Optimal. Leaf size=58 \[ (c \cos (e+f x))^m (c \sec (e+f x))^m \text{Unintegrable}\left ((A+B \cos (e+f x)) (c \cos (e+f x))^{-m} (a+b \cos (e+f x))^n,x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.18063, 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 = {} \[ \int (a+b \cos (e+f x))^n (A+B \cos (e+f x)) (c \sec (e+f x))^m \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int (a+b \cos (e+f x))^n (A+B \cos (e+f x)) (c \sec (e+f x))^m \, dx &=\left ((c \cos (e+f x))^m (c \sec (e+f x))^m\right ) \int (c \cos (e+f x))^{-m} (a+b \cos (e+f x))^n (A+B \cos (e+f x)) \, dx\\ \end{align*}
Mathematica [A] time = 8.45503, size = 0, normalized size = 0. \[ \int (a+b \cos (e+f x))^n (A+B \cos (e+f x)) (c \sec (e+f x))^m \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 3.207, size = 0, normalized size = 0. \begin{align*} \int \left ( a+b\cos \left ( fx+e \right ) \right ) ^{n} \left ( A+B\cos \left ( fx+e \right ) \right ) \left ( c\sec \left ( fx+e \right ) \right ) ^{m}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (B \cos \left (f x + e\right ) + A\right )}{\left (b \cos \left (f x + e\right ) + a\right )}^{n} \left (c \sec \left (f x + e\right )\right )^{m}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left ({\left (B \cos \left (f x + e\right ) + A\right )}{\left (b \cos \left (f x + e\right ) + a\right )}^{n} \left (c \sec \left (f x + e\right )\right )^{m}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (B \cos \left (f x + e\right ) + A\right )}{\left (b \cos \left (f x + e\right ) + a\right )}^{n} \left (c \sec \left (f x + e\right )\right )^{m}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]