Integrand size = 16, antiderivative size = 16 \[ \int \frac {\text {sech}^2(a+b x)}{(c+d x)^2} \, dx=\text {Int}\left (\frac {\text {sech}^2(a+b x)}{(c+d x)^2},x\right ) \]
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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 = {} \[ \int \frac {\text {sech}^2(a+b x)}{(c+d x)^2} \, dx=\int \frac {\text {sech}^2(a+b x)}{(c+d x)^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\text {sech}^2(a+b x)}{(c+d x)^2} \, dx \\ \end{align*}
Not integrable
Time = 25.79 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {sech}^2(a+b x)}{(c+d x)^2} \, dx=\int \frac {\text {sech}^2(a+b x)}{(c+d x)^2} \, dx \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00
\[\int \frac {\operatorname {sech}\left (b x +a \right )^{2}}{\left (d x +c \right )^{2}}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.81 \[ \int \frac {\text {sech}^2(a+b x)}{(c+d x)^2} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{2}}{{\left (d x + c\right )}^{2}} \,d x } \]
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Not integrable
Time = 0.67 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \frac {\text {sech}^2(a+b x)}{(c+d x)^2} \, dx=\int \frac {\operatorname {sech}^{2}{\left (a + b x \right )}}{\left (c + d x\right )^{2}}\, dx \]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 156, normalized size of antiderivative = 9.75 \[ \int \frac {\text {sech}^2(a+b x)}{(c+d x)^2} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{2}}{{\left (d x + c\right )}^{2}} \,d x } \]
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Not integrable
Time = 0.33 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {sech}^2(a+b x)}{(c+d x)^2} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{2}}{{\left (d x + c\right )}^{2}} \,d x } \]
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Not integrable
Time = 1.80 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {sech}^2(a+b x)}{(c+d x)^2} \, dx=\int \frac {1}{{\mathrm {cosh}\left (a+b\,x\right )}^2\,{\left (c+d\,x\right )}^2} \,d x \]
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