Integrand size = 25, antiderivative size = 25 \[ \int \frac {(e \tan (c+d x))^m}{\sqrt {a+b \sec (c+d x)}} \, dx=\text {Int}\left (\frac {(e \tan (c+d x))^m}{\sqrt {a+b \sec (c+d x)}},x\right ) \]
[Out]
Not integrable
Time = 0.07 (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 = {} \[ \int \frac {(e \tan (c+d x))^m}{\sqrt {a+b \sec (c+d x)}} \, dx=\int \frac {(e \tan (c+d x))^m}{\sqrt {a+b \sec (c+d x)}} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {(e \tan (c+d x))^m}{\sqrt {a+b \sec (c+d x)}} \, dx \\ \end{align*}
Not integrable
Time = 15.73 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {(e \tan (c+d x))^m}{\sqrt {a+b \sec (c+d x)}} \, dx=\int \frac {(e \tan (c+d x))^m}{\sqrt {a+b \sec (c+d x)}} \, dx \]
[In]
[Out]
Not integrable
Time = 1.15 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92
\[\int \frac {\left (e \tan \left (d x +c \right )\right )^{m}}{\sqrt {a +b \sec \left (d x +c \right )}}d x\]
[In]
[Out]
Not integrable
Time = 0.38 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00 \[ \int \frac {(e \tan (c+d x))^m}{\sqrt {a+b \sec (c+d x)}} \, dx=\int { \frac {\left (e \tan \left (d x + c\right )\right )^{m}}{\sqrt {b \sec \left (d x + c\right ) + a}} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.72 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.96 \[ \int \frac {(e \tan (c+d x))^m}{\sqrt {a+b \sec (c+d x)}} \, dx=\int \frac {\left (e \tan {\left (c + d x \right )}\right )^{m}}{\sqrt {a + b \sec {\left (c + d x \right )}}}\, dx \]
[In]
[Out]
Not integrable
Time = 1.33 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00 \[ \int \frac {(e \tan (c+d x))^m}{\sqrt {a+b \sec (c+d x)}} \, dx=\int { \frac {\left (e \tan \left (d x + c\right )\right )^{m}}{\sqrt {b \sec \left (d x + c\right ) + a}} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.84 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00 \[ \int \frac {(e \tan (c+d x))^m}{\sqrt {a+b \sec (c+d x)}} \, dx=\int { \frac {\left (e \tan \left (d x + c\right )\right )^{m}}{\sqrt {b \sec \left (d x + c\right ) + a}} \,d x } \]
[In]
[Out]
Not integrable
Time = 20.96 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {(e \tan (c+d x))^m}{\sqrt {a+b \sec (c+d x)}} \, dx=\int \frac {{\left (e\,\mathrm {tan}\left (c+d\,x\right )\right )}^m}{\sqrt {a+\frac {b}{\cos \left (c+d\,x\right )}}} \,d x \]
[In]
[Out]