Optimal. Leaf size=48 \[ \frac{(d+e x) F^{c (a+b x)}}{b c \log (F)}-\frac{e F^{c (a+b x)}}{b^2 c^2 \log ^2(F)} \]
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Rubi [A] time = 0.0365302, antiderivative size = 48, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{(d+e x) F^{c (a+b x)}}{b c \log (F)}-\frac{e F^{c (a+b x)}}{b^2 c^2 \log ^2(F)} \]
Antiderivative was successfully verified.
[In] Int[F^(c*(a + b*x))*(d + e*x),x]
[Out]
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Rubi in Sympy [A] time = 6.63371, size = 41, normalized size = 0.85 \[ \frac{F^{c \left (a + b x\right )} \left (d + e x\right )}{b c \log{\left (F \right )}} - \frac{F^{c \left (a + b x\right )} e}{b^{2} c^{2} \log{\left (F \right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(c*(b*x+a))*(e*x+d),x)
[Out]
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Mathematica [A] time = 0.0260575, size = 34, normalized size = 0.71 \[ \frac{F^{c (a+b x)} (b c \log (F) (d+e x)-e)}{b^2 c^2 \log ^2(F)} \]
Antiderivative was successfully verified.
[In] Integrate[F^(c*(a + b*x))*(d + e*x),x]
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Maple [A] time = 0.004, size = 38, normalized size = 0.8 \[{\frac{ \left ( \ln \left ( F \right ) bcex+\ln \left ( F \right ) bcd-e \right ){F}^{c \left ( bx+a \right ) }}{{b}^{2}{c}^{2} \left ( \ln \left ( F \right ) \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(c*(b*x+a))*(e*x+d),x)
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Maxima [A] time = 0.691583, size = 81, normalized size = 1.69 \[ \frac{F^{b c x + a c} d}{b c \log \left (F\right )} + \frac{{\left (F^{a c} b c x \log \left (F\right ) - F^{a c}\right )} F^{b c x} e}{b^{2} c^{2} \log \left (F\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*F^((b*x + a)*c),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.233659, size = 51, normalized size = 1.06 \[ \frac{{\left ({\left (b c e x + b c d\right )} \log \left (F\right ) - e\right )} F^{b c x + a c}}{b^{2} c^{2} \log \left (F\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*F^((b*x + a)*c),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.293582, size = 60, normalized size = 1.25 \[ \begin{cases} \frac{F^{c \left (a + b x\right )} \left (b c d \log{\left (F \right )} + b c e x \log{\left (F \right )} - e\right )}{b^{2} c^{2} \log{\left (F \right )}^{2}} & \text{for}\: b^{2} c^{2} \log{\left (F \right )}^{2} \neq 0 \\d x + \frac{e x^{2}}{2} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F**(c*(b*x+a))*(e*x+d),x)
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GIAC/XCAS [A] time = 0.260921, size = 1, normalized size = 0.02 \[ \mathit{Done} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*F^((b*x + a)*c),x, algorithm="giac")
[Out]