Integrand size = 15, antiderivative size = 15 \[ \int \frac {f^{\frac {c}{(a+b x)^3}}}{x^3} \, dx=\text {Int}\left (\frac {f^{\frac {c}{(a+b x)^3}}}{x^3},x\right ) \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 15, 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 = {} \[ \int \frac {f^{\frac {c}{(a+b x)^3}}}{x^3} \, dx=\int \frac {f^{\frac {c}{(a+b x)^3}}}{x^3} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {f^{\frac {c}{(a+b x)^3}}}{x^3} \, dx \\ \end{align*}
Not integrable
Time = 0.03 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.13 \[ \int \frac {f^{\frac {c}{(a+b x)^3}}}{x^3} \, dx=\int \frac {f^{\frac {c}{(a+b x)^3}}}{x^3} \, dx \]
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Not integrable
Time = 0.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00
\[\int \frac {f^{\frac {c}{\left (b x +a \right )^{3}}}}{x^{3}}d x\]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 39, normalized size of antiderivative = 2.60 \[ \int \frac {f^{\frac {c}{(a+b x)^3}}}{x^3} \, dx=\int { \frac {f^{\frac {c}{{\left (b x + a\right )}^{3}}}}{x^{3}} \,d x } \]
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Not integrable
Time = 3.96 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {f^{\frac {c}{(a+b x)^3}}}{x^3} \, dx=\int \frac {f^{\frac {c}{\left (a + b x\right )^{3}}}}{x^{3}}\, dx \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.13 \[ \int \frac {f^{\frac {c}{(a+b x)^3}}}{x^3} \, dx=\int { \frac {f^{\frac {c}{{\left (b x + a\right )}^{3}}}}{x^{3}} \,d x } \]
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Not integrable
Time = 0.42 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.13 \[ \int \frac {f^{\frac {c}{(a+b x)^3}}}{x^3} \, dx=\int { \frac {f^{\frac {c}{{\left (b x + a\right )}^{3}}}}{x^{3}} \,d x } \]
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Not integrable
Time = 0.54 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.13 \[ \int \frac {f^{\frac {c}{(a+b x)^3}}}{x^3} \, dx=\int \frac {f^{\frac {c}{{\left (a+b\,x\right )}^3}}}{x^3} \,d x \]
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