Optimal. Leaf size=35 \[ \text{Unintegrable}\left (\frac{i+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2},x\right ) \]
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Rubi [A] time = 0.298996, 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 = {} \[ \int \frac{i+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{544+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx &=\int \frac{544+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx\\ \end{align*}
Mathematica [A] time = 2.98509, size = 0, normalized size = 0. \[ \int \frac{i+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.626, size = 0, normalized size = 0. \begin{align*} \int{\frac{jx+i}{ \left ( hx+g \right ) \left ( a+b\ln \left ( c \left ( d \left ( fx+e \right ) ^{p} \right ) ^{q} \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{f j x^{2} + e i +{\left (f i + e j\right )} x}{a b f g p q +{\left (f g p q \log \left (c\right ) + f g p q \log \left (d^{q}\right )\right )} b^{2} +{\left (a b f h p q +{\left (f h p q \log \left (c\right ) + f h p q \log \left (d^{q}\right )\right )} b^{2}\right )} x +{\left (b^{2} f h p q x + b^{2} f g p q\right )} \log \left ({\left ({\left (f x + e\right )}^{p}\right )}^{q}\right )} + \int \frac{f h j x^{2} + 2 \, f g j x + f g i -{\left (h i - g j\right )} e}{a b f g^{2} p q +{\left (f g^{2} p q \log \left (c\right ) + f g^{2} p q \log \left (d^{q}\right )\right )} b^{2} +{\left (a b f h^{2} p q +{\left (f h^{2} p q \log \left (c\right ) + f h^{2} p q \log \left (d^{q}\right )\right )} b^{2}\right )} x^{2} + 2 \,{\left (a b f g h p q +{\left (f g h p q \log \left (c\right ) + f g h p q \log \left (d^{q}\right )\right )} b^{2}\right )} x +{\left (b^{2} f h^{2} p q x^{2} + 2 \, b^{2} f g h p q x + b^{2} f g^{2} p q\right )} \log \left ({\left ({\left (f x + e\right )}^{p}\right )}^{q}\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{j x + i}{a^{2} h x + a^{2} g +{\left (b^{2} h x + b^{2} g\right )} \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right )^{2} + 2 \,{\left (a b h x + a 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{j x + i}{{\left (h x + g\right )}{\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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