Optimal. Leaf size=20 \[ -\frac{f^{a+\frac{b}{x^3}}}{3 b \log (f)} \]
[Out]
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Rubi [A] time = 0.0360995, antiderivative size = 20, 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 \[ -\frac{f^{a+\frac{b}{x^3}}}{3 b \log (f)} \]
Antiderivative was successfully verified.
[In] Int[f^(a + b/x^3)/x^4,x]
[Out]
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Rubi in Sympy [A] time = 3.40104, size = 15, normalized size = 0.75 \[ - \frac{f^{a + \frac{b}{x^{3}}}}{3 b \log{\left (f \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(a+b/x**3)/x**4,x)
[Out]
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Mathematica [A] time = 0.00623711, size = 20, normalized size = 1. \[ -\frac{f^{a+\frac{b}{x^3}}}{3 b \log (f)} \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b/x^3)/x^4,x]
[Out]
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Maple [A] time = 0.002, size = 19, normalized size = 1. \[ -{\frac{1}{3\,b\ln \left ( f \right ) }{f}^{a+{\frac{b}{{x}^{3}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(a+b/x^3)/x^4,x)
[Out]
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Maxima [A] time = 0.766235, size = 24, normalized size = 1.2 \[ -\frac{f^{a + \frac{b}{x^{3}}}}{3 \, b \log \left (f\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^3)/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.244846, size = 30, normalized size = 1.5 \[ -\frac{f^{\frac{a x^{3} + b}{x^{3}}}}{3 \, b \log \left (f\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^3)/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.215427, size = 29, normalized size = 1.45 \[ \begin{cases} - \frac{f^{a + \frac{b}{x^{3}}}}{3 b \log{\left (f \right )}} & \text{for}\: 3 b \log{\left (f \right )} \neq 0 \\- \frac{1}{3 x^{3}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(a+b/x**3)/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.245394, size = 24, normalized size = 1.2 \[ -\frac{f^{a + \frac{b}{x^{3}}}}{3 \, b{\rm ln}\left (f\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^3)/x^4,x, algorithm="giac")
[Out]