Integrand size = 20, antiderivative size = 20 \[ \int \frac {(c+d x)^m}{a+a \sec (e+f x)} \, dx=\text {Int}\left (\frac {(c+d x)^m}{a+a \sec (e+f x)},x\right ) \]
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Not integrable
Time = 0.06 (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 = {} \[ \int \frac {(c+d x)^m}{a+a \sec (e+f x)} \, dx=\int \frac {(c+d x)^m}{a+a \sec (e+f x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(c+d x)^m}{a+a \sec (e+f x)} \, dx \\ \end{align*}
Not integrable
Time = 1.22 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(c+d x)^m}{a+a \sec (e+f x)} \, dx=\int \frac {(c+d x)^m}{a+a \sec (e+f x)} \, dx \]
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Not integrable
Time = 0.18 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00
\[\int \frac {\left (d x +c \right )^{m}}{a +a \sec \left (f x +e \right )}d x\]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(c+d x)^m}{a+a \sec (e+f x)} \, dx=\int { \frac {{\left (d x + c\right )}^{m}}{a \sec \left (f x + e\right ) + a} \,d x } \]
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Not integrable
Time = 1.82 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85 \[ \int \frac {(c+d x)^m}{a+a \sec (e+f x)} \, dx=\frac {\int \frac {\left (c + d x\right )^{m}}{\sec {\left (e + f x \right )} + 1}\, dx}{a} \]
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Not integrable
Time = 0.57 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(c+d x)^m}{a+a \sec (e+f x)} \, dx=\int { \frac {{\left (d x + c\right )}^{m}}{a \sec \left (f x + e\right ) + a} \,d x } \]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(c+d x)^m}{a+a \sec (e+f x)} \, dx=\int { \frac {{\left (d x + c\right )}^{m}}{a \sec \left (f x + e\right ) + a} \,d x } \]
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Not integrable
Time = 13.38 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.20 \[ \int \frac {(c+d x)^m}{a+a \sec (e+f x)} \, dx=\int \frac {{\left (c+d\,x\right )}^m}{a+\frac {a}{\cos \left (e+f\,x\right )}} \,d x \]
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