Optimal. Leaf size=27 \[ \text{Unintegrable}\left (\sqrt [3]{\sec (c+d x)} \sqrt{a+b \sec (c+d x)},x\right ) \]
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Rubi [A] time = 0.0525696, 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 = {} \[ \int \sqrt [3]{\sec (c+d x)} \sqrt{a+b \sec (c+d x)} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \sqrt [3]{\sec (c+d x)} \sqrt{a+b \sec (c+d x)} \, dx &=\int \sqrt [3]{\sec (c+d x)} \sqrt{a+b \sec (c+d x)} \, dx\\ \end{align*}
Mathematica [A] time = 2.24048, size = 0, normalized size = 0. \[ \int \sqrt [3]{\sec (c+d x)} \sqrt{a+b \sec (c+d x)} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.38, size = 0, normalized size = 0. \begin{align*} \int \sqrt [3]{\sec \left ( dx+c \right ) }\sqrt{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 \sqrt{b \sec \left (d x + c\right ) + a} \sec \left (d x + c\right )^{\frac{1}{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\sqrt{b \sec \left (d x + c\right ) + a} \sec \left (d x + c\right )^{\frac{1}{3}}, x\right ) \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 \sqrt{a + b \sec{\left (c + d x \right )}} \sqrt [3]{\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 \sqrt{b \sec \left (d x + c\right ) + a} \sec \left (d x + c\right )^{\frac{1}{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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