Integrand size = 16, antiderivative size = 16 \[ \int (c+d x)^m \text {sech}^2(a+b x) \, dx=\text {Int}\left ((c+d x)^m \text {sech}^2(a+b x),x\right ) \]
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Not integrable
Time = 0.02 (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 = {} \[ \int (c+d x)^m \text {sech}^2(a+b x) \, dx=\int (c+d x)^m \text {sech}^2(a+b x) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int (c+d x)^m \text {sech}^2(a+b x) \, dx \\ \end{align*}
Not integrable
Time = 3.01 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \text {sech}^2(a+b x) \, dx=\int (c+d x)^m \text {sech}^2(a+b x) \, dx \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00
\[\int \left (d x +c \right )^{m} \operatorname {sech}\left (b x +a \right )^{2}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \text {sech}^2(a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \operatorname {sech}\left (b x + a\right )^{2} \,d x } \]
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Not integrable
Time = 4.18 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int (c+d x)^m \text {sech}^2(a+b x) \, dx=\int \left (c + d x\right )^{m} \operatorname {sech}^{2}{\left (a + b x \right )}\, dx \]
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Not integrable
Time = 0.29 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \text {sech}^2(a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \operatorname {sech}\left (b x + a\right )^{2} \,d x } \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \text {sech}^2(a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \operatorname {sech}\left (b x + a\right )^{2} \,d x } \]
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Not integrable
Time = 1.80 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \text {sech}^2(a+b x) \, dx=\int \frac {{\left (c+d\,x\right )}^m}{{\mathrm {cosh}\left (a+b\,x\right )}^2} \,d x \]
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