Optimal. Leaf size=24 \[ \text {Int}\left (\sec ^n(e+f x) (a+b \sec (e+f x))^m,x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.04, 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 = {} \[ \int \sec ^n(e+f x) (a+b \sec (e+f x))^m \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \sec ^n(e+f x) (a+b \sec (e+f x))^m \, dx &=\int \sec ^n(e+f x) (a+b \sec (e+f x))^m \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 2.70, size = 0, normalized size = 0.00 \[ \int \sec ^n(e+f x) (a+b \sec (e+f x))^m \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.59, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (b \sec \left (f x + e\right ) + a\right )}^{m} \sec \left (f x + e\right )^{n}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (b \sec \left (f x + e\right ) + a\right )}^{m} \sec \left (f x + e\right )^{n}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 3.00, size = 0, normalized size = 0.00 \[ \int \left (\sec ^{n}\left (f x +e \right )\right ) \left (a +b \sec \left (f x +e \right )\right )^{m}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (b \sec \left (f x + e\right ) + a\right )}^{m} \sec \left (f x + e\right )^{n}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int {\left (a+\frac {b}{\cos \left (e+f\,x\right )}\right )}^m\,{\left (\frac {1}{\cos \left (e+f\,x\right )}\right )}^n \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (a + b \sec {\left (e + f x \right )}\right )^{m} \sec ^{n}{\left (e + f x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________