Integrand size = 16, antiderivative size = 16 \[ \int \frac {\text {sech}^3(a+b x)}{c+d x} \, dx=\text {Int}\left (\frac {\text {sech}^3(a+b x)}{c+d x},x\right ) \]
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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 = {} \[ \int \frac {\text {sech}^3(a+b x)}{c+d x} \, dx=\int \frac {\text {sech}^3(a+b x)}{c+d x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\text {sech}^3(a+b x)}{c+d x} \, dx \\ \end{align*}
Not integrable
Time = 124.56 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {sech}^3(a+b x)}{c+d x} \, dx=\int \frac {\text {sech}^3(a+b x)}{c+d x} \, dx \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00
\[\int \frac {\operatorname {sech}\left (b x +a \right )^{3}}{d x +c}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {sech}^3(a+b x)}{c+d x} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{3}}{d x + c} \,d x } \]
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Not integrable
Time = 0.52 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {\text {sech}^3(a+b x)}{c+d x} \, dx=\int \frac {\operatorname {sech}^{3}{\left (a + b x \right )}}{c + d x}\, dx \]
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Not integrable
Time = 0.44 (sec) , antiderivative size = 321, normalized size of antiderivative = 20.06 \[ \int \frac {\text {sech}^3(a+b x)}{c+d x} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{3}}{d x + c} \,d x } \]
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Not integrable
Time = 2.52 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {sech}^3(a+b x)}{c+d x} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{3}}{d x + c} \,d x } \]
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Not integrable
Time = 1.74 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {sech}^3(a+b x)}{c+d x} \, dx=\int \frac {1}{{\mathrm {cosh}\left (a+b\,x\right )}^3\,\left (c+d\,x\right )} \,d x \]
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