Integrand size = 14, antiderivative size = 14 \[ \int \sqrt [3]{a+b \sec (c+d x)} \, dx=\text {Int}\left (\sqrt [3]{a+b \sec (c+d x)},x\right ) \]
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Not integrable
Time = 0.02 (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 = {} \[ \int \sqrt [3]{a+b \sec (c+d x)} \, dx=\int \sqrt [3]{a+b \sec (c+d x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \sqrt [3]{a+b \sec (c+d x)} \, dx \\ \end{align*}
Not integrable
Time = 18.05 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \sqrt [3]{a+b \sec (c+d x)} \, dx=\int \sqrt [3]{a+b \sec (c+d x)} \, dx \]
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Not integrable
Time = 0.37 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86
\[\int \left (a +b \sec \left (d x +c \right )\right )^{\frac {1}{3}}d x\]
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Timed out. \[ \int \sqrt [3]{a+b \sec (c+d x)} \, dx=\text {Timed out} \]
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Not integrable
Time = 0.49 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \sqrt [3]{a+b \sec (c+d x)} \, dx=\int \sqrt [3]{a + b \sec {\left (c + d x \right )}}\, dx \]
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Not integrable
Time = 0.58 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \sqrt [3]{a+b \sec (c+d x)} \, dx=\int { {\left (b \sec \left (d x + c\right ) + a\right )}^{\frac {1}{3}} \,d x } \]
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Not integrable
Time = 0.42 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \sqrt [3]{a+b \sec (c+d x)} \, dx=\int { {\left (b \sec \left (d x + c\right ) + a\right )}^{\frac {1}{3}} \,d x } \]
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Not integrable
Time = 13.71 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \sqrt [3]{a+b \sec (c+d x)} \, dx=\int {\left (a+\frac {b}{\cos \left (c+d\,x\right )}\right )}^{1/3} \,d x \]
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