Optimal. Leaf size=62 \[ \frac{f^{a+b x^2}}{b^3 \log ^3(f)}-\frac{x^2 f^{a+b x^2}}{b^2 \log ^2(f)}+\frac{x^4 f^{a+b x^2}}{2 b \log (f)} \]
[Out]
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Rubi [A] time = 0.103509, antiderivative size = 62, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{f^{a+b x^2}}{b^3 \log ^3(f)}-\frac{x^2 f^{a+b x^2}}{b^2 \log ^2(f)}+\frac{x^4 f^{a+b x^2}}{2 b \log (f)} \]
Antiderivative was successfully verified.
[In] Int[f^(a + b*x^2)*x^5,x]
[Out]
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Rubi in Sympy [A] time = 9.92569, size = 54, normalized size = 0.87 \[ \frac{f^{a + b x^{2}} x^{4}}{2 b \log{\left (f \right )}} - \frac{f^{a + b x^{2}} x^{2}}{b^{2} \log{\left (f \right )}^{2}} + \frac{f^{a + b x^{2}}}{b^{3} \log{\left (f \right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(b*x**2+a)*x**5,x)
[Out]
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Mathematica [A] time = 0.0140354, size = 41, normalized size = 0.66 \[ \frac{f^{a+b x^2} \left (b^2 x^4 \log ^2(f)-2 b x^2 \log (f)+2\right )}{2 b^3 \log ^3(f)} \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b*x^2)*x^5,x]
[Out]
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Maple [A] time = 0.01, size = 40, normalized size = 0.7 \[{\frac{ \left ({b}^{2}{x}^{4} \left ( \ln \left ( f \right ) \right ) ^{2}-2\,b{x}^{2}\ln \left ( f \right ) +2 \right ){f}^{b{x}^{2}+a}}{2\, \left ( \ln \left ( f \right ) \right ) ^{3}{b}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(b*x^2+a)*x^5,x)
[Out]
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Maxima [A] time = 0.774554, size = 63, normalized size = 1.02 \[ \frac{{\left (b^{2} f^{a} x^{4} \log \left (f\right )^{2} - 2 \, b f^{a} x^{2} \log \left (f\right ) + 2 \, f^{a}\right )} f^{b x^{2}}}{2 \, b^{3} \log \left (f\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^2 + a)*x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.244174, size = 53, normalized size = 0.85 \[ \frac{{\left (b^{2} x^{4} \log \left (f\right )^{2} - 2 \, b x^{2} \log \left (f\right ) + 2\right )} f^{b x^{2} + a}}{2 \, b^{3} \log \left (f\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^2 + a)*x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.239402, size = 54, normalized size = 0.87 \[ \begin{cases} \frac{f^{a + b x^{2}} \left (b^{2} x^{4} \log{\left (f \right )}^{2} - 2 b x^{2} \log{\left (f \right )} + 2\right )}{2 b^{3} \log{\left (f \right )}^{3}} & \text{for}\: 2 b^{3} \log{\left (f \right )}^{3} \neq 0 \\\frac{x^{6}}{6} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(b*x**2+a)*x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.248299, size = 58, normalized size = 0.94 \[ \frac{{\left (b^{2} x^{4}{\rm ln}\left (f\right )^{2} - 2 \, b x^{2}{\rm ln}\left (f\right ) + 2\right )} e^{\left (b x^{2}{\rm ln}\left (f\right ) + a{\rm ln}\left (f\right )\right )}}{2 \, b^{3}{\rm ln}\left (f\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^2 + a)*x^5,x, algorithm="giac")
[Out]