3.6 \(\int F^{c (a+b x)} \, dx\)

Optimal. Leaf size=20 \[ \frac{F^{c (a+b x)}}{b c \log (F)} \]

[Out]

F^(c*(a + b*x))/(b*c*Log[F])

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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]

F^(c*(a + b*x))/(b*c*Log[F])

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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]

F**(c*(a + b*x))/(b*c*log(F))

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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]

F^(a*c + b*c*x)/(b*c*Log[F])

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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]

F^(c*(b*x+a))/b/c/ln(F)

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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]

F^((b*x + a)*c)/(b*c*log(F))

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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]

F^(b*c*x + a*c)/(b*c*log(F))

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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]

Piecewise((F**(c*(a + b*x))/(b*c*log(F)), Ne(b*c*log(F), 0)), (x, True))

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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]

F^((b*x + a)*c)/(b*c*ln(F))