Optimal. Leaf size=21 \[ 2 \text{Unintegrable}\left (\frac{\csc (2 a+2 b x)}{c+d x},x\right ) \]
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Rubi [A] time = 0.04482, 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 = {} \[ \int \frac{\csc (a+b x) \sec (a+b x)}{c+d x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\csc (a+b x) \sec (a+b x)}{c+d x} \, dx &=2 \int \frac{\csc (2 a+2 b x)}{c+d x} \, dx\\ \end{align*}
Mathematica [A] time = 4.52966, size = 0, normalized size = 0. \[ \int \frac{\csc (a+b x) \sec (a+b x)}{c+d x} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.2, size = 0, normalized size = 0. \begin{align*} \int{\frac{\csc \left ( bx+a \right ) \sec \left ( bx+a \right ) }{dx+c}}\, 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{\csc \left (b x + a\right ) \sec \left (b x + a\right )}{d x + c}\,{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{\csc \left (b x + a\right ) \sec \left (b x + a\right )}{d x + c}, 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{\csc{\left (a + b x \right )} \sec{\left (a + b x \right )}}{c + d x}\, 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{\csc \left (b x + a\right ) \sec \left (b x + a\right )}{d x + c}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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