Optimal. Leaf size=34 \[ -\frac{x^4 f^a \text{Gamma}\left (\frac{4}{3},-b x^3 \log (f)\right )}{3 \left (-b x^3 \log (f)\right )^{4/3}} \]
[Out]
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Rubi [A] time = 0.037701, antiderivative size = 34, 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 \[ -\frac{x^4 f^a \text{Gamma}\left (\frac{4}{3},-b x^3 \log (f)\right )}{3 \left (-b x^3 \log (f)\right )^{4/3}} \]
Antiderivative was successfully verified.
[In] Int[f^(a + b*x^3)*x^3,x]
[Out]
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Rubi in Sympy [A] time = 3.11918, size = 36, normalized size = 1.06 \[ - \frac{f^{a} x^{4} \Gamma{\left (\frac{4}{3},- b x^{3} \log{\left (f \right )} \right )}}{3 \left (- b x^{3} \log{\left (f \right )}\right )^{\frac{4}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(b*x**3+a)*x**3,x)
[Out]
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Mathematica [A] time = 0.0307404, size = 56, normalized size = 1.65 \[ -\frac{x^4 f^a \left (\text{Gamma}\left (\frac{1}{3},-b x^3 \log (f)\right )+3 f^{b x^3} \sqrt [3]{-b x^3 \log (f)}\right )}{9 \left (-b x^3 \log (f)\right )^{4/3}} \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b*x^3)*x^3,x]
[Out]
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Maple [B] time = 0.033, size = 109, normalized size = 3.2 \[ -{\frac{{f}^{a}}{3\,b} \left ( -{\frac{2\,x\pi \,\sqrt{3}}{9\,b\Gamma \left ( 2/3 \right ) } \left ( -b \right ) ^{{\frac{4}{3}}}\sqrt [3]{\ln \left ( f \right ) }{\frac{1}{\sqrt [3]{-b{x}^{3}\ln \left ( f \right ) }}}}+{\frac{x{{\rm e}^{b{x}^{3}\ln \left ( f \right ) }}}{b} \left ( -b \right ) ^{{\frac{4}{3}}}\sqrt [3]{\ln \left ( f \right ) }}+{\frac{x}{3\,b} \left ( -b \right ) ^{{\frac{4}{3}}}\sqrt [3]{\ln \left ( f \right ) }\Gamma \left ({\frac{1}{3}},-b{x}^{3}\ln \left ( f \right ) \right ){\frac{1}{\sqrt [3]{-b{x}^{3}\ln \left ( f \right ) }}}} \right ) \left ( \ln \left ( f \right ) \right ) ^{-{\frac{4}{3}}}{\frac{1}{\sqrt [3]{-b}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(b*x^3+a)*x^3,x)
[Out]
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Maxima [A] time = 0.868942, size = 73, normalized size = 2.15 \[ \frac{f^{b x^{3}} f^{a} x}{3 \, b \log \left (f\right )} + \frac{f^{a} x \Gamma \left (\frac{1}{3}, -b x^{3} \log \left (f\right )\right )}{9 \, \left (-b x^{3} \log \left (f\right )\right )^{\frac{1}{3}} b \log \left (f\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^3 + a)*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.270085, size = 68, normalized size = 2. \[ \frac{3 \, \left (-b \log \left (f\right )\right )^{\frac{1}{3}} f^{b x^{3} + a} x + f^{a} \Gamma \left (\frac{1}{3}, -b x^{3} \log \left (f\right )\right )}{9 \, \left (-b \log \left (f\right )\right )^{\frac{1}{3}} b \log \left (f\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^3 + a)*x^3,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int f^{a + b x^{3}} x^{3}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(b*x**3+a)*x**3,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int f^{b x^{3} + a} x^{3}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^3 + a)*x^3,x, algorithm="giac")
[Out]