Integrand size = 14, antiderivative size = 14 \[ \int (c+d x)^m \cot (a+b x) \, dx=\text {Int}\left ((c+d x)^m \cot (a+b x),x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 14, 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 = {} \[ \int (c+d x)^m \cot (a+b x) \, dx=\int (c+d x)^m \cot (a+b x) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int (c+d x)^m \cot (a+b x) \, dx \\ \end{align*}
Not integrable
Time = 3.55 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int (c+d x)^m \cot (a+b x) \, dx=\int (c+d x)^m \cot (a+b x) \, dx \]
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Not integrable
Time = 0.29 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.43
\[\int \left (d x +c \right )^{m} \cos \left (x b +a \right ) \csc \left (x b +a \right )d x\]
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Not integrable
Time = 0.23 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.57 \[ \int (c+d x)^m \cot (a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \cos \left (b x + a\right ) \csc \left (b x + a\right ) \,d x } \]
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Not integrable
Time = 18.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.43 \[ \int (c+d x)^m \cot (a+b x) \, dx=\int \left (c + d x\right )^{m} \cos {\left (a + b x \right )} \csc {\left (a + b x \right )}\, dx \]
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Not integrable
Time = 0.38 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.57 \[ \int (c+d x)^m \cot (a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \cos \left (b x + a\right ) \csc \left (b x + a\right ) \,d x } \]
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Not integrable
Time = 0.29 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.57 \[ \int (c+d x)^m \cot (a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \cos \left (b x + a\right ) \csc \left (b x + a\right ) \,d x } \]
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Not integrable
Time = 23.55 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.71 \[ \int (c+d x)^m \cot (a+b x) \, dx=\int \frac {\cos \left (a+b\,x\right )\,{\left (c+d\,x\right )}^m}{\sin \left (a+b\,x\right )} \,d x \]
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