Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{1}{x \log ^3\left (c \left (a+b x^2\right )^p\right )},x\right ) \]
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Rubi [A] time = 0.0163287, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{1}{x \log ^3\left (c \left (a+b x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{x \log ^3\left (c \left (a+b x^2\right )^p\right )} \, dx &=\int \frac{1}{x \log ^3\left (c \left (a+b x^2\right )^p\right )} \, dx\\ \end{align*}
Mathematica [A] time = 0.550545, size = 0, normalized size = 0. \[ \int \frac{1}{x \log ^3\left (c \left (a+b x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 3.704, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x \left ( \ln \left ( c \left ( b{x}^{2}+a \right ) ^{p} \right ) \right ) ^{3}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{b^{2} p x^{4} + a b{\left (p - \log \left (c\right )\right )} x^{2} - a^{2} \log \left (c\right ) -{\left (a b x^{2} + a^{2}\right )} \log \left ({\left (b x^{2} + a\right )}^{p}\right )}{4 \,{\left (b^{2} p^{2} x^{4} \log \left ({\left (b x^{2} + a\right )}^{p}\right )^{2} + 2 \, b^{2} p^{2} x^{4} \log \left ({\left (b x^{2} + a\right )}^{p}\right ) \log \left (c\right ) + b^{2} p^{2} x^{4} \log \left (c\right )^{2}\right )}} + \int \frac{a b x^{2} + 2 \, a^{2}}{2 \,{\left (b^{2} p^{2} x^{5} \log \left ({\left (b x^{2} + a\right )}^{p}\right ) + b^{2} p^{2} x^{5} \log \left (c\right )\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{x \log \left ({\left (b x^{2} + a\right )}^{p} c\right )^{3}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \log{\left (c \left (a + b x^{2}\right )^{p} \right )}^{3}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \log \left ({\left (b x^{2} + a\right )}^{p} c\right )^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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