Optimal. Leaf size=100 \[ \frac{8}{15} \sqrt{\pi } b^{5/2} F^a \log ^{\frac{5}{2}}(F) \text{Erfi}\left (\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right )-\frac{8 b^2 \log ^2(F) F^{a+b x}}{15 \sqrt{x}}-\frac{2 F^{a+b x}}{5 x^{5/2}}-\frac{4 b \log (F) F^{a+b x}}{15 x^{3/2}} \]
[Out]
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Rubi [A] time = 0.139042, antiderivative size = 100, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{8}{15} \sqrt{\pi } b^{5/2} F^a \log ^{\frac{5}{2}}(F) \text{Erfi}\left (\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right )-\frac{8 b^2 \log ^2(F) F^{a+b x}}{15 \sqrt{x}}-\frac{2 F^{a+b x}}{5 x^{5/2}}-\frac{4 b \log (F) F^{a+b x}}{15 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b*x)/x^(7/2),x]
[Out]
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Rubi in Sympy [A] time = 15.7628, size = 100, normalized size = 1. \[ \frac{8 \sqrt{\pi } F^{a} b^{\frac{5}{2}} \log{\left (F \right )}^{\frac{5}{2}} \operatorname{erfi}{\left (\sqrt{b} \sqrt{x} \sqrt{\log{\left (F \right )}} \right )}}{15} - \frac{8 F^{a + b x} b^{2} \log{\left (F \right )}^{2}}{15 \sqrt{x}} - \frac{4 F^{a + b x} b \log{\left (F \right )}}{15 x^{\frac{3}{2}}} - \frac{2 F^{a + b x}}{5 x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(b*x+a)/x**(7/2),x)
[Out]
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Mathematica [A] time = 0.079998, size = 76, normalized size = 0.76 \[ \frac{2}{15} F^a \left (4 \sqrt{\pi } b^{5/2} \log ^{\frac{5}{2}}(F) \text{Erfi}\left (\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right )-\frac{F^{b x} \left (4 b^2 x^2 \log ^2(F)+2 b x \log (F)+3\right )}{x^{5/2}}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b*x)/x^(7/2),x]
[Out]
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Maple [A] time = 0.02, size = 84, normalized size = 0.8 \[ -{\frac{{F}^{a}}{b} \left ( -b \right ) ^{{\frac{7}{2}}} \left ( \ln \left ( F \right ) \right ) ^{{\frac{5}{2}}} \left ( -{\frac{2\,{{\rm e}^{b\ln \left ( F \right ) x}}}{5} \left ({\frac{4\,{b}^{2}{x}^{2} \left ( \ln \left ( F \right ) \right ) ^{2}}{3}}+{\frac{2\,b\ln \left ( F \right ) x}{3}}+1 \right ){x}^{-{\frac{5}{2}}} \left ( -b \right ) ^{-{\frac{5}{2}}} \left ( \ln \left ( F \right ) \right ) ^{-{\frac{5}{2}}}}+{\frac{8\,\sqrt{\pi }}{15}{b}^{{\frac{5}{2}}}{\it erfi} \left ( \sqrt{b}\sqrt{x}\sqrt{\ln \left ( F \right ) } \right ) \left ( -b \right ) ^{-{\frac{5}{2}}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(b*x+a)/x^(7/2),x)
[Out]
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Maxima [A] time = 0.836354, size = 32, normalized size = 0.32 \[ -\frac{\left (-b x \log \left (F\right )\right )^{\frac{5}{2}} F^{a} \Gamma \left (-\frac{5}{2}, -b x \log \left (F\right )\right )}{x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(b*x + a)/x^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.270217, size = 107, normalized size = 1.07 \[ \frac{2 \,{\left (4 \, \sqrt{\pi } F^{a} b^{3} x^{\frac{5}{2}} \operatorname{erf}\left (\sqrt{-b \log \left (F\right )} \sqrt{x}\right ) \log \left (F\right )^{3} -{\left (4 \, b^{2} x^{2} \log \left (F\right )^{2} + 2 \, b x \log \left (F\right ) + 3\right )} \sqrt{-b \log \left (F\right )} F^{b x + a}\right )}}{15 \, \sqrt{-b \log \left (F\right )} x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(b*x + a)/x^(7/2),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F**(b*x+a)/x**(7/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{b x + a}}{x^{\frac{7}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(b*x + a)/x^(7/2),x, algorithm="giac")
[Out]