Integrand size = 16, antiderivative size = 16 \[ \int \frac {\sec ^2(a+b x)}{c+d x} \, dx=\text {Int}\left (\frac {\sec ^2(a+b x)}{c+d x},x\right ) \]
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Not integrable
Time = 0.05 (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 = {} \[ \int \frac {\sec ^2(a+b x)}{c+d x} \, dx=\int \frac {\sec ^2(a+b x)}{c+d x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\sec ^2(a+b x)}{c+d x} \, dx \\ \end{align*}
Not integrable
Time = 6.06 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\sec ^2(a+b x)}{c+d x} \, dx=\int \frac {\sec ^2(a+b x)}{c+d x} \, dx \]
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Not integrable
Time = 0.53 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00
\[\int \frac {\sec ^{2}\left (b x +a \right )}{d x +c}d x\]
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Not integrable
Time = 0.29 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\sec ^2(a+b x)}{c+d x} \, dx=\int { \frac {\sec \left (b x + a\right )^{2}}{d x + c} \,d x } \]
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Not integrable
Time = 0.41 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {\sec ^2(a+b x)}{c+d x} \, dx=\int \frac {\sec ^{2}{\left (a + b x \right )}}{c + d x}\, dx \]
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Not integrable
Time = 0.55 (sec) , antiderivative size = 290, normalized size of antiderivative = 18.12 \[ \int \frac {\sec ^2(a+b x)}{c+d x} \, dx=\int { \frac {\sec \left (b x + a\right )^{2}}{d x + c} \,d x } \]
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Not integrable
Time = 0.38 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\sec ^2(a+b x)}{c+d x} \, dx=\int { \frac {\sec \left (b x + a\right )^{2}}{d x + c} \,d x } \]
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Not integrable
Time = 13.70 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\sec ^2(a+b x)}{c+d x} \, dx=\int \frac {1}{{\cos \left (a+b\,x\right )}^2\,\left (c+d\,x\right )} \,d x \]
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