Optimal. Leaf size=16 \[ \text{Unintegrable}\left (\frac{1}{\sqrt [3]{a+b \sec (c+d x)}},x\right ) \]
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Rubi [A] time = 0.0107156, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{1}{\sqrt [3]{a+b \sec (c+d x)}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{\sqrt [3]{a+b \sec (c+d x)}} \, dx &=\int \frac{1}{\sqrt [3]{a+b \sec (c+d x)}} \, dx\\ \end{align*}
Mathematica [A] time = 0.9116, size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt [3]{a+b \sec (c+d x)}} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.114, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{\sqrt [3]{a+b\sec \left ( dx+c \right ) }}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b \sec \left (d x + c\right ) + a\right )}^{\frac{1}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\sqrt [3]{a + b \sec{\left (c + d x \right )}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b \sec \left (d x + c\right ) + a\right )}^{\frac{1}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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