Optimal. Leaf size=16 \[ \frac{f^{b x+c x^2}}{\log (f)} \]
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Rubi [A] time = 0.0141611, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {2236} \[ \frac{f^{b x+c x^2}}{\log (f)} \]
Antiderivative was successfully verified.
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Rule 2236
Rubi steps
\begin{align*} \int f^{b x+c x^2} (b+2 c x) \, dx &=\frac{f^{b x+c x^2}}{\log (f)}\\ \end{align*}
Mathematica [A] time = 0.0272758, size = 16, normalized size = 1. \[ \frac{f^{b x+c x^2}}{\log (f)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 17, normalized size = 1.1 \begin{align*}{\frac{{f}^{c{x}^{2}+bx}}{\ln \left ( f \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.994273, size = 22, normalized size = 1.38 \begin{align*} \frac{f^{c x^{2} + b x}}{\log \left (f\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.52006, size = 32, normalized size = 2. \begin{align*} \frac{f^{c x^{2} + b x}}{\log \left (f\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.113387, size = 22, normalized size = 1.38 \begin{align*} \begin{cases} \frac{f^{b x + c x^{2}}}{\log{\left (f \right )}} & \text{for}\: \log{\left (f \right )} \neq 0 \\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 = 1.26103, size = 22, normalized size = 1.38 \begin{align*} \frac{f^{c x^{2} + b x}}{\log \left (f\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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