Optimal. Leaf size=49 \[ \text{Unintegrable}\left (\frac{1}{\left (d^2-e^2 x^2\right ) \left (a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right )},x\right ) \]
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Rubi [A] time = 0.23251, 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 = {} \[ \int \frac{1}{\left (a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right ) \left (d^2-e^2 x^2\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{\left (a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right ) \left (d^2-e^2 x^2\right )} \, dx &=\int \frac{1}{\left (a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right ) \left (d^2-e^2 x^2\right )} \, dx\\ \end{align*}
Mathematica [A] time = 0.4697, size = 0, normalized size = 0. \[ \int \frac{1}{\left (a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right ) \left (d^2-e^2 x^2\right )} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.021, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{-{e}^{2}{x}^{2}+{d}^{2}} \left ( a+b{F}^{{c\sqrt{ex+d}{\frac{1}{\sqrt{-efx+df}}}}} \right ) ^{-1}}\, 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 (e^{2} x^{2} - d^{2}\right )}{\left (F^{\frac{\sqrt{e x + d} c}{\sqrt{-e f x + d f}}} b + a\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{1}{a e^{2} x^{2} - a d^{2} + \frac{b e^{2} x^{2} - b d^{2}}{F^{\frac{\sqrt{-e f x + d f} \sqrt{e x + d} c}{e f x - d f}}}}, 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{1}{- F^{\frac{c \sqrt{d + e x}}{\sqrt{d f - e f x}}} b d^{2} + F^{\frac{c \sqrt{d + e x}}{\sqrt{d f - e f x}}} b e^{2} x^{2} - a d^{2} + a e^{2} x^{2}}\, 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 (e^{2} x^{2} - d^{2}\right )}{\left (F^{\frac{\sqrt{e x + d} c}{\sqrt{-e f x + d f}}} b + a\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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