Optimal. Leaf size=50 \[ \text{Unintegrable}\left (\frac{\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(g k+h k x) \left (t \log \left (i (g+h x)^n\right )+s\right )^2},x\right ) \]
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Rubi [A] time = 0.0525536, 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 = {} \[ \int \frac{\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(g k+h k x) \left (s+t \log \left (i (g+h x)^n\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(g k+h k x) \left (s+t \log \left (55 (g+h x)^n\right )\right )^2} \, dx &=\int \frac{\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(g k+h k x) \left (s+t \log \left (55 (g+h x)^n\right )\right )^2} \, dx\\ \end{align*}
Mathematica [A] time = 2.74292, size = 0, normalized size = 0. \[ \int \frac{\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(g k+h k x) \left (s+t \log \left (i (g+h x)^n\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.739, size = 0, normalized size = 0. \begin{align*} \int{\frac{\ln \left ( e \left ( f \left ( bx+a \right ) ^{p} \left ( dx+c \right ) ^{q} \right ) ^{r} \right ) }{ \left ( hkx+gk \right ) \left ( s+t\ln \left ( i \left ( hx+g \right ) ^{n} \right ) \right ) ^{2}}}\, 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{\log \left ({\left ({\left (b x + a\right )}^{p}\right )}^{r}\right ) + \log \left ({\left ({\left (d x + c\right )}^{q}\right )}^{r}\right ) + \log \left (e\right ) + \log \left (f^{r}\right )}{h k n t^{2} \log \left ({\left (h x + g\right )}^{n}\right ) +{\left (k n t^{2} \log \left (i\right ) + k n s t\right )} h} + \int \frac{b c p r + a d q r +{\left (p r + q r\right )} b d x}{{\left (k n t^{2} \log \left (i\right ) + k n s t\right )} b d h x^{2} +{\left (k n t^{2} \log \left (i\right ) + k n s t\right )} a c h +{\left ({\left (k n t^{2} \log \left (i\right ) + k n s t\right )} b c h +{\left (k n t^{2} \log \left (i\right ) + k n s t\right )} a d h\right )} x +{\left (b d h k n t^{2} x^{2} + a c h k n t^{2} +{\left (b c h k n t^{2} + a d h k n t^{2}\right )} x\right )} \log \left ({\left (h x + g\right )}^{n}\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{\log \left (\left ({\left (b x + a\right )}^{p}{\left (d x + c\right )}^{q} f\right )^{r} e\right )}{h k s^{2} x + g k s^{2} +{\left (h k t^{2} x + g k t^{2}\right )} \log \left ({\left (h x + g\right )}^{n} i\right )^{2} + 2 \,{\left (h k s t x + g k s t\right )} \log \left ({\left (h x + g\right )}^{n} i\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{\log \left (\left ({\left (b x + a\right )}^{p}{\left (d x + c\right )}^{q} f\right )^{r} e\right )}{{\left (h k x + g k\right )}{\left (t \log \left ({\left (h x + g\right )}^{n} i\right ) + s\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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