Optimal. Leaf size=20 \[ -\frac{F^{\frac{1}{a+b x+c x^2}}}{\log (F)} \]
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Rubi [A] time = 0.166147, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 33, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.03, Rules used = {6706} \[ -\frac{F^{\frac{1}{a+b x+c x^2}}}{\log (F)} \]
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin{align*} \int \frac{F^{\frac{1}{a+b x+c x^2}} (b+2 c x)}{\left (a+b x+c x^2\right )^2} \, dx &=-\frac{F^{\frac{1}{a+b x+c x^2}}}{\log (F)}\\ \end{align*}
Mathematica [A] time = 0.384291, size = 19, normalized size = 0.95 \[ -\frac{F^{\frac{1}{a+x (b+c x)}}}{\log (F)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.042, size = 21, normalized size = 1.1 \begin{align*} -{\frac{{F}^{ \left ( c{x}^{2}+bx+a \right ) ^{-1}}}{\ln \left ( F \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.977901, size = 27, normalized size = 1.35 \begin{align*} -\frac{F^{\left (\frac{1}{c x^{2} + b x + a}\right )}}{\log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.779014, size = 45, normalized size = 2.25 \begin{align*} -\frac{F^{\left (\frac{1}{c x^{2} + b x + a}\right )}}{\log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.679001, size = 32, normalized size = 1.6 \begin{align*} \begin{cases} - \frac{F^{\frac{1}{a + b x + c x^{2}}}}{\log{\left (F \right )}} & \text{for}\: \log{\left (F \right )} \neq 0 \\- \frac{1}{a + b x + c x^{2}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.30072, size = 27, normalized size = 1.35 \begin{align*} -\frac{F^{\left (\frac{1}{c x^{2} + b x + a}\right )}}{\log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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