Optimal. Leaf size=20 \[ \frac{F^{c (a+b x)}}{b c \log (F)} \]
[Out]
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Rubi [A] time = 0.0109114, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{F^{c (a+b x)}}{b c \log (F)} \]
Antiderivative was successfully verified.
[In] Int[F^(c*(a + b*x)),x]
[Out]
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Rubi in Sympy [A] time = 2.00204, size = 14, normalized size = 0.7 \[ \frac{F^{c \left (a + b x\right )}}{b c \log{\left (F \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(c*(b*x+a)),x)
[Out]
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Mathematica [A] time = 0.00222036, size = 21, normalized size = 1.05 \[ \frac{F^{a c+b c x}}{b c \log (F)} \]
Antiderivative was successfully verified.
[In] Integrate[F^(c*(a + b*x)),x]
[Out]
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Maple [A] time = 0.003, size = 21, normalized size = 1.1 \[{\frac{{F}^{c \left ( bx+a \right ) }}{cb\ln \left ( F \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(c*(b*x+a)),x)
[Out]
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Maxima [A] time = 0.680698, size = 27, normalized size = 1.35 \[ \frac{F^{{\left (b x + a\right )} c}}{b c \log \left (F\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((b*x + a)*c),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.230142, size = 28, normalized size = 1.4 \[ \frac{F^{b c x + a c}}{b c \log \left (F\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((b*x + a)*c),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.165517, size = 20, normalized size = 1. \[ \begin{cases} \frac{F^{c \left (a + b x\right )}}{b c \log{\left (F \right )}} & \text{for}\: b c \log{\left (F \right )} \neq 0 \\x & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F**(c*(b*x+a)),x)
[Out]
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GIAC/XCAS [A] time = 0.241298, size = 27, normalized size = 1.35 \[ \frac{F^{{\left (b x + a\right )} c}}{b c{\rm ln}\left (F\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((b*x + a)*c),x, algorithm="giac")
[Out]