Optimal. Leaf size=37 \[ -\frac{f^a \left (-b \log (f) x^n\right )^{\frac{1}{n}} \text{Gamma}\left (-\frac{1}{n},-b \log (f) x^n\right )}{n x} \]
[Out]
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Rubi [A] time = 0.0406282, antiderivative size = 37, 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 \[ -\frac{f^a \left (-b \log (f) x^n\right )^{\frac{1}{n}} \text{Gamma}\left (-\frac{1}{n},-b \log (f) x^n\right )}{n x} \]
Antiderivative was successfully verified.
[In] Int[f^(a + b*x^n)/x^2,x]
[Out]
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Rubi in Sympy [A] time = 3.78294, size = 36, normalized size = 0.97 \[ - \frac{f^{a} \left (- b x^{n} \log{\left (f \right )}\right )^{\frac{1}{n}} \Gamma{\left (- \frac{1}{n},- b x^{n} \log{\left (f \right )} \right )}}{n x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(a+b*x**n)/x**2,x)
[Out]
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Mathematica [A] time = 0.0146427, size = 37, normalized size = 1. \[ -\frac{f^a \left (-b \log (f) x^n\right )^{\frac{1}{n}} \text{Gamma}\left (-\frac{1}{n},-b \log (f) x^n\right )}{n x} \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b*x^n)/x^2,x]
[Out]
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Maple [F] time = 0.056, size = 0, normalized size = 0. \[ \int{\frac{{f}^{a+b{x}^{n}}}{{x}^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(a+b*x^n)/x^2,x)
[Out]
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Maxima [A] time = 0.943157, size = 50, normalized size = 1.35 \[ -\frac{\left (-b x^{n} \log \left (f\right )\right )^{\left (\frac{1}{n}\right )} f^{a} \Gamma \left (-\frac{1}{n}, -b x^{n} \log \left (f\right )\right )}{n x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^n + a)/x^2,x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{f^{b x^{n} + a}}{x^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^n + a)/x^2,x, algorithm="fricas")
[Out]
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(a+b*x**n)/x**2,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{b x^{n} + a}}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^n + a)/x^2,x, algorithm="giac")
[Out]