Optimal. Leaf size=49 \[ \text{Unintegrable}\left (\frac{\left (a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right )^n}{d^2-e^2 x^2},x\right ) \]
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Rubi [A] time = 0.229538, 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 = {} \[ \int \frac{\left (a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right )^n}{d^2-e^2 x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\left (a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right )^n}{d^2-e^2 x^2} \, dx &=\int \frac{\left (a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right )^n}{d^2-e^2 x^2} \, dx\\ \end{align*}
Mathematica [A] time = 0.71925, size = 0, normalized size = 0. \[ \int \frac{\left (a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right )^n}{d^2-e^2 x^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.04, 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 ) ^{n}}\, 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 (F^{\frac{\sqrt{e x + d} c}{\sqrt{-e f x + d f}}} b + a\right )}^{n}}{e^{2} x^{2} - d^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \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{{\left (F^{\frac{\sqrt{e x + d} c}{\sqrt{-e f x + d f}}} b + a\right )}^{n}}{e^{2} x^{2} - d^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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