Integrand size = 19, antiderivative size = 19 \[ \int \frac {\sqrt {c+d x}}{\left (a+b e^x\right )^2} \, dx=\text {Int}\left (\frac {\sqrt {c+d x}}{\left (a+b e^x\right )^2},x\right ) \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 19, 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 = {} \[ \int \frac {\sqrt {c+d x}}{\left (a+b e^x\right )^2} \, dx=\int \frac {\sqrt {c+d x}}{\left (a+b e^x\right )^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\sqrt {c+d x}}{\left (a+b e^x\right )^2} \, dx \\ \end{align*}
Not integrable
Time = 1.65 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.11 \[ \int \frac {\sqrt {c+d x}}{\left (a+b e^x\right )^2} \, dx=\int \frac {\sqrt {c+d x}}{\left (a+b e^x\right )^2} \, dx \]
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Not integrable
Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.84
\[\int \frac {\sqrt {d x +c}}{\left (a +b \,{\mathrm e}^{x}\right )^{2}}d x\]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.58 \[ \int \frac {\sqrt {c+d x}}{\left (a+b e^x\right )^2} \, dx=\int { \frac {\sqrt {d x + c}}{{\left (b e^{x} + a\right )}^{2}} \,d x } \]
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Not integrable
Time = 5.03 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {\sqrt {c+d x}}{\left (a+b e^x\right )^2} \, dx=\int \frac {\sqrt {c + d x}}{\left (a + b e^{x}\right )^{2}}\, dx \]
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Not integrable
Time = 0.29 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95 \[ \int \frac {\sqrt {c+d x}}{\left (a+b e^x\right )^2} \, dx=\int { \frac {\sqrt {d x + c}}{{\left (b e^{x} + a\right )}^{2}} \,d x } \]
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Not integrable
Time = 0.38 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95 \[ \int \frac {\sqrt {c+d x}}{\left (a+b e^x\right )^2} \, dx=\int { \frac {\sqrt {d x + c}}{{\left (b e^{x} + a\right )}^{2}} \,d x } \]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95 \[ \int \frac {\sqrt {c+d x}}{\left (a+b e^x\right )^2} \, dx=\int \frac {\sqrt {c+d\,x}}{{\left (a+b\,{\mathrm {e}}^x\right )}^2} \,d x \]
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