Optimal. Leaf size=25 \[ -\frac{1}{b d \log (F) \left (a+b F^{c+d x}\right )} \]
[Out]
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Rubi [A] time = 0.0571669, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.095 \[ -\frac{1}{b d \log (F) \left (a+b F^{c+d x}\right )} \]
Antiderivative was successfully verified.
[In] Int[F^(c + d*x)/(a + b*F^(c + d*x))^2,x]
[Out]
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Rubi in Sympy [A] time = 7.62534, size = 19, normalized size = 0.76 \[ - \frac{1}{b d \left (F^{c + d x} b + a\right ) \log{\left (F \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(d*x+c)/(a+b*F**(d*x+c))**2,x)
[Out]
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Mathematica [A] time = 0.0199145, size = 25, normalized size = 1. \[ -\frac{1}{b d \log (F) \left (a+b F^{c+d x}\right )} \]
Antiderivative was successfully verified.
[In] Integrate[F^(c + d*x)/(a + b*F^(c + d*x))^2,x]
[Out]
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Maple [A] time = 0.003, size = 26, normalized size = 1. \[ -{\frac{1}{bd \left ( a+b{F}^{dx+c} \right ) \ln \left ( F \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(d*x+c)/(a+b*F^(d*x+c))^2,x)
[Out]
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Maxima [A] time = 0.776674, size = 34, normalized size = 1.36 \[ -\frac{1}{{\left (F^{d x + c} b + a\right )} b d \log \left (F\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(d*x + c)/(F^(d*x + c)*b + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.256049, size = 34, normalized size = 1.36 \[ -\frac{1}{F^{d x + c} b^{2} d \log \left (F\right ) + a b d \log \left (F\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(d*x + c)/(F^(d*x + c)*b + a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.267698, size = 26, normalized size = 1.04 \[ - \frac{1}{F^{c + d x} b^{2} d \log{\left (F \right )} + a b d \log{\left (F \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F**(d*x+c)/(a+b*F**(d*x+c))**2,x)
[Out]
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GIAC/XCAS [A] time = 0.227116, size = 34, normalized size = 1.36 \[ -\frac{1}{{\left (F^{d x + c} b + a\right )} b d{\rm ln}\left (F\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(d*x + c)/(F^(d*x + c)*b + a)^2,x, algorithm="giac")
[Out]