Optimal. Leaf size=46 \[ \frac{(c+d x) F^{a+\frac{b}{c+d x}}}{d}-\frac{b F^a \log (F) \text{ExpIntegralEi}\left (\frac{b \log (F)}{c+d x}\right )}{d} \]
[Out]
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Rubi [A] time = 0.0856284, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{(c+d x) F^{a+\frac{b}{c+d x}}}{d}-\frac{b F^a \log (F) \text{ExpIntegralEi}\left (\frac{b \log (F)}{c+d x}\right )}{d} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b/(c + d*x)),x]
[Out]
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Rubi in Sympy [A] time = 6.16692, size = 37, normalized size = 0.8 \[ - \frac{F^{a} b \log{\left (F \right )} \operatorname{Ei}{\left (\frac{b \log{\left (F \right )}}{c + d x} \right )}}{d} + \frac{F^{a + \frac{b}{c + d x}} \left (c + d x\right )}{d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(a+b/(d*x+c)),x)
[Out]
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Mathematica [A] time = 0.0259141, size = 42, normalized size = 0.91 \[ \frac{F^a \left ((c+d x) F^{\frac{b}{c+d x}}-b \log (F) \text{ExpIntegralEi}\left (\frac{b \log (F)}{c+d x}\right )\right )}{d} \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b/(c + d*x)),x]
[Out]
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Maple [A] time = 0.023, size = 71, normalized size = 1.5 \[{F}^{{\frac{xda+ac+b}{dx+c}}}x+{\frac{c}{d}{F}^{{\frac{xda+ac+b}{dx+c}}}}+{\frac{b\ln \left ( F \right ){F}^{a}}{d}{\it Ei} \left ( 1,-{\frac{b\ln \left ( F \right ) }{dx+c}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(a+b/(d*x+c)),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ F^{a} b d \int \frac{F^{\frac{b}{d x + c}} x}{d^{2} x^{2} + 2 \, c d x + c^{2}}\,{d x} \log \left (F\right ) + F^{a} F^{\frac{b}{d x + c}} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(a + b/(d*x + c)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.251727, size = 69, normalized size = 1.5 \[ -\frac{F^{a} b{\rm Ei}\left (\frac{b \log \left (F\right )}{d x + c}\right ) \log \left (F\right ) -{\left (d x + c\right )} F^{\frac{a d x + a c + b}{d x + c}}}{d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(a + b/(d*x + c)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int F^{a + \frac{b}{c + d x}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F**(a+b/(d*x+c)),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int F^{a + \frac{b}{d x + c}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(a + b/(d*x + c)),x, algorithm="giac")
[Out]