Integrand size = 20, antiderivative size = 20 \[ \int (c+d x)^m \sec (a+b x) \tan (a+b x) \, dx=\text {Int}\left ((c+d x)^m \sec (a+b x) \tan (a+b x),x\right ) \]
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Not integrable
Time = 0.18 (sec) , antiderivative size = 20, 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 = {} \[ \int (c+d x)^m \sec (a+b x) \tan (a+b x) \, dx=\int (c+d x)^m \sec (a+b x) \tan (a+b x) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int (c+d x)^m \sec (a+b x) \tan (a+b x) \, dx \\ \end{align*}
Not integrable
Time = 3.09 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m \sec (a+b x) \tan (a+b x) \, dx=\int (c+d x)^m \sec (a+b x) \tan (a+b x) \, dx \]
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Not integrable
Time = 0.29 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00
\[\int \left (d x +c \right )^{m} \sec \left (x b +a \right ) \tan \left (x b +a \right )d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m \sec (a+b x) \tan (a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \sec \left (b x + a\right ) \tan \left (b x + a\right ) \,d x } \]
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Not integrable
Time = 3.97 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int (c+d x)^m \sec (a+b x) \tan (a+b x) \, dx=\int \left (c + d x\right )^{m} \tan {\left (a + b x \right )} \sec {\left (a + b x \right )}\, dx \]
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Not integrable
Time = 0.64 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m \sec (a+b x) \tan (a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \sec \left (b x + a\right ) \tan \left (b x + a\right ) \,d x } \]
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Not integrable
Time = 0.34 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m \sec (a+b x) \tan (a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \sec \left (b x + a\right ) \tan \left (b x + a\right ) \,d x } \]
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Not integrable
Time = 23.76 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.20 \[ \int (c+d x)^m \sec (a+b x) \tan (a+b x) \, dx=\int \frac {\mathrm {tan}\left (a+b\,x\right )\,{\left (c+d\,x\right )}^m}{\cos \left (a+b\,x\right )} \,d x \]
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