Optimal. Leaf size=25 \[ \text{Unintegrable}\left ((c+d x)^m (a+i a \cot (e+f x))^2,x\right ) \]
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Rubi [A] time = 0.0509656, 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 = {} \[ \int (c+d x)^m (a+i a \cot (e+f x))^2 \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int (c+d x)^m (a+i a \cot (e+f x))^2 \, dx &=\int (c+d x)^m (a+i a \cot (e+f x))^2 \, dx\\ \end{align*}
Mathematica [A] time = 9.88873, size = 0, normalized size = 0. \[ \int (c+d x)^m (a+i a \cot (e+f x))^2 \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.224, size = 0, normalized size = 0. \begin{align*} \int \left ( dx+c \right ) ^{m} \left ( a+ia\cot \left ( fx+e \right ) \right ) ^{2}\, dx \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*} \frac{2 i \,{\left (d x + c\right )}^{m} a^{2} +{\left (f e^{\left (2 i \, f x + 2 i \, e\right )} - f\right )}{\rm integral}\left (\frac{{\left (4 \, a^{2} d f x + 4 \, a^{2} c f + 2 i \, a^{2} d m\right )}{\left (d x + c\right )}^{m}}{d f x + c f -{\left (d f x + c f\right )} e^{\left (2 i \, f x + 2 i \, e\right )}}, x\right )}{f e^{\left (2 i \, f x + 2 i \, e\right )} - f} \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 (i \, a \cot \left (f x + e\right ) + a\right )}^{2}{\left (d x + c\right )}^{m}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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