Integrand size = 24, antiderivative size = 24 \[ \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^3 x^2} \, dx=-\frac {1}{2 b d \left (a+b F^{c+d x}\right )^2 x^2 \log (F)}-\frac {\text {Int}\left (\frac {1}{\left (a+b F^{c+d x}\right )^2 x^3},x\right )}{b d \log (F)} \]
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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 = {} \[ \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^3 x^2} \, dx=\int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^3 x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = -\frac {1}{2 b d \left (a+b F^{c+d x}\right )^2 x^2 \log (F)}-\frac {\int \frac {1}{\left (a+b F^{c+d x}\right )^2 x^3} \, dx}{b d \log (F)} \\ \end{align*}
Not integrable
Time = 0.90 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^3 x^2} \, dx=\int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^3 x^2} \, dx \]
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Not integrable
Time = 0.01 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00
\[\int \frac {F^{d x +c}}{\left (a +b \,F^{d x +c}\right )^{3} x^{2}}d x\]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 72, normalized size of antiderivative = 3.00 \[ \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^3 x^2} \, dx=\int { \frac {F^{d x + c}}{{\left (F^{d x + c} b + a\right )}^{3} x^{2}} \,d x } \]
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Not integrable
Time = 2.84 (sec) , antiderivative size = 172, normalized size of antiderivative = 7.17 \[ \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^3 x^2} \, dx=\frac {- 2 F^{c + d x} b - a d x \log {\left (F \right )} - 2 a}{4 F^{c + d x} a^{2} b^{2} d^{2} x^{3} \log {\left (F \right )}^{2} + 2 F^{2 c + 2 d x} a b^{3} d^{2} x^{3} \log {\left (F \right )}^{2} + 2 a^{3} b d^{2} x^{3} \log {\left (F \right )}^{2}} - \frac {\int \frac {d x \log {\left (F \right )}}{a x^{4} + b x^{4} e^{c \log {\left (F \right )}} e^{d x \log {\left (F \right )}}}\, dx + \int \frac {3}{a x^{4} + b x^{4} e^{c \log {\left (F \right )}} e^{d x \log {\left (F \right )}}}\, dx}{a b d^{2} \log {\left (F \right )}^{2}} \]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 147, normalized size of antiderivative = 6.12 \[ \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^3 x^2} \, dx=\int { \frac {F^{d x + c}}{{\left (F^{d x + c} b + a\right )}^{3} x^{2}} \,d x } \]
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Not integrable
Time = 0.42 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^3 x^2} \, dx=\int { \frac {F^{d x + c}}{{\left (F^{d x + c} b + a\right )}^{3} x^{2}} \,d x } \]
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Not integrable
Time = 0.17 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^3 x^2} \, dx=\int \frac {F^{c+d\,x}}{x^2\,{\left (a+F^{c+d\,x}\,b\right )}^3} \,d x \]
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