Integrand size = 24, antiderivative size = 24 \[ \int \frac {x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx=\text {Int}\left (\frac {x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)},x\right ) \]
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Not integrable
Time = 0.05 (sec) , antiderivative size = 24, 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 = {} \[ \int \frac {x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx=\int \frac {x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx \\ \end{align*}
Not integrable
Time = 10.68 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx=\int \frac {x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx \]
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Not integrable
Time = 0.18 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00
\[\int \frac {x^{m} \sinh \left (d x +c \right )^{3}}{a +b \cosh \left (d x +c \right )}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx=\int { \frac {x^{m} \sinh \left (d x + c\right )^{3}}{b \cosh \left (d x + c\right ) + a} \,d x } \]
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Not integrable
Time = 2.51 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx=\int \frac {x^{m} \sinh ^{3}{\left (c + d x \right )}}{a + b \cosh {\left (c + d x \right )}}\, dx \]
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Not integrable
Time = 0.40 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx=\int { \frac {x^{m} \sinh \left (d x + c\right )^{3}}{b \cosh \left (d x + c\right ) + a} \,d x } \]
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Not integrable
Time = 0.29 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx=\int { \frac {x^{m} \sinh \left (d x + c\right )^{3}}{b \cosh \left (d x + c\right ) + a} \,d x } \]
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Not integrable
Time = 1.76 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx=\int \frac {x^m\,{\mathrm {sinh}\left (c+d\,x\right )}^3}{a+b\,\mathrm {cosh}\left (c+d\,x\right )} \,d x \]
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