Integrand size = 35, antiderivative size = 35 \[ \int \frac {\cos ^2(e+f x) (c+d \sin (e+f x))^{4/3}}{a+b \sin (e+f x)} \, dx=\text {Int}\left (\frac {\cos ^2(e+f x) (c+d \sin (e+f x))^{4/3}}{a+b \sin (e+f x)},x\right ) \]
[Out]
Not integrable
Time = 0.13 (sec) , antiderivative size = 35, 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 = {} \[ \int \frac {\cos ^2(e+f x) (c+d \sin (e+f x))^{4/3}}{a+b \sin (e+f x)} \, dx=\int \frac {\cos ^2(e+f x) (c+d \sin (e+f x))^{4/3}}{a+b \sin (e+f x)} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {\cos ^2(e+f x) (c+d \sin (e+f x))^{4/3}}{a+b \sin (e+f x)} \, dx \\ \end{align*}
Not integrable
Time = 71.20 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.06 \[ \int \frac {\cos ^2(e+f x) (c+d \sin (e+f x))^{4/3}}{a+b \sin (e+f x)} \, dx=\int \frac {\cos ^2(e+f x) (c+d \sin (e+f x))^{4/3}}{a+b \sin (e+f x)} \, dx \]
[In]
[Out]
Not integrable
Time = 0.51 (sec) , antiderivative size = 33, normalized size of antiderivative = 0.94
\[\int \frac {\left (\cos ^{2}\left (f x +e \right )\right ) \left (c +d \sin \left (f x +e \right )\right )^{\frac {4}{3}}}{a +b \sin \left (f x +e \right )}d x\]
[In]
[Out]
Timed out. \[ \int \frac {\cos ^2(e+f x) (c+d \sin (e+f x))^{4/3}}{a+b \sin (e+f x)} \, dx=\text {Timed out} \]
[In]
[Out]
Timed out. \[ \int \frac {\cos ^2(e+f x) (c+d \sin (e+f x))^{4/3}}{a+b \sin (e+f x)} \, dx=\text {Timed out} \]
[In]
[Out]
Exception generated. \[ \int \frac {\cos ^2(e+f x) (c+d \sin (e+f x))^{4/3}}{a+b \sin (e+f x)} \, dx=\text {Exception raised: RuntimeError} \]
[In]
[Out]
Not integrable
Time = 0.98 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.00 \[ \int \frac {\cos ^2(e+f x) (c+d \sin (e+f x))^{4/3}}{a+b \sin (e+f x)} \, dx=\int { \frac {{\left (d \sin \left (f x + e\right ) + c\right )}^{\frac {4}{3}} \cos \left (f x + e\right )^{2}}{b \sin \left (f x + e\right ) + a} \,d x } \]
[In]
[Out]
Not integrable
Time = 12.59 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.00 \[ \int \frac {\cos ^2(e+f x) (c+d \sin (e+f x))^{4/3}}{a+b \sin (e+f x)} \, dx=\int \frac {{\cos \left (e+f\,x\right )}^2\,{\left (c+d\,\sin \left (e+f\,x\right )\right )}^{4/3}}{a+b\,\sin \left (e+f\,x\right )} \,d x \]
[In]
[Out]