Integrand size = 16, antiderivative size = 16 \[ \int (c+d x)^m \cot ^2(a+b x) \, dx=\text {Int}\left ((c+d x)^m \cot ^2(a+b x),x\right ) \]
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Not integrable
Time = 0.04 (sec) , antiderivative size = 16, 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 = {} \[ \int (c+d x)^m \cot ^2(a+b x) \, dx=\int (c+d x)^m \cot ^2(a+b x) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int (c+d x)^m \cot ^2(a+b x) \, dx \\ \end{align*}
Not integrable
Time = 1.29 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \cot ^2(a+b x) \, dx=\int (c+d x)^m \cot ^2(a+b x) \, dx \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00
\[\int \left (d x +c \right )^{m} \cot \left (x b +a \right )^{2}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \cot ^2(a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \cot \left (b x + a\right )^{2} \,d x } \]
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Not integrable
Time = 1.54 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int (c+d x)^m \cot ^2(a+b x) \, dx=\int \left (c + d x\right )^{m} \cot ^{2}{\left (a + b x \right )}\, dx \]
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Not integrable
Time = 0.57 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \cot ^2(a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \cot \left (b x + a\right )^{2} \,d x } \]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \cot ^2(a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \cot \left (b x + a\right )^{2} \,d x } \]
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Not integrable
Time = 22.99 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \cot ^2(a+b x) \, dx=\int {\mathrm {cot}\left (a+b\,x\right )}^2\,{\left (c+d\,x\right )}^m \,d x \]
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