Optimal. Leaf size=30 \[ \text{Unintegrable}\left (\frac{1}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3},x\right ) \]
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Rubi [A] time = 0.0653549, 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 = {} \[ \int \frac{1}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3} \, dx &=\int \frac{1}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3} \, dx\\ \end{align*}
Mathematica [A] time = 1.66756, size = 0, normalized size = 0. \[ \int \frac{1}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.655, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( hx+g \right ) \left ( a+b\ln \left ( c \left ( d \left ( fx+e \right ) ^{p} \right ) ^{q} \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*} \text{result too large to display} \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}{a^{3} h x + a^{3} g +{\left (b^{3} h x + b^{3} g\right )} \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right )^{3} + 3 \,{\left (a b^{2} h x + a b^{2} g\right )} \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right )^{2} + 3 \,{\left (a^{2} b h x + a^{2} b g\right )} \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right )}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \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}{{\left (h x + g\right )}{\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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