Optimal. Leaf size=21 \[ \text{CannotIntegrate}\left (\sin (c+d x) (a+b \tan (c+d x))^n,x\right ) \]
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Rubi [A] time = 0.855052, 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 = {} \[ \int \sin (c+d x) (a+b \tan (c+d x))^n \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \sin (c+d x) (a+b \tan (c+d x))^n \, dx &=\int \sin (c+d x) (a+b \tan (c+d x))^n \, dx\\ \end{align*}
Mathematica [A] time = 2.18546, size = 0, normalized size = 0. \[ \int \sin (c+d x) (a+b \tan (c+d x))^n \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.041, size = 0, normalized size = 0. \begin{align*} \int \sin \left ( dx+c \right ) \left ( a+b\tan \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{\left (b \tan \left (d x + c\right ) + a\right )}^{n} \sin \left (d x + c\right )\,{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 \tan \left (d x + c\right ) + a\right )}^{n} \sin \left (d x + c\right ), 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 \left (a + b \tan{\left (c + d x \right )}\right )^{n} \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{\left (b \tan \left (d x + c\right ) + a\right )}^{n} \sin \left (d x + c\right )\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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