Optimal. Leaf size=17 \[ \frac{F^{a+b x+c x^3}}{\log (F)} \]
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Rubi [A] time = 0.0520096, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048, Rules used = {6706} \[ \frac{F^{a+b x+c x^3}}{\log (F)} \]
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin{align*} \int F^{a+b x+c x^3} \left (b+3 c x^2\right ) \, dx &=\frac{F^{a+b x+c x^3}}{\log (F)}\\ \end{align*}
Mathematica [A] time = 0.0519045, size = 17, normalized size = 1. \[ \frac{F^{a+b x+c x^3}}{\log (F)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 18, normalized size = 1.1 \begin{align*}{\frac{{F}^{c{x}^{3}+bx+a}}{\ln \left ( F \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.959697, size = 23, normalized size = 1.35 \begin{align*} \frac{F^{c x^{3} + b x + a}}{\log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.924443, size = 38, normalized size = 2.24 \begin{align*} \frac{F^{c x^{3} + b x + a}}{\log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.12406, size = 24, normalized size = 1.41 \begin{align*} \begin{cases} \frac{F^{a + b x + c x^{3}}}{\log{\left (F \right )}} & \text{for}\: \log{\left (F \right )} \neq 0 \\b x + c x^{3} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.33893, size = 23, normalized size = 1.35 \begin{align*} \frac{F^{c x^{3} + b x + a}}{\log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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