Integrand size = 25, antiderivative size = 25 \[ \int \sec ^{\frac {7}{3}}(c+d x) (a+b \sec (c+d x))^{5/2} \, dx=\text {Int}\left (\sec ^{\frac {7}{3}}(c+d x) (a+b \sec (c+d x))^{5/2},x\right ) \]
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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 = {} \[ \int \sec ^{\frac {7}{3}}(c+d x) (a+b \sec (c+d x))^{5/2} \, dx=\int \sec ^{\frac {7}{3}}(c+d x) (a+b \sec (c+d x))^{5/2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \sec ^{\frac {7}{3}}(c+d x) (a+b \sec (c+d x))^{5/2} \, dx \\ \end{align*}
Not integrable
Time = 168.43 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \sec ^{\frac {7}{3}}(c+d x) (a+b \sec (c+d x))^{5/2} \, dx=\int \sec ^{\frac {7}{3}}(c+d x) (a+b \sec (c+d x))^{5/2} \, dx \]
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Not integrable
Time = 0.43 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.84
\[\int \sec \left (d x +c \right )^{\frac {7}{3}} \left (a +b \sec \left (d x +c \right )\right )^{\frac {5}{2}}d x\]
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Not integrable
Time = 0.34 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.40 \[ \int \sec ^{\frac {7}{3}}(c+d x) (a+b \sec (c+d x))^{5/2} \, dx=\int { {\left (b \sec \left (d x + c\right ) + a\right )}^{\frac {5}{2}} \sec \left (d x + c\right )^{\frac {7}{3}} \,d x } \]
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Timed out. \[ \int \sec ^{\frac {7}{3}}(c+d x) (a+b \sec (c+d x))^{5/2} \, dx=\text {Timed out} \]
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Not integrable
Time = 2.48 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92 \[ \int \sec ^{\frac {7}{3}}(c+d x) (a+b \sec (c+d x))^{5/2} \, dx=\int { {\left (b \sec \left (d x + c\right ) + a\right )}^{\frac {5}{2}} \sec \left (d x + c\right )^{\frac {7}{3}} \,d x } \]
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Not integrable
Time = 4.42 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92 \[ \int \sec ^{\frac {7}{3}}(c+d x) (a+b \sec (c+d x))^{5/2} \, dx=\int { {\left (b \sec \left (d x + c\right ) + a\right )}^{\frac {5}{2}} \sec \left (d x + c\right )^{\frac {7}{3}} \,d x } \]
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Not integrable
Time = 16.96 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \sec ^{\frac {7}{3}}(c+d x) (a+b \sec (c+d x))^{5/2} \, dx=\int {\left (a+\frac {b}{\cos \left (c+d\,x\right )}\right )}^{5/2}\,{\left (\frac {1}{\cos \left (c+d\,x\right )}\right )}^{7/3} \,d x \]
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