Optimal. Leaf size=25 \[ -\frac{F^{a+\frac{b}{c+d x}}}{b d \log (F)} \]
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Rubi [A] time = 0.0423626, antiderivative size = 25, 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 = {2209} \[ -\frac{F^{a+\frac{b}{c+d x}}}{b d \log (F)} \]
Antiderivative was successfully verified.
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Rule 2209
Rubi steps
\begin{align*} \int \frac{F^{a+\frac{b}{c+d x}}}{(c+d x)^2} \, dx &=-\frac{F^{a+\frac{b}{c+d x}}}{b d \log (F)}\\ \end{align*}
Mathematica [A] time = 0.0065504, size = 25, normalized size = 1. \[ -\frac{F^{a+\frac{b}{c+d x}}}{b d \log (F)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 26, normalized size = 1. \begin{align*} -{\frac{1}{\ln \left ( F \right ) bd}{F}^{a+{\frac{b}{dx+c}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.999679, size = 34, normalized size = 1.36 \begin{align*} -\frac{F^{a + \frac{b}{d x + c}}}{b d \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.54189, size = 63, normalized size = 2.52 \begin{align*} -\frac{F^{\frac{a d x + a c + b}{d x + c}}}{b d \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.371855, size = 34, normalized size = 1.36 \begin{align*} \begin{cases} - \frac{F^{a + \frac{b}{c + d x}}}{b d \log{\left (F \right )}} & \text{for}\: b d \log{\left (F \right )} \neq 0 \\- \frac{1}{c d + d^{2} x} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.34049, size = 34, normalized size = 1.36 \begin{align*} -\frac{F^{a + \frac{b}{d x + c}}}{b d \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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