Optimal. Leaf size=25 \[ \text{Unintegrable}\left (\frac{\tan ^m(c+d x)}{a+b \sin ^n(c+d x)},x\right ) \]
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Rubi [A] time = 0.0577452, 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 = {} \[ \int \frac{\tan ^m(c+d x)}{a+b \sin ^n(c+d x)} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\tan ^m(c+d x)}{a+b \sin ^n(c+d x)} \, dx &=\int \frac{\tan ^m(c+d x)}{a+b \sin ^n(c+d x)} \, dx\\ \end{align*}
Mathematica [A] time = 2.37861, size = 0, normalized size = 0. \[ \int \frac{\tan ^m(c+d x)}{a+b \sin ^n(c+d x)} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.75, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \tan \left ( dx+c \right ) \right ) ^{m}}{a+b \left ( \sin \left ( dx+c \right ) \right ) ^{n}}}\, 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{\tan \left (d x + c\right )^{m}}{b \sin \left (d x + c\right )^{n} + 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{\tan \left (d x + c\right )^{m}}{b \sin \left (d x + c\right )^{n} + 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{\tan ^{m}{\left (c + d x \right )}}{a + b \sin ^{n}{\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{\tan \left (d x + c\right )^{m}}{b \sin \left (d x + c\right )^{n} + a}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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