Optimal. Leaf size=27 \[ \text{Unintegrable}\left (\sqrt{a+b \sec (c+d x)} (e \tan (c+d x))^m,x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0610669, 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 = {} \[ \int \sqrt{a+b \sec (c+d x)} (e \tan (c+d x))^m \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \sqrt{a+b \sec (c+d x)} (e \tan (c+d x))^m \, dx &=\int \sqrt{a+b \sec (c+d x)} (e \tan (c+d x))^m \, dx\\ \end{align*}
Mathematica [A] time = 0.700808, size = 0, normalized size = 0. \[ \int \sqrt{a+b \sec (c+d x)} (e \tan (c+d x))^m \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.3, size = 0, normalized size = 0. \begin{align*} \int \sqrt{a+b\sec \left ( dx+c \right ) } \left ( e\tan \left ( dx+c \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 \sqrt{b \sec \left (d x + c\right ) + a} \left (e \tan \left (d x + c\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 (\sqrt{b \sec \left (d x + c\right ) + a} \left (e \tan \left (d x + c\right )\right )^{m}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (e \tan{\left (c + d x \right )}\right )^{m} \sqrt{a + b \sec{\left (c + d x \right )}}\, dx \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 \sqrt{b \sec \left (d x + c\right ) + a} \left (e \tan \left (d x + c\right )\right )^{m}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]