Optimal. Leaf size=25 \[ \text{Unintegrable}\left (\frac{(a+b \sec (c+d x))^n}{\sqrt{\tan (c+d x)}},x\right ) \]
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Rubi [A] time = 0.0440214, 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 = {} \[ \int \frac{(a+b \sec (c+d x))^n}{\sqrt{\tan (c+d x)}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{(a+b \sec (c+d x))^n}{\sqrt{\tan (c+d x)}} \, dx &=\int \frac{(a+b \sec (c+d x))^n}{\sqrt{\tan (c+d x)}} \, dx\\ \end{align*}
Mathematica [A] time = 4.8888, size = 0, normalized size = 0. \[ \int \frac{(a+b \sec (c+d x))^n}{\sqrt{\tan (c+d x)}} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.297, size = 0, normalized size = 0. \begin{align*} \int{ \left ( a+b\sec \left ( dx+c \right ) \right ) ^{n}{\frac{1}{\sqrt{\tan \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{{\left (b \sec \left (d x + c\right ) + a\right )}^{n}}{\sqrt{\tan \left (d x + c\right )}}\,{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 (\frac{{\left (b \sec \left (d x + c\right ) + a\right )}^{n}}{\sqrt{\tan \left (d x + c\right )}}, 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 \frac{\left (a + b \sec{\left (c + d x \right )}\right )^{n}}{\sqrt{\tan{\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{{\left (b \sec \left (d x + c\right ) + a\right )}^{n}}{\sqrt{\tan \left (d x + c\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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