Optimal. Leaf size=15 \[ \frac{1}{3} f^a \text{ExpIntegralEi}\left (b x^3 \log (f)\right ) \]
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Rubi [A] time = 0.0344289, antiderivative size = 15, 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 \[ \frac{1}{3} f^a \text{ExpIntegralEi}\left (b x^3 \log (f)\right ) \]
Antiderivative was successfully verified.
[In] Int[f^(a + b*x^3)/x,x]
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Rubi in Sympy [A] time = 3.05968, size = 14, normalized size = 0.93 \[ \frac{f^{a} \operatorname{Ei}{\left (b x^{3} \log{\left (f \right )} \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(b*x**3+a)/x,x)
[Out]
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Mathematica [A] time = 0.0045556, size = 15, normalized size = 1. \[ \frac{1}{3} f^a \text{ExpIntegralEi}\left (b x^3 \log (f)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b*x^3)/x,x]
[Out]
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Maple [B] time = 0.022, size = 41, normalized size = 2.7 \[{\frac{{f}^{a} \left ( 3\,\ln \left ( x \right ) +\ln \left ( -b \right ) +\ln \left ( \ln \left ( f \right ) \right ) -\ln \left ( -b{x}^{3}\ln \left ( f \right ) \right ) -{\it Ei} \left ( 1,-b{x}^{3}\ln \left ( f \right ) \right ) \right ) }{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(b*x^3+a)/x,x)
[Out]
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Maxima [A] time = 0.958367, size = 18, normalized size = 1.2 \[ \frac{1}{3} \, f^{a}{\rm Ei}\left (b x^{3} \log \left (f\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^3 + a)/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.269873, size = 18, normalized size = 1.2 \[ \frac{1}{3} \, f^{a}{\rm Ei}\left (b x^{3} \log \left (f\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^3 + a)/x,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{a + b x^{3}}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(b*x**3+a)/x,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{b x^{3} + a}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^3 + a)/x,x, algorithm="giac")
[Out]