Optimal. Leaf size=32 \[ -\frac{x f^a \text{Gamma}\left (\frac{1}{3},-b x^3 \log (f)\right )}{3 \sqrt [3]{-b x^3 \log (f)}} \]
[Out]
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Rubi [A] time = 0.0109559, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ -\frac{x f^a \text{Gamma}\left (\frac{1}{3},-b x^3 \log (f)\right )}{3 \sqrt [3]{-b x^3 \log (f)}} \]
Antiderivative was successfully verified.
[In] Int[f^(a + b*x^3),x]
[Out]
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Rubi in Sympy [A] time = 1.17719, size = 34, normalized size = 1.06 \[ - \frac{f^{a} x \Gamma{\left (\frac{1}{3},- b x^{3} \log{\left (f \right )} \right )}}{3 \sqrt [3]{- b x^{3} \log{\left (f \right )}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(b*x**3+a),x)
[Out]
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Mathematica [A] time = 0.00663037, size = 32, normalized size = 1. \[ -\frac{x f^a \text{Gamma}\left (\frac{1}{3},-b x^3 \log (f)\right )}{3 \sqrt [3]{-b x^3 \log (f)}} \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b*x^3),x]
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Maple [B] time = 0.018, size = 78, normalized size = 2.4 \[{\frac{{f}^{a}}{3} \left ({\frac{2\,x\pi \,\sqrt{3}}{3\,\Gamma \left ( 2/3 \right ) }\sqrt [3]{-b}\sqrt [3]{\ln \left ( f \right ) }{\frac{1}{\sqrt [3]{-b{x}^{3}\ln \left ( f \right ) }}}}-{x\sqrt [3]{-b}\sqrt [3]{\ln \left ( f \right ) }\Gamma \left ({\frac{1}{3}},-b{x}^{3}\ln \left ( f \right ) \right ){\frac{1}{\sqrt [3]{-b{x}^{3}\ln \left ( f \right ) }}}} \right ){\frac{1}{\sqrt [3]{-b}}}{\frac{1}{\sqrt [3]{\ln \left ( f \right ) }}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(b*x^3+a),x)
[Out]
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Maxima [A] time = 0.833744, size = 35, normalized size = 1.09 \[ -\frac{f^{a} x \Gamma \left (\frac{1}{3}, -b x^{3} \log \left (f\right )\right )}{3 \, \left (-b x^{3} \log \left (f\right )\right )^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^3 + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.267201, size = 30, normalized size = 0.94 \[ -\frac{f^{a} \Gamma \left (\frac{1}{3}, -b x^{3} \log \left (f\right )\right )}{3 \, \left (-b \log \left (f\right )\right )^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^3 + a),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int f^{a + b x^{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(b*x**3+a),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int f^{b x^{3} + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^3 + a),x, algorithm="giac")
[Out]