Integrand size = 18, antiderivative size = 18 \[ \int \frac {a+a \sec (e+f x)}{c+d x} \, dx=\text {Int}\left (\frac {a+a \sec (e+f x)}{c+d x},x\right ) \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 18, 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 = {} \[ \int \frac {a+a \sec (e+f x)}{c+d x} \, dx=\int \frac {a+a \sec (e+f x)}{c+d x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {a+a \sec (e+f x)}{c+d x} \, dx \\ \end{align*}
Not integrable
Time = 6.84 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {a+a \sec (e+f x)}{c+d x} \, dx=\int \frac {a+a \sec (e+f x)}{c+d x} \, dx \]
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Not integrable
Time = 0.44 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00
\[\int \frac {a +a \sec \left (f x +e \right )}{d x +c}d x\]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {a+a \sec (e+f x)}{c+d x} \, dx=\int { \frac {a \sec \left (f x + e\right ) + a}{d x + c} \,d x } \]
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Not integrable
Time = 0.66 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {a+a \sec (e+f x)}{c+d x} \, dx=a \left (\int \frac {\sec {\left (e + f x \right )}}{c + d x}\, dx + \int \frac {1}{c + d x}\, dx\right ) \]
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Not integrable
Time = 0.54 (sec) , antiderivative size = 116, normalized size of antiderivative = 6.44 \[ \int \frac {a+a \sec (e+f x)}{c+d x} \, dx=\int { \frac {a \sec \left (f x + e\right ) + a}{d x + c} \,d x } \]
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Not integrable
Time = 0.40 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {a+a \sec (e+f x)}{c+d x} \, dx=\int { \frac {a \sec \left (f x + e\right ) + a}{d x + c} \,d x } \]
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Not integrable
Time = 12.77 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {a+a \sec (e+f x)}{c+d x} \, dx=\int \frac {a+\frac {a}{\cos \left (e+f\,x\right )}}{c+d\,x} \,d x \]
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