Optimal. Leaf size=36 \[ \text {Int}\left ((A+B \sec (e+f x)) (c \sec (e+f x))^n (a+b \sec (e+f x))^m,x\right ) \]
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Rubi [A] time = 0.09, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int (c \sec (e+f x))^n (a+b \sec (e+f x))^m (A+B \sec (e+f x)) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int (c \sec (e+f x))^n (a+b \sec (e+f x))^m (A+B \sec (e+f x)) \, dx &=\int (c \sec (e+f x))^n (a+b \sec (e+f x))^m (A+B \sec (e+f x)) \, dx\\ \end {align*}
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Mathematica [A] time = 4.78, size = 0, normalized size = 0.00 \[ \int (c \sec (e+f x))^n (a+b \sec (e+f x))^m (A+B \sec (e+f x)) \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.92, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (B \sec \left (f x + e\right ) + A\right )} {\left (b \sec \left (f x + e\right ) + a\right )}^{m} \left (c \sec \left (f x + e\right )\right )^{n}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (B \sec \left (f x + e\right ) + A\right )} {\left (b \sec \left (f x + e\right ) + a\right )}^{m} \left (c \sec \left (f x + e\right )\right )^{n}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 3.33, size = 0, normalized size = 0.00 \[ \int \left (c \sec \left (f x +e \right )\right )^{n} \left (a +b \sec \left (f x +e \right )\right )^{m} \left (A +B \sec \left (f x +e \right )\right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (B \sec \left (f x + e\right ) + A\right )} {\left (b \sec \left (f x + e\right ) + a\right )}^{m} \left (c \sec \left (f x + e\right )\right )^{n}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \left (A+\frac {B}{\cos \left (e+f\,x\right )}\right )\,{\left (a+\frac {b}{\cos \left (e+f\,x\right )}\right )}^m\,{\left (\frac {c}{\cos \left (e+f\,x\right )}\right )}^n \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (c \sec {\left (e + f x \right )}\right )^{n} \left (A + B \sec {\left (e + f x \right )}\right ) \left (a + b \sec {\left (e + f x \right )}\right )^{m}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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