Integrand size = 22, antiderivative size = 22 \[ \int (c+d x)^m \csc ^2(a+b x) \sec (a+b x) \, dx=\text {Int}\left ((c+d x)^m \csc ^2(a+b x) \sec (a+b x),x\right ) \]
[Out]
Not integrable
Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int (c+d x)^m \csc ^2(a+b x) \sec (a+b x) \, dx=\int (c+d x)^m \csc ^2(a+b x) \sec (a+b x) \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int (c+d x)^m \csc ^2(a+b x) \sec (a+b x) \, dx \\ \end{align*}
Not integrable
Time = 23.11 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int (c+d x)^m \csc ^2(a+b x) \sec (a+b x) \, dx=\int (c+d x)^m \csc ^2(a+b x) \sec (a+b x) \, dx \]
[In]
[Out]
Not integrable
Time = 0.29 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00
\[\int \left (d x +c \right )^{m} \csc \left (x b +a \right )^{2} \sec \left (x b +a \right )d x\]
[In]
[Out]
Not integrable
Time = 0.24 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int (c+d x)^m \csc ^2(a+b x) \sec (a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \csc \left (b x + a\right )^{2} \sec \left (b x + a\right ) \,d x } \]
[In]
[Out]
Not integrable
Time = 118.63 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int (c+d x)^m \csc ^2(a+b x) \sec (a+b x) \, dx=\int \left (c + d x\right )^{m} \csc ^{2}{\left (a + b x \right )} \sec {\left (a + b x \right )}\, dx \]
[In]
[Out]
Not integrable
Time = 0.54 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int (c+d x)^m \csc ^2(a+b x) \sec (a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \csc \left (b x + a\right )^{2} \sec \left (b x + a\right ) \,d x } \]
[In]
[Out]
Not integrable
Time = 0.33 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int (c+d x)^m \csc ^2(a+b x) \sec (a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \csc \left (b x + a\right )^{2} \sec \left (b x + a\right ) \,d x } \]
[In]
[Out]
Not integrable
Time = 25.45 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.18 \[ \int (c+d x)^m \csc ^2(a+b x) \sec (a+b x) \, dx=\int \frac {{\left (c+d\,x\right )}^m}{\cos \left (a+b\,x\right )\,{\sin \left (a+b\,x\right )}^2} \,d x \]
[In]
[Out]