Integrand size = 24, antiderivative size = 24 \[ \int \frac {x^m \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx=\text {Int}\left (\frac {x^m \cosh ^3(c+d x)}{a+b \sinh (c+d x)},x\right ) \]
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Not integrable
Time = 0.04 (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 = {} \[ \int \frac {x^m \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx=\int \frac {x^m \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {x^m \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx \\ \end{align*}
Not integrable
Time = 10.44 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {x^m \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx=\int \frac {x^m \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx \]
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Not integrable
Time = 0.68 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00
\[\int \frac {x^{m} \cosh \left (d x +c \right )^{3}}{a +b \sinh \left (d x +c \right )}d x\]
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Not integrable
Time = 0.23 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {x^m \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx=\int { \frac {x^{m} \cosh \left (d x + c\right )^{3}}{b \sinh \left (d x + c\right ) + a} \,d x } \]
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Not integrable
Time = 2.71 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {x^m \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx=\int \frac {x^{m} \cosh ^{3}{\left (c + d x \right )}}{a + b \sinh {\left (c + d x \right )}}\, dx \]
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Not integrable
Time = 0.39 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {x^m \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx=\int { \frac {x^{m} \cosh \left (d x + c\right )^{3}}{b \sinh \left (d x + c\right ) + a} \,d x } \]
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Not integrable
Time = 0.38 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {x^m \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx=\int { \frac {x^{m} \cosh \left (d x + c\right )^{3}}{b \sinh \left (d x + c\right ) + a} \,d x } \]
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Not integrable
Time = 1.04 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {x^m \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx=\int \frac {x^m\,{\mathrm {cosh}\left (c+d\,x\right )}^3}{a+b\,\mathrm {sinh}\left (c+d\,x\right )} \,d x \]
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