Integrand size = 18, antiderivative size = 18 \[ \int \frac {1}{x^3 \log \left (c \left (a+b x^2\right )^p\right )} \, dx=\text {Int}\left (\frac {1}{x^3 \log \left (c \left (a+b x^2\right )^p\right )},x\right ) \]
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Not integrable
Time = 0.01 (sec) , antiderivative size = 18, 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 = {} \[ \int \frac {1}{x^3 \log \left (c \left (a+b x^2\right )^p\right )} \, dx=\int \frac {1}{x^3 \log \left (c \left (a+b x^2\right )^p\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{x^3 \log \left (c \left (a+b x^2\right )^p\right )} \, dx \\ \end{align*}
Not integrable
Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {1}{x^3 \log \left (c \left (a+b x^2\right )^p\right )} \, dx=\int \frac {1}{x^3 \log \left (c \left (a+b x^2\right )^p\right )} \, dx \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00
\[\int \frac {1}{x^{3} \ln \left (c \left (b \,x^{2}+a \right )^{p}\right )}d x\]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {1}{x^3 \log \left (c \left (a+b x^2\right )^p\right )} \, dx=\int { \frac {1}{x^{3} \log \left ({\left (b x^{2} + a\right )}^{p} c\right )} \,d x } \]
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Not integrable
Time = 4.35 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \frac {1}{x^3 \log \left (c \left (a+b x^2\right )^p\right )} \, dx=\int \frac {1}{x^{3} \log {\left (c \left (a + b x^{2}\right )^{p} \right )}}\, dx \]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {1}{x^3 \log \left (c \left (a+b x^2\right )^p\right )} \, dx=\int { \frac {1}{x^{3} \log \left ({\left (b x^{2} + a\right )}^{p} c\right )} \,d x } \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {1}{x^3 \log \left (c \left (a+b x^2\right )^p\right )} \, dx=\int { \frac {1}{x^{3} \log \left ({\left (b x^{2} + a\right )}^{p} c\right )} \,d x } \]
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Not integrable
Time = 1.32 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {1}{x^3 \log \left (c \left (a+b x^2\right )^p\right )} \, dx=\int \frac {1}{x^3\,\ln \left (c\,{\left (b\,x^2+a\right )}^p\right )} \,d x \]
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