm e}^{d x +c}\right )^{3} x^{2}}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 61, normalized size of antiderivative = 3.59 \[ \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x^2} \, dx=\int { \frac {1}{{\left (b e^{\left (d x + c\right )} + a\right )}^{3} x^{2}} \,d x } \]
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Not integrable
Time = 2.08 (sec) , antiderivative size = 165, normalized size of antiderivative = 9.71 \[ \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x^2} \, dx=\frac {3 a d x + 2 a + \left (2 b d x + 2 b\right ) e^{c + d x}}{2 a^{4} d^{2} x^{3} + 4 a^{3} b d^{2} x^{3} e^{c + d x} + 2 a^{2} b^{2} d^{2} x^{3} e^{2 c + 2 d x}} + \frac {\int \frac {3 d x}{a x^{4} + b x^{4} e^{c} e^{d x}}\, dx + \int \frac {d^{2} x^{2}}{a x^{4} + b x^{4} e^{c} e^{d x}}\, dx + \int \frac {3}{a x^{4} + b x^{4} e^{c} e^{d x}}\, dx}{a^{2} d^{2}} \]
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Not integrable
Time = 0.23 (sec) , antiderivative size = 128, normalized size of antiderivative = 7.53 \[ \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x^2} \, dx=\int { \frac {1}{{\left (b e^{\left (d x + c\right )} + a\right )}^{3} x^{2}} \,d x } \]
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Not integrable
Time = 0.37 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x^2} \, dx=\int { \frac {1}{{\left (b e^{\left (d x + c\right )} + a\right )}^{3} x^{2}} \,d x } \]
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Not integrable
Time = 0.16 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x^2} \, dx=\int \frac {1}{x^2\,{\left (a+b\,{\mathrm {e}}^{c+d\,x}\right )}^3} \,d x \]
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