Integrand size = 20, antiderivative size = 20 \[ \int (c+d x)^m (a+b \sinh (e+f x))^n \, dx=\text {Int}\left ((c+d x)^m (a+b \sinh (e+f x))^n,x\right ) \]
[Out]
Not integrable
Time = 0.03 (sec) , antiderivative size = 20, 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 = {} \[ \int (c+d x)^m (a+b \sinh (e+f x))^n \, dx=\int (c+d x)^m (a+b \sinh (e+f x))^n \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int (c+d x)^m (a+b \sinh (e+f x))^n \, dx \\ \end{align*}
Not integrable
Time = 3.17 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m (a+b \sinh (e+f x))^n \, dx=\int (c+d x)^m (a+b \sinh (e+f x))^n \, dx \]
[In]
[Out]
Not integrable
Time = 0.44 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00
\[\int \left (d x +c \right )^{m} \left (a +b \sinh \left (f x +e \right )\right )^{n}d x\]
[In]
[Out]
Not integrable
Time = 0.26 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m (a+b \sinh (e+f x))^n \, dx=\int { {\left (d x + c\right )}^{m} {\left (b \sinh \left (f x + e\right ) + a\right )}^{n} \,d x } \]
[In]
[Out]
Timed out. \[ \int (c+d x)^m (a+b \sinh (e+f x))^n \, dx=\text {Timed out} \]
[In]
[Out]
Not integrable
Time = 0.34 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m (a+b \sinh (e+f x))^n \, dx=\int { {\left (d x + c\right )}^{m} {\left (b \sinh \left (f x + e\right ) + a\right )}^{n} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.41 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m (a+b \sinh (e+f x))^n \, dx=\int { {\left (d x + c\right )}^{m} {\left (b \sinh \left (f x + e\right ) + a\right )}^{n} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.98 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m (a+b \sinh (e+f x))^n \, dx=\int {\left (a+b\,\mathrm {sinh}\left (e+f\,x\right )\right )}^n\,{\left (c+d\,x\right )}^m \,d x \]
[In]
[Out]