Integrand size = 25, antiderivative size = 25 \[ \int \cos ^3(e+f x) \left (a+b (c \tan (e+f x))^n\right )^p \, dx=\text {Int}\left (\cos ^3(e+f x) \left (a+b (c \tan (e+f x))^n\right )^p,x\right ) \]
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Not integrable
Time = 0.06 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \cos ^3(e+f x) \left (a+b (c \tan (e+f x))^n\right )^p \, dx=\int \cos ^3(e+f x) \left (a+b (c \tan (e+f x))^n\right )^p \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \cos ^3(e+f x) \left (a+b (c \tan (e+f x))^n\right )^p \, dx \\ \end{align*}
Not integrable
Time = 8.00 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \cos ^3(e+f x) \left (a+b (c \tan (e+f x))^n\right )^p \, dx=\int \cos ^3(e+f x) \left (a+b (c \tan (e+f x))^n\right )^p \, dx \]
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Not integrable
Time = 1.20 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00
\[\int \cos \left (f x +e \right )^{3} \left (a +b \left (c \tan \left (f x +e \right )\right )^{n}\right )^{p}d x\]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \cos ^3(e+f x) \left (a+b (c \tan (e+f x))^n\right )^p \, dx=\int { {\left (\left (c \tan \left (f x + e\right )\right )^{n} b + a\right )}^{p} \cos \left (f x + e\right )^{3} \,d x } \]
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Timed out. \[ \int \cos ^3(e+f x) \left (a+b (c \tan (e+f x))^n\right )^p \, dx=\text {Timed out} \]
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Not integrable
Time = 9.79 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \cos ^3(e+f x) \left (a+b (c \tan (e+f x))^n\right )^p \, dx=\int { {\left (\left (c \tan \left (f x + e\right )\right )^{n} b + a\right )}^{p} \cos \left (f x + e\right )^{3} \,d x } \]
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Not integrable
Time = 69.79 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \cos ^3(e+f x) \left (a+b (c \tan (e+f x))^n\right )^p \, dx=\int { {\left (\left (c \tan \left (f x + e\right )\right )^{n} b + a\right )}^{p} \cos \left (f x + e\right )^{3} \,d x } \]
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Not integrable
Time = 14.06 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \cos ^3(e+f x) \left (a+b (c \tan (e+f x))^n\right )^p \, dx=\int {\cos \left (e+f\,x\right )}^3\,{\left (a+b\,{\left (c\,\mathrm {tan}\left (e+f\,x\right )\right )}^n\right )}^p \,d x \]
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