Optimal. Leaf size=86 \[ -\frac{3 f^{a+b x^2}}{b^4 \log ^4(f)}+\frac{3 x^2 f^{a+b x^2}}{b^3 \log ^3(f)}-\frac{3 x^4 f^{a+b x^2}}{2 b^2 \log ^2(f)}+\frac{x^6 f^{a+b x^2}}{2 b \log (f)} \]
[Out]
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Rubi [A] time = 0.152245, antiderivative size = 86, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{3 f^{a+b x^2}}{b^4 \log ^4(f)}+\frac{3 x^2 f^{a+b x^2}}{b^3 \log ^3(f)}-\frac{3 x^4 f^{a+b x^2}}{2 b^2 \log ^2(f)}+\frac{x^6 f^{a+b x^2}}{2 b \log (f)} \]
Antiderivative was successfully verified.
[In] Int[f^(a + b*x^2)*x^7,x]
[Out]
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Rubi in Sympy [A] time = 15.1668, size = 82, normalized size = 0.95 \[ \frac{f^{a + b x^{2}} x^{6}}{2 b \log{\left (f \right )}} - \frac{3 f^{a + b x^{2}} x^{4}}{2 b^{2} \log{\left (f \right )}^{2}} + \frac{3 f^{a + b x^{2}} x^{2}}{b^{3} \log{\left (f \right )}^{3}} - \frac{3 f^{a + b x^{2}}}{b^{4} \log{\left (f \right )}^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(b*x**2+a)*x**7,x)
[Out]
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Mathematica [A] time = 0.0155025, size = 53, normalized size = 0.62 \[ \frac{f^{a+b x^2} \left (b^3 x^6 \log ^3(f)-3 b^2 x^4 \log ^2(f)+6 b x^2 \log (f)-6\right )}{2 b^4 \log ^4(f)} \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b*x^2)*x^7,x]
[Out]
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Maple [A] time = 0.012, size = 52, normalized size = 0.6 \[{\frac{ \left ({b}^{3}{x}^{6} \left ( \ln \left ( f \right ) \right ) ^{3}-3\,{b}^{2}{x}^{4} \left ( \ln \left ( f \right ) \right ) ^{2}+6\,b{x}^{2}\ln \left ( f \right ) -6 \right ){f}^{b{x}^{2}+a}}{2\, \left ( \ln \left ( f \right ) \right ) ^{4}{b}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(b*x^2+a)*x^7,x)
[Out]
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Maxima [A] time = 0.816518, size = 84, normalized size = 0.98 \[ \frac{{\left (b^{3} f^{a} x^{6} \log \left (f\right )^{3} - 3 \, b^{2} f^{a} x^{4} \log \left (f\right )^{2} + 6 \, b f^{a} x^{2} \log \left (f\right ) - 6 \, f^{a}\right )} f^{b x^{2}}}{2 \, b^{4} \log \left (f\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^2 + a)*x^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.237203, size = 69, normalized size = 0.8 \[ \frac{{\left (b^{3} x^{6} \log \left (f\right )^{3} - 3 \, b^{2} x^{4} \log \left (f\right )^{2} + 6 \, b x^{2} \log \left (f\right ) - 6\right )} f^{b x^{2} + a}}{2 \, b^{4} \log \left (f\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^2 + a)*x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.267173, size = 68, normalized size = 0.79 \[ \begin{cases} \frac{f^{a + b x^{2}} \left (b^{3} x^{6} \log{\left (f \right )}^{3} - 3 b^{2} x^{4} \log{\left (f \right )}^{2} + 6 b x^{2} \log{\left (f \right )} - 6\right )}{2 b^{4} \log{\left (f \right )}^{4}} & \text{for}\: 2 b^{4} \log{\left (f \right )}^{4} \neq 0 \\\frac{x^{8}}{8} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(b*x**2+a)*x**7,x)
[Out]
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GIAC/XCAS [A] time = 0.289775, size = 74, normalized size = 0.86 \[ \frac{{\left (b^{3} x^{6}{\rm ln}\left (f\right )^{3} - 3 \, b^{2} x^{4}{\rm ln}\left (f\right )^{2} + 6 \, b x^{2}{\rm ln}\left (f\right ) - 6\right )} e^{\left (b x^{2}{\rm ln}\left (f\right ) + a{\rm ln}\left (f\right )\right )}}{2 \, b^{4}{\rm ln}\left (f\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^2 + a)*x^7,x, algorithm="giac")
[Out]