Optimal. Leaf size=27 \[ \text{Unintegrable}\left (\sec ^3(e+f x) \left (a+b (c \tan (e+f x))^n\right )^p,x\right ) \]
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Rubi [A] time = 0.0532297, 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 = {} \[ \int \sec ^3(e+f x) \left (a+b (c \tan (e+f x))^n\right )^p \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \sec ^3(e+f x) \left (a+b (c \tan (e+f x))^n\right )^p \, dx &=\int \sec ^3(e+f x) \left (a+b (c \tan (e+f x))^n\right )^p \, dx\\ \end{align*}
Mathematica [A] time = 3.62258, size = 0, normalized size = 0. \[ \int \sec ^3(e+f x) \left (a+b (c \tan (e+f x))^n\right )^p \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.381, size = 0, normalized size = 0. \begin{align*} \int \left ( \sec \left ( fx+e \right ) \right ) ^{3} \left ( a+b \left ( c\tan \left ( fx+e \right ) \right ) ^{n} \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 (\left (c \tan \left (f x + e\right )\right )^{n} b + a\right )}^{p} \sec \left (f x + e\right )^{3}\,{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 (\left (c \tan \left (f x + e\right )\right )^{n} b + a\right )}^{p} \sec \left (f x + e\right )^{3}, 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 (\left (c \tan \left (f x + e\right )\right )^{n} b + a\right )}^{p} \sec \left (f x + e\right )^{3}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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