Integrand size = 10, antiderivative size = 10 \[ \int x^m \tanh (a+b x) \, dx=\text {Int}\left (x^m \tanh (a+b x),x\right ) \]
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Not integrable
Time = 0.01 (sec) , antiderivative size = 10, 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 = {} \[ \int x^m \tanh (a+b x) \, dx=\int x^m \tanh (a+b x) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int x^m \tanh (a+b x) \, dx \\ \end{align*}
Not integrable
Time = 0.34 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \tanh (a+b x) \, dx=\int x^m \tanh (a+b x) \, dx \]
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Not integrable
Time = 0.13 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.60
\[\int x^{m} \operatorname {sech}\left (b x +a \right ) \sinh \left (b x +a \right )d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.80 \[ \int x^m \tanh (a+b x) \, dx=\int { x^{m} \operatorname {sech}\left (b x + a\right ) \sinh \left (b x + a\right ) \,d x } \]
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Not integrable
Time = 10.12 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.70 \[ \int x^m \tanh (a+b x) \, dx=\int x^{m} \sinh {\left (a + b x \right )} \operatorname {sech}{\left (a + b x \right )}\, dx \]
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Not integrable
Time = 0.49 (sec) , antiderivative size = 100, normalized size of antiderivative = 10.00 \[ \int x^m \tanh (a+b x) \, dx=\int { x^{m} \operatorname {sech}\left (b x + a\right ) \sinh \left (b x + a\right ) \,d x } \]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.80 \[ \int x^m \tanh (a+b x) \, dx=\int { x^{m} \operatorname {sech}\left (b x + a\right ) \sinh \left (b x + a\right ) \,d x } \]
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Not integrable
Time = 2.17 (sec) , antiderivative size = 20, normalized size of antiderivative = 2.00 \[ \int x^m \tanh (a+b x) \, dx=\int \frac {x^m\,\mathrm {sinh}\left (a+b\,x\right )}{\mathrm {cosh}\left (a+b\,x\right )} \,d x \]
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