Optimal. Leaf size=29 \[ -\text{Unintegrable}\left ((d x)^m \log \left (1-e x^q\right ) \left (a+b \log \left (c x^n\right )\right ),x\right ) \]
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Rubi [A] time = 0.0215918, 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 = {} \[ \int -(d x)^m \left (a+b \log \left (c x^n\right )\right ) \log \left (1-e x^q\right ) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int -(d x)^m \left (a+b \log \left (c x^n\right )\right ) \log \left (1-e x^q\right ) \, dx &=-\int (d x)^m \left (a+b \log \left (c x^n\right )\right ) \log \left (1-e x^q\right ) \, dx\\ \end{align*}
Mathematica [A] time = 0.232955, size = 266, normalized size = 9.17 \[ -\frac{x (d x)^m \left (-b n q \, _3F_2\left (1,\frac{m}{q}+\frac{1}{q},\frac{m}{q}+\frac{1}{q};\frac{m}{q}+\frac{1}{q}+1,\frac{m}{q}+\frac{1}{q}+1;e x^q\right )+q \, _2F_1\left (1,\frac{m+1}{q};\frac{m+q+1}{q};e x^q\right ) \left (a m+a+b (m+1) \log \left (c x^n\right )-b n\right )+a m^2 \log \left (1-e x^q\right )+2 a m \log \left (1-e x^q\right )+a \log \left (1-e x^q\right )-a m q-a q+b m^2 \log \left (c x^n\right ) \log \left (1-e x^q\right )+2 b m \log \left (c x^n\right ) \log \left (1-e x^q\right )+b \log \left (c x^n\right ) \log \left (1-e x^q\right )-b m q \log \left (c x^n\right )-b q \log \left (c x^n\right )-b m n \log \left (1-e x^q\right )-b n \log \left (1-e x^q\right )+2 b n q\right )}{(m+1)^3} \]
Warning: Unable to verify antiderivative.
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Maple [A] time = 0.468, size = 844, normalized size = 29.1 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \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 (-\left (d x\right )^{m} b \log \left (c x^{n}\right ) \log \left (-e x^{q} + 1\right ) - \left (d x\right )^{m} a \log \left (-e x^{q} + 1\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 -{\left (b \log \left (c x^{n}\right ) + a\right )} \left (d x\right )^{m} \log \left (-e x^{q} + 1\right )\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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