Integrand size = 16, antiderivative size = 16 \[ \int x^m \text {sech}(a+b x) \tanh (a+b x) \, dx=\text {Int}\left (x^m \text {sech}(a+b x) \tanh (a+b x),x\right ) \]
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Not integrable
Time = 0.30 (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 = {} \[ \int x^m \text {sech}(a+b x) \tanh (a+b x) \, dx=\int x^m \text {sech}(a+b x) \tanh (a+b x) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int x^m \text {sech}(a+b x) \tanh (a+b x) \, dx \\ \end{align*}
Not integrable
Time = 48.18 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int x^m \text {sech}(a+b x) \tanh (a+b x) \, dx=\int x^m \text {sech}(a+b x) \tanh (a+b x) \, dx \]
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Not integrable
Time = 0.12 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12
\[\int x^{m} \operatorname {sech}\left (b x +a \right )^{2} \sinh \left (b x +a \right )d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.25 \[ \int x^m \text {sech}(a+b x) \tanh (a+b x) \, dx=\int { x^{m} \operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right ) \,d x } \]
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Not integrable
Time = 35.58 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.19 \[ \int x^m \text {sech}(a+b x) \tanh (a+b x) \, dx=\int x^{m} \sinh {\left (a + b x \right )} \operatorname {sech}^{2}{\left (a + b x \right )}\, dx \]
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Not integrable
Time = 0.36 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.25 \[ \int x^m \text {sech}(a+b x) \tanh (a+b x) \, dx=\int { x^{m} \operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right ) \,d x } \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.25 \[ \int x^m \text {sech}(a+b x) \tanh (a+b x) \, dx=\int { x^{m} \operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right ) \,d x } \]
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Not integrable
Time = 2.21 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.25 \[ \int x^m \text {sech}(a+b x) \tanh (a+b x) \, dx=\int \frac {x^m\,\mathrm {sinh}\left (a+b\,x\right )}{{\mathrm {cosh}\left (a+b\,x\right )}^2} \,d x \]
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