Integrand size = 24, antiderivative size = 24 \[ \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^2 x^2} \, dx=-\frac {1}{b d \left (a+b F^{c+d x}\right ) x^2 \log (F)}-\frac {2 \text {Int}\left (\frac {1}{\left (a+b F^{c+d x}\right ) x^3},x\right )}{b d \log (F)} \]
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Not integrable
Time = 0.07 (sec) , antiderivative size = 24, 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 = {} \[ \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^2 x^2} \, dx=\int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^2 x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = -\frac {1}{b d \left (a+b F^{c+d x}\right ) x^2 \log (F)}-\frac {2 \int \frac {1}{\left (a+b F^{c+d x}\right ) x^3} \, dx}{b d \log (F)} \\ \end{align*}
Not integrable
Time = 0.31 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^2 x^2} \, dx=\int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^2 x^2} \, dx \]
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Not integrable
Time = 0.01 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00
\[\int \frac {F^{d x +c}}{\left (a +b \,F^{d x +c}\right )^{2} x^{2}}d x\]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.12 \[ \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^2 x^2} \, dx=\int { \frac {F^{d x + c}}{{\left (F^{d x + c} b + a\right )}^{2} x^{2}} \,d x } \]
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Not integrable
Time = 0.81 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.92 \[ \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^2 x^2} \, dx=- \frac {1}{F^{c + d x} b^{2} d x^{2} \log {\left (F \right )} + a b d x^{2} \log {\left (F \right )}} - \frac {2 \int \frac {1}{a x^{3} + b x^{3} e^{c \log {\left (F \right )}} e^{d x \log {\left (F \right )}}}\, dx}{b d \log {\left (F \right )}} \]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 67, normalized size of antiderivative = 2.79 \[ \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^2 x^2} \, dx=\int { \frac {F^{d x + c}}{{\left (F^{d x + c} b + a\right )}^{2} x^{2}} \,d x } \]
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Not integrable
Time = 0.42 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^2 x^2} \, dx=\int { \frac {F^{d x + c}}{{\left (F^{d x + c} b + a\right )}^{2} x^{2}} \,d x } \]
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Not integrable
Time = 0.15 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^2 x^2} \, dx=\int \frac {F^{c+d\,x}}{x^2\,{\left (a+F^{c+d\,x}\,b\right )}^2} \,d x \]
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