Optimal. Leaf size=52 \[ \text{Unintegrable}\left (\frac{1}{\left (x (d g+e f)+d f+e g x^2\right ) \left (a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}\right )},x\right ) \]
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Rubi [A] time = 0.152223, 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 = {} \[ \int \frac{1}{\left (a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}\right ) \left (d f+(e f+d g) x+e g x^2\right )} \, dx \]
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{f+g x}}}\right ) \left (d f+(e f+d g) x+e g x^2\right )} \, dx &=\int \frac{1}{\left (a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}\right ) \left (d f+(e f+d g) x+e g x^2\right )} \, dx\\ \end{align*}
Mathematica [A] time = 0.378046, size = 0, normalized size = 0. \[ \int \frac{1}{\left (a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}\right ) \left (d f+(e f+d g) x+e g x^2\right )} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.076, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{df+ \left ( dg+fe \right ) x+eg{x}^{2}} \left ( a+b{F}^{{c\sqrt{ex+d}{\frac{1}{\sqrt{gx+f}}}}} \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 g x^{2} + d f +{\left (e f + d g\right )} x\right )}{\left (F^{\frac{\sqrt{e x + d} c}{\sqrt{g x + 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 g x^{2} + a d f +{\left (b e g x^{2} + b d f +{\left (b e f + b d g\right )} x\right )} F^{\frac{\sqrt{e x + d} c}{\sqrt{g x + f}}} +{\left (a e f + a d g\right )} x}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [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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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (e g x^{2} + d f +{\left (e f + d g\right )} x\right )}{\left (F^{\frac{\sqrt{e x + d} c}{\sqrt{g x + f}}} b + a\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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