Optimal. Leaf size=31 \[ \frac{F^{c \left (a-\frac{b d}{e}\right )} \text{ExpIntegralEi}\left (\frac{b c \log (F) (d+e x)}{e}\right )}{e} \]
[Out]
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Rubi [A] time = 0.0404631, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{F^{c \left (a-\frac{b d}{e}\right )} \text{ExpIntegralEi}\left (\frac{b c \log (F) (d+e x)}{e}\right )}{e} \]
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 = 5.15295, size = 27, normalized size = 0.87 \[ \frac{F^{\frac{c \left (a e - b d\right )}{e}} \operatorname{Ei}{\left (\frac{b c \left (d + e x\right ) \log{\left (F \right )}}{e} \right )}}{e} \]
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 = 0.0161601, size = 31, normalized size = 1. \[ \frac{F^{c \left (a-\frac{b d}{e}\right )} \text{ExpIntegralEi}\left (\frac{b c \log (F) (d+e x)}{e}\right )}{e} \]
Antiderivative was successfully verified.
[In] Integrate[F^(c*(a + b*x))/(d + e*x),x]
[Out]
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Maple [A] time = 0.034, size = 56, normalized size = 1.8 \[ -{\frac{1}{e}{F}^{{\frac{c \left ( ea-bd \right ) }{e}}}{\it Ei} \left ( 1,-bcx\ln \left ( F \right ) -\ln \left ( F \right ) ac-{\frac{-eac\ln \left ( F \right ) +\ln \left ( F \right ) bcd}{e}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(c*(b*x+a))/(e*x+d),x)
[Out]
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Maxima [A] time = 0.752654, size = 50, normalized size = 1.61 \[ -\frac{F^{a c} exp_integral_e\left (1, -\frac{{\left (e x + d\right )} b c \log \left (F\right )}{e}\right )}{F^{\frac{b c d}{e}} e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((b*x + a)*c)/(e*x + d),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.247157, size = 53, normalized size = 1.71 \[ \frac{{\rm Ei}\left (\frac{{\left (b c e x + b c d\right )} \log \left (F\right )}{e}\right )}{F^{\frac{b c d - a c e}{e}} e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((b*x + a)*c)/(e*x + d),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{c \left (a + b x\right )}}{d + e x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F**(c*(b*x+a))/(e*x+d),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{{\left (b x + a\right )} c}}{e x + d}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((b*x + a)*c)/(e*x + d),x, algorithm="giac")
[Out]