Optimal. Leaf size=24 \[ -\frac{f^a \text{Gamma}\left (5,-\frac{b \log (f)}{x^3}\right )}{3 b^5 \log ^5(f)} \]
[Out]
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Rubi [A] time = 0.0378146, antiderivative size = 24, 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 \[ -\frac{f^a \text{Gamma}\left (5,-\frac{b \log (f)}{x^3}\right )}{3 b^5 \log ^5(f)} \]
Antiderivative was successfully verified.
[In] Int[f^(a + b/x^3)/x^16,x]
[Out]
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Rubi in Sympy [A] time = 3.6305, size = 26, normalized size = 1.08 \[ - \frac{f^{a} \Gamma{\left (5,- \frac{b \log{\left (f \right )}}{x^{3}} \right )}}{3 b^{5} \log{\left (f \right )}^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(a+b/x**3)/x**16,x)
[Out]
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Mathematica [B] time = 0.0198981, size = 69, normalized size = 2.88 \[ -\frac{f^{a+\frac{b}{x^3}} \left (b^4 \log ^4(f)-4 b^3 x^3 \log ^3(f)+12 b^2 x^6 \log ^2(f)-24 b x^9 \log (f)+24 x^{12}\right )}{3 b^5 x^{12} \log ^5(f)} \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b/x^3)/x^16,x]
[Out]
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Maple [A] time = 0.045, size = 121, normalized size = 5. \[{\frac{1}{{x}^{15}} \left ( -8\,{\frac{{x}^{15}}{ \left ( \ln \left ( f \right ) \right ) ^{5}{b}^{5}}{{\rm e}^{ \left ( a+{\frac{b}{{x}^{3}}} \right ) \ln \left ( f \right ) }}}+8\,{\frac{{x}^{12}}{ \left ( \ln \left ( f \right ) \right ) ^{4}{b}^{4}}{{\rm e}^{ \left ( a+{\frac{b}{{x}^{3}}} \right ) \ln \left ( f \right ) }}}-4\,{\frac{{x}^{9}}{ \left ( \ln \left ( f \right ) \right ) ^{3}{b}^{3}}{{\rm e}^{ \left ( a+{\frac{b}{{x}^{3}}} \right ) \ln \left ( f \right ) }}}+{\frac{4\,{x}^{6}}{3\, \left ( \ln \left ( f \right ) \right ) ^{2}{b}^{2}}{{\rm e}^{ \left ( a+{\frac{b}{{x}^{3}}} \right ) \ln \left ( f \right ) }}}-{\frac{{x}^{3}}{3\,b\ln \left ( f \right ) }{{\rm e}^{ \left ( a+{\frac{b}{{x}^{3}}} \right ) \ln \left ( f \right ) }}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(a+b/x^3)/x^16,x)
[Out]
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Maxima [A] time = 0.846981, size = 30, normalized size = 1.25 \[ -\frac{f^{a} \Gamma \left (5, -\frac{b \log \left (f\right )}{x^{3}}\right )}{3 \, b^{5} \log \left (f\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^3)/x^16,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.239199, size = 96, normalized size = 4. \[ -\frac{{\left (24 \, x^{12} - 24 \, b x^{9} \log \left (f\right ) + 12 \, b^{2} x^{6} \log \left (f\right )^{2} - 4 \, b^{3} x^{3} \log \left (f\right )^{3} + b^{4} \log \left (f\right )^{4}\right )} f^{\frac{a x^{3} + b}{x^{3}}}}{3 \, b^{5} x^{12} \log \left (f\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^3)/x^16,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.363744, size = 71, normalized size = 2.96 \[ \frac{f^{a + \frac{b}{x^{3}}} \left (- b^{4} \log{\left (f \right )}^{4} + 4 b^{3} x^{3} \log{\left (f \right )}^{3} - 12 b^{2} x^{6} \log{\left (f \right )}^{2} + 24 b x^{9} \log{\left (f \right )} - 24 x^{12}\right )}{3 b^{5} x^{12} \log{\left (f \right )}^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(a+b/x**3)/x**16,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{a + \frac{b}{x^{3}}}}{x^{16}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^3)/x^16,x, algorithm="giac")
[Out]