Integrand size = 17, antiderivative size = 17 \[ \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x} \, dx=\text {Int}\left (\frac {1}{\left (a+b e^{c+d x}\right )^3 x},x\right ) \]
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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 = {} \[ \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x} \, dx=\int \frac {1}{\left (a+b e^{c+d x}\right )^3 x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x} \, dx \\ \end{align*}
Not integrable
Time = 2.21 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.12 \[ \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x} \, dx=\int \frac {1}{\left (a+b e^{c+d x}\right )^3 x} \, dx \]
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Not integrable
Time = 0.16 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.94
\[\int \frac {1}{\left (a +b \,{\mathrm e}^{d x +c}\right )^{3} x}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 53, normalized size of antiderivative = 3.12 \[ \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x} \, dx=\int { \frac {1}{{\left (b e^{\left (d x + c\right )} + a\right )}^{3} x} \,d x } \]
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Not integrable
Time = 2.22 (sec) , antiderivative size = 165, normalized size of antiderivative = 9.71 \[ \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x} \, dx=\frac {3 a d x + a + \left (2 b d x + b\right ) e^{c + d x}}{2 a^{4} d^{2} x^{2} + 4 a^{3} b d^{2} x^{2} e^{c + d x} + 2 a^{2} b^{2} d^{2} x^{2} e^{2 c + 2 d x}} + \frac {\int \frac {3 d x}{a x^{3} + b x^{3} e^{c} e^{d x}}\, dx + \int \frac {2 d^{2} x^{2}}{a x^{3} + b x^{3} e^{c} e^{d x}}\, dx + \int \frac {2}{a x^{3} + b x^{3} e^{c} e^{d x}}\, dx}{2 a^{2} d^{2}} \]
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Not integrable
Time = 0.23 (sec) , antiderivative size = 128, normalized size of antiderivative = 7.53 \[ \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x} \, dx=\int { \frac {1}{{\left (b e^{\left (d x + c\right )} + a\right )}^{3} x} \,d x } \]
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Not integrable
Time = 0.32 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x} \, dx=\int { \frac {1}{{\left (b e^{\left (d x + c\right )} + a\right )}^{3} x} \,d x } \]
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Not integrable
Time = 0.16 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x} \, dx=\int \frac {1}{x\,{\left (a+b\,{\mathrm {e}}^{c+d\,x}\right )}^3} \,d x \]
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