Integrand size = 25, antiderivative size = 25 \[ \int \frac {(3+b \sin (e+f x))^m}{c+d \sin (e+f x)} \, dx=\text {Int}\left (\frac {(3+b \sin (e+f x))^m}{c+d \sin (e+f x)},x\right ) \]
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Not integrable
Time = 0.04 (sec) , antiderivative size = 25, 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 = {} \[ \int \frac {(3+b \sin (e+f x))^m}{c+d \sin (e+f x)} \, dx=\int \frac {(a+b \sin (e+f x))^m}{c+d \sin (e+f x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(a+b \sin (e+f x))^m}{c+d \sin (e+f x)} \, dx \\ \end{align*}
Not integrable
Time = 4.82 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {(3+b \sin (e+f x))^m}{c+d \sin (e+f x)} \, dx=\int \frac {(3+b \sin (e+f x))^m}{c+d \sin (e+f x)} \, dx \]
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Not integrable
Time = 0.94 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00
\[\int \frac {\left (a +b \sin \left (f x +e \right )\right )^{m}}{c +d \sin \left (f x +e \right )}d x\]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {(3+b \sin (e+f x))^m}{c+d \sin (e+f x)} \, dx=\int { \frac {{\left (b \sin \left (f x + e\right ) + a\right )}^{m}}{d \sin \left (f x + e\right ) + c} \,d x } \]
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Timed out. \[ \int \frac {(3+b \sin (e+f x))^m}{c+d \sin (e+f x)} \, dx=\text {Timed out} \]
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Not integrable
Time = 2.37 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {(3+b \sin (e+f x))^m}{c+d \sin (e+f x)} \, dx=\int { \frac {{\left (b \sin \left (f x + e\right ) + a\right )}^{m}}{d \sin \left (f x + e\right ) + c} \,d x } \]
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Not integrable
Time = 0.37 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {(3+b \sin (e+f x))^m}{c+d \sin (e+f x)} \, dx=\int { \frac {{\left (b \sin \left (f x + e\right ) + a\right )}^{m}}{d \sin \left (f x + e\right ) + c} \,d x } \]
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Not integrable
Time = 8.73 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {(3+b \sin (e+f x))^m}{c+d \sin (e+f x)} \, dx=\int \frac {{\left (a+b\,\sin \left (e+f\,x\right )\right )}^m}{c+d\,\sin \left (e+f\,x\right )} \,d x \]
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