Optimal. Leaf size=22 \[ \text{CannotIntegrate}\left (\frac{\cot (a+b x) \csc (a+b x)}{(c+d x)^2},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.152228, 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 = {} \[ \int \frac{\cot (a+b x) \csc (a+b x)}{(c+d x)^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{\cot (a+b x) \csc (a+b x)}{(c+d x)^2} \, dx &=\int \frac{\cot (a+b x) \csc (a+b x)}{(c+d x)^2} \, dx\\ \end{align*}
Mathematica [A] time = 20.204, size = 0, normalized size = 0. \[ \int \frac{\cot (a+b x) \csc (a+b x)}{(c+d x)^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.411, size = 0, normalized size = 0. \begin{align*} \int{\frac{\cos \left ( bx+a \right ) \left ( \csc \left ( bx+a \right ) \right ) ^{2}}{ \left ( dx+c \right ) ^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [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]
________________________________________________________________________________________
Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\cos \left (b x + a\right ) \csc \left (b x + a\right )^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, 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 \frac{\cos{\left (a + b x \right )} \csc ^{2}{\left (a + b x \right )}}{\left (c + d x\right )^{2}}\, 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 \frac{\cos \left (b x + a\right ) \csc \left (b x + a\right )^{2}}{{\left (d x + c\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]