Integrand size = 20, antiderivative size = 20 \[ \int \frac {(c+d x)^m}{a+b \sin (e+f x)} \, dx=\text {Int}\left (\frac {(c+d x)^m}{a+b \sin (e+f x)},x\right ) \]
[Out]
Not integrable
Time = 0.04 (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 = {} \[ \int \frac {(c+d x)^m}{a+b \sin (e+f x)} \, dx=\int \frac {(c+d x)^m}{a+b \sin (e+f x)} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {(c+d x)^m}{a+b \sin (e+f x)} \, dx \\ \end{align*}
Not integrable
Time = 0.62 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(c+d x)^m}{a+b \sin (e+f x)} \, dx=\int \frac {(c+d x)^m}{a+b \sin (e+f x)} \, dx \]
[In]
[Out]
Not integrable
Time = 0.06 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00
\[\int \frac {\left (d x +c \right )^{m}}{a +b \sin \left (f x +e \right )}d x\]
[In]
[Out]
Not integrable
Time = 0.26 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(c+d x)^m}{a+b \sin (e+f x)} \, dx=\int { \frac {{\left (d x + c\right )}^{m}}{b \sin \left (f x + e\right ) + a} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.95 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85 \[ \int \frac {(c+d x)^m}{a+b \sin (e+f x)} \, dx=\int \frac {\left (c + d x\right )^{m}}{a + b \sin {\left (e + f x \right )}}\, dx \]
[In]
[Out]
Not integrable
Time = 0.40 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(c+d x)^m}{a+b \sin (e+f x)} \, dx=\int { \frac {{\left (d x + c\right )}^{m}}{b \sin \left (f x + e\right ) + a} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.31 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(c+d x)^m}{a+b \sin (e+f x)} \, dx=\int { \frac {{\left (d x + c\right )}^{m}}{b \sin \left (f x + e\right ) + a} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.43 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(c+d x)^m}{a+b \sin (e+f x)} \, dx=\int \frac {{\left (c+d\,x\right )}^m}{a+b\,\sin \left (e+f\,x\right )} \,d x \]
[In]
[Out]