Optimal. Leaf size=25 \[ \text{Unintegrable}\left (\cot ^2(c+d x) \left (a+b \sin ^4(c+d x)\right )^p,x\right ) \]
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Rubi [A] time = 0.0407652, 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 = {} \[ \int \cot ^2(c+d x) \left (a+b \sin ^4(c+d x)\right )^p \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \cot ^2(c+d x) \left (a+b \sin ^4(c+d x)\right )^p \, dx &=\int \cot ^2(c+d x) \left (a+b \sin ^4(c+d x)\right )^p \, dx\\ \end{align*}
Mathematica [A] time = 1.41614, size = 0, normalized size = 0. \[ \int \cot ^2(c+d x) \left (a+b \sin ^4(c+d x)\right )^p \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.904, size = 0, normalized size = 0. \begin{align*} \int \left ( \cot \left ( dx+c \right ) \right ) ^{2} \left ( a+b \left ( \sin \left ( dx+c \right ) \right ) ^{4} \right ) ^{p}\, 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*} \int{\left (b \sin \left (d x + c\right )^{4} + a\right )}^{p} \cot \left (d x + c\right )^{2}\,{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 ({\left (b \cos \left (d x + c\right )^{4} - 2 \, b \cos \left (d x + c\right )^{2} + a + b\right )}^{p} \cot \left (d x + c\right )^{2}, 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 \sin \left (d x + c\right )^{4} + a\right )}^{p} \cot \left (d x + c\right )^{2}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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