Optimal. Leaf size=23 \[ \text{Unintegrable}\left (\sin ^2(e+f x) (a+b \csc (e+f x))^m,x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.040237, 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 = {} \[ \int (a+b \csc (e+f x))^m \sin ^2(e+f x) \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int (a+b \csc (e+f x))^m \sin ^2(e+f x) \, dx &=\int (a+b \csc (e+f x))^m \sin ^2(e+f x) \, dx\\ \end{align*}
Mathematica [A] time = 5.90403, size = 0, normalized size = 0. \[ \int (a+b \csc (e+f x))^m \sin ^2(e+f x) \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.567, size = 0, normalized size = 0. \begin{align*} \int \left ( a+b\csc \left ( fx+e \right ) \right ) ^{m} \left ( \sin \left ( fx+e \right ) \right ) ^{2}\, 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 \csc \left (f x + e\right ) + a\right )}^{m} \sin \left (f x + e\right )^{2}\,{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 (\cos \left (f x + e\right )^{2} - 1\right )}{\left (b \csc \left (f x + e\right ) + a\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 \csc \left (f x + e\right ) + a\right )}^{m} \sin \left (f x + e\right )^{2}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]