Integrand size = 16, antiderivative size = 16 \[ \int \frac {\text {sech}^2(a+b x)}{c+d x} \, dx=\text {Int}\left (\frac {\text {sech}^2(a+b x)}{c+d x},x\right ) \]
[Out]
Not integrable
Time = 0.03 (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 = {} \[ \int \frac {\text {sech}^2(a+b x)}{c+d x} \, dx=\int \frac {\text {sech}^2(a+b x)}{c+d x} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {\text {sech}^2(a+b x)}{c+d x} \, dx \\ \end{align*}
Not integrable
Time = 25.54 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {sech}^2(a+b x)}{c+d x} \, dx=\int \frac {\text {sech}^2(a+b x)}{c+d x} \, dx \]
[In]
[Out]
Not integrable
Time = 0.03 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00
\[\int \frac {\operatorname {sech}\left (b x +a \right )^{2}}{d x +c}d x\]
[In]
[Out]
Not integrable
Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {sech}^2(a+b x)}{c+d x} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{2}}{d x + c} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.49 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {\text {sech}^2(a+b x)}{c+d x} \, dx=\int \frac {\operatorname {sech}^{2}{\left (a + b x \right )}}{c + d x}\, dx \]
[In]
[Out]
Not integrable
Time = 0.27 (sec) , antiderivative size = 102, normalized size of antiderivative = 6.38 \[ \int \frac {\text {sech}^2(a+b x)}{c+d x} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{2}}{d x + c} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.27 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {sech}^2(a+b x)}{c+d x} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{2}}{d x + c} \,d x } \]
[In]
[Out]
Not integrable
Time = 1.76 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {sech}^2(a+b x)}{c+d x} \, dx=\int \frac {1}{{\mathrm {cosh}\left (a+b\,x\right )}^2\,\left (c+d\,x\right )} \,d x \]
[In]
[Out]