Integrand size = 14, antiderivative size = 14 \[ \int \frac {1}{(a+b \sec (c+d x))^{4/3}} \, dx=\text {Int}\left (\frac {1}{(a+b \sec (c+d x))^{4/3}},x\right ) \]
[Out]
Not integrable
Time = 0.01 (sec) , antiderivative size = 14, 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 = {} \[ \int \frac {1}{(a+b \sec (c+d x))^{4/3}} \, dx=\int \frac {1}{(a+b \sec (c+d x))^{4/3}} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{(a+b \sec (c+d x))^{4/3}} \, dx \\ \end{align*}
Not integrable
Time = 91.41 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {1}{(a+b \sec (c+d x))^{4/3}} \, dx=\int \frac {1}{(a+b \sec (c+d x))^{4/3}} \, dx \]
[In]
[Out]
Not integrable
Time = 0.34 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86
\[\int \frac {1}{\left (a +b \sec \left (d x +c \right )\right )^{\frac {4}{3}}}d x\]
[In]
[Out]
Timed out. \[ \int \frac {1}{(a+b \sec (c+d x))^{4/3}} \, dx=\text {Timed out} \]
[In]
[Out]
Not integrable
Time = 1.26 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07 \[ \int \frac {1}{(a+b \sec (c+d x))^{4/3}} \, dx=\int \frac {1}{\left (a + b \sec {\left (c + d x \right )}\right )^{\frac {4}{3}}}\, dx \]
[In]
[Out]
Not integrable
Time = 0.57 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {1}{(a+b \sec (c+d x))^{4/3}} \, dx=\int { \frac {1}{{\left (b \sec \left (d x + c\right ) + a\right )}^{\frac {4}{3}}} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.88 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {1}{(a+b \sec (c+d x))^{4/3}} \, dx=\int { \frac {1}{{\left (b \sec \left (d x + c\right ) + a\right )}^{\frac {4}{3}}} \,d x } \]
[In]
[Out]
Not integrable
Time = 15.53 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {1}{(a+b \sec (c+d x))^{4/3}} \, dx=\int \frac {1}{{\left (a+\frac {b}{\cos \left (c+d\,x\right )}\right )}^{4/3}} \,d x \]
[In]
[Out]