Integrand size = 29, antiderivative size = 29 \[ \int \frac {\sinh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx=\text {Int}\left (\frac {\sinh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))},x\right ) \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 29, 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 = {} \[ \int \frac {\sinh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx=\int \frac {\sinh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\sinh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx \\ \end{align*}
Not integrable
Time = 37.76 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.07 \[ \int \frac {\sinh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx=\int \frac {\sinh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx \]
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Not integrable
Time = 0.46 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.93
\[\int \frac {\sinh \left (d x +c \right )}{\left (f x +e \right ) \left (a +i a \sinh \left (d x +c \right )\right )}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 154, normalized size of antiderivative = 5.31 \[ \int \frac {\sinh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx=\int { \frac {\sinh \left (d x + c\right )}{{\left (f x + e\right )} {\left (i \, a \sinh \left (d x + c\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 12.08 (sec) , antiderivative size = 425, normalized size of antiderivative = 14.66 \[ \int \frac {\sinh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx=- \frac {2}{- i a d e - i a d f x + \left (a d e e^{c} + a d f x e^{c}\right ) e^{d x}} - \frac {i \left (\int \left (- \frac {2 i f}{e^{2} e^{c} e^{d x} - i e^{2} + 2 e f x e^{c} e^{d x} - 2 i e f x + f^{2} x^{2} e^{c} e^{d x} - i f^{2} x^{2}}\right )\, dx + \int \left (- \frac {i d e}{e^{2} e^{c} e^{d x} - i e^{2} + 2 e f x e^{c} e^{d x} - 2 i e f x + f^{2} x^{2} e^{c} e^{d x} - i f^{2} x^{2}}\right )\, dx + \int \left (- \frac {i d f x}{e^{2} e^{c} e^{d x} - i e^{2} + 2 e f x e^{c} e^{d x} - 2 i e f x + f^{2} x^{2} e^{c} e^{d x} - i f^{2} x^{2}}\right )\, dx + \int \frac {d e e^{c} e^{d x}}{e^{2} e^{c} e^{d x} - i e^{2} + 2 e f x e^{c} e^{d x} - 2 i e f x + f^{2} x^{2} e^{c} e^{d x} - i f^{2} x^{2}}\, dx + \int \frac {d f x e^{c} e^{d x}}{e^{2} e^{c} e^{d x} - i e^{2} + 2 e f x e^{c} e^{d x} - 2 i e f x + f^{2} x^{2} e^{c} e^{d x} - i f^{2} x^{2}}\, dx\right )}{a d} \]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 116, normalized size of antiderivative = 4.00 \[ \int \frac {\sinh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx=\int { \frac {\sinh \left (d x + c\right )}{{\left (f x + e\right )} {\left (i \, a \sinh \left (d x + c\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.00 \[ \int \frac {\sinh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx=\int { \frac {\sinh \left (d x + c\right )}{{\left (f x + e\right )} {\left (i \, a \sinh \left (d x + c\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 1.01 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.03 \[ \int \frac {\sinh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx=\int \frac {\mathrm {sinh}\left (c+d\,x\right )}{\left (e+f\,x\right )\,\left (a+a\,\mathrm {sinh}\left (c+d\,x\right )\,1{}\mathrm {i}\right )} \,d x \]
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