Optimal. Leaf size=27 \[ -\frac{F^{a+\frac{b}{(c+d x)^3}}}{3 b d \log (F)} \]
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Rubi [A] time = 0.0425225, antiderivative size = 27, 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} \[ -\frac{F^{a+\frac{b}{(c+d x)^3}}}{3 b d \log (F)} \]
Antiderivative was successfully verified.
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Rule 2209
Rubi steps
\begin{align*} \int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^4} \, dx &=-\frac{F^{a+\frac{b}{(c+d x)^3}}}{3 b d \log (F)}\\ \end{align*}
Mathematica [A] time = 0.0119075, size = 27, normalized size = 1. \[ -\frac{F^{a+\frac{b}{(c+d x)^3}}}{3 b d \log (F)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 26, normalized size = 1. \begin{align*} -{\frac{1}{3\,\ln \left ( F \right ) bd}{F}^{a+{\frac{b}{ \left ( dx+c \right ) ^{3}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.974407, size = 34, normalized size = 1.26 \begin{align*} -\frac{F^{a + \frac{b}{{\left (d x + c\right )}^{3}}}}{3 \, b d \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.57842, size = 161, normalized size = 5.96 \begin{align*} -\frac{F^{\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}}}{3 \, 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 = 0.521485, size = 66, normalized size = 2.44 \begin{align*} \begin{cases} - \frac{F^{a + \frac{b}{\left (c + d x\right )^{3}}}}{3 b d \log{\left (F \right )}} & \text{for}\: 3 b d \log{\left (F \right )} \neq 0 \\- \frac{1}{3 c^{3} d + 9 c^{2} d^{2} x + 9 c d^{3} x^{2} + 3 d^{4} 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 = 1.38827, size = 34, normalized size = 1.26 \begin{align*} -\frac{F^{a + \frac{b}{{\left (d x + c\right )}^{3}}}}{3 \, b d \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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