Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{1}{(c+d x)^2 (a \sec (e+f x)+a)},x\right ) \]
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Rubi [A] time = 0.0524957, 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 = {} \[ \int \frac{1}{(c+d x)^2 (a+a \sec (e+f x))} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{(c+d x)^2 (a+a \sec (e+f x))} \, dx &=\int \frac{1}{(c+d x)^2 (a+a \sec (e+f x))} \, dx\\ \end{align*}
Mathematica [A] time = 5.91418, size = 0, normalized size = 0. \[ \int \frac{1}{(c+d x)^2 (a+a \sec (e+f x))} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.182, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( dx+c \right ) ^{2} \left ( a+a\sec \left ( fx+e \right ) \right ) }}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [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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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{a d^{2} x^{2} + 2 \, a c d x + a c^{2} +{\left (a d^{2} x^{2} + 2 \, a c d x + a c^{2}\right )} \sec \left (f x + e\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*} \frac{\int \frac{1}{c^{2} \sec{\left (e + f x \right )} + c^{2} + 2 c d x \sec{\left (e + f x \right )} + 2 c d x + d^{2} x^{2} \sec{\left (e + f x \right )} + d^{2} x^{2}}\, dx}{a} \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 (d x + c\right )}^{2}{\left (a \sec \left (f x + e\right ) + a\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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