Integrand size = 20, antiderivative size = 20 \[ \int (c+d x)^m (a+a \sin (e+f x))^n \, dx=\text {Int}\left ((c+d x)^m (a+a \sin (e+f x))^n,x\right ) \]
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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 = {} \[ \int (c+d x)^m (a+a \sin (e+f x))^n \, dx=\int (c+d x)^m (a+a \sin (e+f x))^n \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int (c+d x)^m (a+a \sin (e+f x))^n \, dx \\ \end{align*}
Not integrable
Time = 0.73 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m (a+a \sin (e+f x))^n \, dx=\int (c+d x)^m (a+a \sin (e+f x))^n \, dx \]
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Not integrable
Time = 0.06 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00
\[\int \left (d x +c \right )^{m} \left (a +a \sin \left (f x +e \right )\right )^{n}d x\]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m (a+a \sin (e+f x))^n \, dx=\int { {\left (d x + c\right )}^{m} {\left (a \sin \left (f x + e\right ) + a\right )}^{n} \,d x } \]
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Timed out. \[ \int (c+d x)^m (a+a \sin (e+f x))^n \, dx=\text {Timed out} \]
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Not integrable
Time = 0.64 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m (a+a \sin (e+f x))^n \, dx=\int { {\left (d x + c\right )}^{m} {\left (a \sin \left (f x + e\right ) + a\right )}^{n} \,d x } \]
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Not integrable
Time = 1.14 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m (a+a \sin (e+f x))^n \, dx=\int { {\left (d x + c\right )}^{m} {\left (a \sin \left (f x + e\right ) + a\right )}^{n} \,d x } \]
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Not integrable
Time = 0.67 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m (a+a \sin (e+f x))^n \, dx=\int {\left (a+a\,\sin \left (e+f\,x\right )\right )}^n\,{\left (c+d\,x\right )}^m \,d x \]
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