Optimal. Leaf size=28 \[ \text{Unintegrable}\left (\frac{\sec (c+d x) (e+f x)^m}{a+b \sin (c+d x)},x\right ) \]
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Rubi [A] time = 0.044306, 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 = {} \[ \int \frac{(e+f x)^m \sec (c+d x)}{a+b \sin (c+d x)} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{(e+f x)^m \sec (c+d x)}{a+b \sin (c+d x)} \, dx &=\int \frac{(e+f x)^m \sec (c+d x)}{a+b \sin (c+d x)} \, dx\\ \end{align*}
Mathematica [A] time = 139.158, size = 0, normalized size = 0. \[ \int \frac{(e+f x)^m \sec (c+d x)}{a+b \sin (c+d x)} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.079, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( fx+e \right ) ^{m}\sec \left ( dx+c \right ) }{a+b\sin \left ( dx+c \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 \frac{{\left (f x + e\right )}^{m} \sec \left (d x + c\right )}{b \sin \left (d x + c\right ) + a}\,{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{{\left (f x + e\right )}^{m} \sec \left (d x + c\right )}{b \sin \left (d x + c\right ) + a}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (e + f x\right )^{m} \sec{\left (c + d x \right )}}{a + b \sin{\left (c + d x \right )}}\, dx \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{{\left (f x + e\right )}^{m} \sec \left (d x + c\right )}{b \sin \left (d x + c\right ) + a}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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