Optimal. Leaf size=53 \[ \text {Int}\left (\frac {1}{\left (a+b F^{\frac {c \sqrt {d+e x}}{\sqrt {f+g x}}}\right ) \left (d f+(e f+d g) x+e g x^2\right )},x\right ) \]
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Rubi [A]
time = 0.11, 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 = {}
\begin {gather*} \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 {gather*}
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 = 0.16, size = 0, normalized size = 0.00 \begin {gather*} \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 {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.03, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (a +b \,F^{\frac {c \sqrt {e x +d}}{\sqrt {g x +f}}}\right ) \left (d f +\left (d g +e f \right ) x +e g \,x^{2}\right )}\, dx\]
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \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 \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \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 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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