Optimal. Leaf size=39 \[ \text{Unintegrable}\left ((A+B \sin (e+f x)) (g \cos (e+f x))^{-m-1} (a+b \sin (e+f x))^m,x\right ) \]
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Rubi [A] time = 0.0973966, 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 = {} \[ \int (g \cos (e+f x))^{-1-m} (a+b \sin (e+f x))^m (A+B \sin (e+f x)) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int (g \cos (e+f x))^{-1-m} (a+b \sin (e+f x))^m (A+B \sin (e+f x)) \, dx &=\int (g \cos (e+f x))^{-1-m} (a+b \sin (e+f x))^m (A+B \sin (e+f x)) \, dx\\ \end{align*}
Mathematica [A] time = 4.73579, size = 0, normalized size = 0. \[ \int (g \cos (e+f x))^{-1-m} (a+b \sin (e+f x))^m (A+B \sin (e+f x)) \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.451, size = 0, normalized size = 0. \begin{align*} \int \left ( g\cos \left ( fx+e \right ) \right ) ^{-1-m} \left ( a+b\sin \left ( fx+e \right ) \right ) ^{m} \left ( A+B\sin \left ( fx+e \right ) \right ) \, 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 (f x + e\right ) + A\right )} \left (g \cos \left (f x + e\right )\right )^{-m - 1}{\left (b \sin \left (f x + e\right ) + a\right )}^{m}\,{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 \sin \left (f x + e\right ) + A\right )} \left (g \cos \left (f x + e\right )\right )^{-m - 1}{\left (b \sin \left (f x + e\right ) + a\right )}^{m}, 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 [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: AttributeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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