Integrand size = 14, antiderivative size = 14 \[ \int \frac {\cot (a+b x)}{c+d x} \, dx=\text {Int}\left (\frac {\cot (a+b x)}{c+d x},x\right ) \]
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Not integrable
Time = 0.03 (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 = {} \[ \int \frac {\cot (a+b x)}{c+d x} \, dx=\int \frac {\cot (a+b x)}{c+d x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\cot (a+b x)}{c+d x} \, dx \\ \end{align*}
Not integrable
Time = 4.96 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {\cot (a+b x)}{c+d x} \, dx=\int \frac {\cot (a+b x)}{c+d x} \, dx \]
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Not integrable
Time = 0.56 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.43
\[\int \frac {\cos \left (x b +a \right ) \csc \left (x b +a \right )}{d x +c}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.57 \[ \int \frac {\cot (a+b x)}{c+d x} \, dx=\int { \frac {\cos \left (b x + a\right ) \csc \left (b x + a\right )}{d x + c} \,d x } \]
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Not integrable
Time = 0.56 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.36 \[ \int \frac {\cot (a+b x)}{c+d x} \, dx=\int \frac {\cos {\left (a + b x \right )} \csc {\left (a + b x \right )}}{c + d x}\, dx \]
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Not integrable
Time = 0.42 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.57 \[ \int \frac {\cot (a+b x)}{c+d x} \, dx=\int { \frac {\cos \left (b x + a\right ) \csc \left (b x + a\right )}{d x + c} \,d x } \]
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Not integrable
Time = 0.29 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.57 \[ \int \frac {\cot (a+b x)}{c+d x} \, dx=\int { \frac {\cos \left (b x + a\right ) \csc \left (b x + a\right )}{d x + c} \,d x } \]
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Not integrable
Time = 22.97 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.71 \[ \int \frac {\cot (a+b x)}{c+d x} \, dx=\int \frac {\cos \left (a+b\,x\right )}{\sin \left (a+b\,x\right )\,\left (c+d\,x\right )} \,d x \]
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