Optimal. Leaf size=22 \[ -b^5 f^a \log ^5(f) \text{Gamma}\left (-5,-\frac{b \log (f)}{x}\right ) \]
[Out]
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Rubi [A] time = 0.0346772, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -b^5 f^a \log ^5(f) \text{Gamma}\left (-5,-\frac{b \log (f)}{x}\right ) \]
Antiderivative was successfully verified.
[In] Int[f^(a + b/x)*x^4,x]
[Out]
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Rubi in Sympy [A] time = 3.65573, size = 24, normalized size = 1.09 \[ - b^{5} f^{a} \Gamma{\left (-5,- \frac{b \log{\left (f \right )}}{x} \right )} \log{\left (f \right )}^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(a+b/x)*x**4,x)
[Out]
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Mathematica [B] time = 0.047434, size = 77, normalized size = 3.5 \[ \frac{1}{120} f^a \left (x f^{b/x} \left (b^4 \log ^4(f)+b^3 x \log ^3(f)+2 b^2 x^2 \log ^2(f)+6 b x^3 \log (f)+24 x^4\right )-b^5 \log ^5(f) \text{ExpIntegralEi}\left (\frac{b \log (f)}{x}\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b/x)*x^4,x]
[Out]
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Maple [B] time = 0.039, size = 126, normalized size = 5.7 \[{\frac{{x}^{5}}{5}{f}^{{\frac{ax+b}{x}}}}+{\frac{b\ln \left ( f \right ){x}^{4}}{20}{f}^{{\frac{ax+b}{x}}}}+{\frac{ \left ( \ln \left ( f \right ) \right ) ^{2}{b}^{2}{x}^{3}}{60}{f}^{{\frac{ax+b}{x}}}}+{\frac{ \left ( \ln \left ( f \right ) \right ) ^{3}{b}^{3}{x}^{2}}{120}{f}^{{\frac{ax+b}{x}}}}+{\frac{ \left ( \ln \left ( f \right ) \right ) ^{4}{b}^{4}x}{120}{f}^{{\frac{ax+b}{x}}}}+{\frac{ \left ( \ln \left ( f \right ) \right ) ^{5}{b}^{5}{f}^{a}}{120}{\it Ei} \left ( 1,-{\frac{b\ln \left ( f \right ) }{x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(a+b/x)*x^4,x)
[Out]
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Maxima [A] time = 0.818673, size = 123, normalized size = 5.59 \[ -\frac{1}{120} \, b^{5} f^{a}{\rm Ei}\left (\frac{b \log \left (f\right )}{x}\right ) \log \left (f\right )^{5} + \frac{1}{120} \,{\left (b^{4} f^{a} x \log \left (f\right )^{4} + b^{3} f^{a} x^{2} \log \left (f\right )^{3} + 2 \, b^{2} f^{a} x^{3} \log \left (f\right )^{2} + 6 \, b f^{a} x^{4} \log \left (f\right ) + 24 \, f^{a} x^{5}\right )} f^{\frac{b}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x)*x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.261188, size = 108, normalized size = 4.91 \[ -\frac{1}{120} \, b^{5} f^{a}{\rm Ei}\left (\frac{b \log \left (f\right )}{x}\right ) \log \left (f\right )^{5} + \frac{1}{120} \,{\left (b^{4} x \log \left (f\right )^{4} + b^{3} x^{2} \log \left (f\right )^{3} + 2 \, b^{2} x^{3} \log \left (f\right )^{2} + 6 \, b x^{4} \log \left (f\right ) + 24 \, x^{5}\right )} f^{\frac{a x + b}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x)*x^4,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int f^{a + \frac{b}{x}} x^{4}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(a+b/x)*x**4,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int f^{a + \frac{b}{x}} x^{4}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x)*x^4,x, algorithm="giac")
[Out]