Optimal. Leaf size=53 \[ \text {Int}\left (\frac {1}{\left (x (d g+e f)+d f+e g x^2\right ) \left (a+b F^{\frac {c \sqrt {d+e x}}{\sqrt {f+g x}}}\right )},x\right ) \]
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Rubi [A] time = 0.15, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, 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*}
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Mathematica [A] time = 0.39, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (a+b F^{\frac {c \sqrt {d+e x}}{\sqrt {f+g x}}}\right ) \left (d f+(e f+d g) x+e g x^2\right )} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{a e g x^{2} + a d f + {\left (b e g x^{2} + b d f + {\left (b e f + b d g\right )} x\right )} F^{\frac {\sqrt {e x + d} c}{\sqrt {g x + f}}} + {\left (a e f + a d g\right )} x}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (e g x^{2} + d f + {\left (e f + d g\right )} x\right )} {\left (F^{\frac {\sqrt {e x + d} c}{\sqrt {g x + f}}} b + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (b \,F^{\frac {\sqrt {e x +d}\, c}{\sqrt {g x +f}}}+a \right ) \left (e g \,x^{2}+d f +\left (d g +e f \right ) x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (e g x^{2} + d f + {\left (e f + d g\right )} x\right )} {\left (F^{\frac {\sqrt {e x + d} c}{\sqrt {g x + f}}} b + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.02 \[ \int \frac {1}{\left (a+F^{\frac {c\,\sqrt {d+e\,x}}{\sqrt {f+g\,x}}}\,b\right )\,\left (e\,g\,x^2+\left (d\,g+e\,f\right )\,x+d\,f\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (d + e x\right ) \left (f + g x\right ) \left (F^{\frac {c \sqrt {d + e x}}{\sqrt {f + g x}}} b + a\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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