Optimal. Leaf size=25 \[ -\frac {F^{a+\frac {b}{c+d x}}}{b d \log (F)} \]
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Rubi [A] time = 0.04, antiderivative size = 25, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 25, normalized size = 1.00 \[ -\frac {F^{a+\frac {b}{c+d x}}}{b d \log (F)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 31, normalized size = 1.24 \[ -\frac {F^{\frac {a d x + a c + b}{d x + c}}}{b d \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 31, normalized size = 1.24 \[ -\frac {F^{\frac {a d x + a c + b}{d x + c}}}{b d \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 26, normalized size = 1.04 \[ -\frac {F^{a +\frac {b}{d x +c}}}{b d \ln \relax (F )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.90, size = 25, normalized size = 1.00 \[ -\frac {F^{a + \frac {b}{d x + c}}}{b d \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.04, size = 25, normalized size = 1.00 \[ -\frac {F^{a+\frac {b}{c+d\,x}}}{b\,d\,\ln \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.24, size = 34, normalized size = 1.36 \[ \begin {cases} - \frac {F^{a + \frac {b}{c + d x}}}{b d \log {\relax (F )}} & \text {for}\: b d \log {\relax (F )} \neq 0 \\- \frac {1}{c d + d^{2} x} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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