Optimal. Leaf size=183 \[ -\frac{105 \sqrt{\pi } F^a \text{Erfi}\left (\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right )}{32 b^{9/2} d \log ^{\frac{9}{2}}(F)}+\frac{105 F^{a+\frac{b}{(c+d x)^2}}}{16 b^4 d \log ^4(F) (c+d x)}-\frac{35 F^{a+\frac{b}{(c+d x)^2}}}{8 b^3 d \log ^3(F) (c+d x)^3}+\frac{7 F^{a+\frac{b}{(c+d x)^2}}}{4 b^2 d \log ^2(F) (c+d x)^5}-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F) (c+d x)^7} \]
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Rubi [A] time = 0.438499, antiderivative size = 183, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 3, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ -\frac{105 \sqrt{\pi } F^a \text{Erfi}\left (\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right )}{32 b^{9/2} d \log ^{\frac{9}{2}}(F)}+\frac{105 F^{a+\frac{b}{(c+d x)^2}}}{16 b^4 d \log ^4(F) (c+d x)}-\frac{35 F^{a+\frac{b}{(c+d x)^2}}}{8 b^3 d \log ^3(F) (c+d x)^3}+\frac{7 F^{a+\frac{b}{(c+d x)^2}}}{4 b^2 d \log ^2(F) (c+d x)^5}-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F) (c+d x)^7} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b/(c + d*x)^2)/(c + d*x)^10,x]
[Out]
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Rubi in Sympy [A] time = 44.2207, size = 165, normalized size = 0.9 \[ - \frac{105 \sqrt{\pi } F^{a} \operatorname{erfi}{\left (\frac{\sqrt{b} \sqrt{\log{\left (F \right )}}}{c + d x} \right )}}{32 b^{\frac{9}{2}} d \log{\left (F \right )}^{\frac{9}{2}}} - \frac{F^{a + \frac{b}{\left (c + d x\right )^{2}}}}{2 b d \left (c + d x\right )^{7} \log{\left (F \right )}} + \frac{7 F^{a + \frac{b}{\left (c + d x\right )^{2}}}}{4 b^{2} d \left (c + d x\right )^{5} \log{\left (F \right )}^{2}} - \frac{35 F^{a + \frac{b}{\left (c + d x\right )^{2}}}}{8 b^{3} d \left (c + d x\right )^{3} \log{\left (F \right )}^{3}} + \frac{105 F^{a + \frac{b}{\left (c + d x\right )^{2}}}}{16 b^{4} d \left (c + d x\right ) \log{\left (F \right )}^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(a+b/(d*x+c)**2)/(d*x+c)**10,x)
[Out]
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Mathematica [A] time = 0.185695, size = 127, normalized size = 0.69 \[ \frac{F^a \left (\frac{2 \sqrt{b} \sqrt{\log (F)} F^{\frac{b}{(c+d x)^2}} \left (-8 b^3 \log ^3(F)+28 b^2 \log ^2(F) (c+d x)^2-70 b \log (F) (c+d x)^4+105 (c+d x)^6\right )}{(c+d x)^7}-105 \sqrt{\pi } \text{Erfi}\left (\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right )\right )}{32 b^{9/2} d \log ^{\frac{9}{2}}(F)} \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b/(c + d*x)^2)/(c + d*x)^10,x]
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Maple [A] time = 0.197, size = 175, normalized size = 1. \[ -{\frac{{F}^{a}}{2\,d \left ( dx+c \right ) ^{7}b\ln \left ( F \right ) }{F}^{{\frac{b}{ \left ( dx+c \right ) ^{2}}}}}+{\frac{7\,{F}^{a}}{4\, \left ( \ln \left ( F \right ) \right ) ^{2}{b}^{2}d \left ( dx+c \right ) ^{5}}{F}^{{\frac{b}{ \left ( dx+c \right ) ^{2}}}}}-{\frac{35\,{F}^{a}}{8\,d{b}^{3} \left ( \ln \left ( F \right ) \right ) ^{3} \left ( dx+c \right ) ^{3}}{F}^{{\frac{b}{ \left ( dx+c \right ) ^{2}}}}}+{\frac{105\,{F}^{a}}{16\,d{b}^{4} \left ( \ln \left ( F \right ) \right ) ^{4} \left ( dx+c \right ) }{F}^{{\frac{b}{ \left ( dx+c \right ) ^{2}}}}}-{\frac{105\,{F}^{a}\sqrt{\pi }}{32\,d{b}^{4} \left ( \ln \left ( F \right ) \right ) ^{4}}{\it Erf} \left ({\frac{1}{dx+c}\sqrt{-b\ln \left ( F \right ) }} \right ){\frac{1}{\sqrt{-b\ln \left ( F \right ) }}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(a+b/(d*x+c)^2)/(d*x+c)^10,x)
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{a + \frac{b}{{\left (d x + c\right )}^{2}}}}{{\left (d x + c\right )}^{10}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(a + b/(d*x + c)^2)/(d*x + c)^10,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.286014, size = 587, normalized size = 3.21 \[ -\frac{105 \, \sqrt{\pi }{\left (d^{7} x^{7} + 7 \, c d^{6} x^{6} + 21 \, c^{2} d^{5} x^{5} + 35 \, c^{3} d^{4} x^{4} + 35 \, c^{4} d^{3} x^{3} + 21 \, c^{5} d^{2} x^{2} + 7 \, c^{6} d x + c^{7}\right )} F^{a} \operatorname{erf}\left (\frac{d \sqrt{-\frac{b \log \left (F\right )}{d^{2}}}}{d x + c}\right ) - 2 \,{\left (105 \, d^{7} x^{6} + 630 \, c d^{6} x^{5} + 1575 \, c^{2} d^{5} x^{4} + 2100 \, c^{3} d^{4} x^{3} + 1575 \, c^{4} d^{3} x^{2} + 630 \, c^{5} d^{2} x + 105 \, c^{6} d - 8 \, b^{3} d \log \left (F\right )^{3} + 28 \,{\left (b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right )} \log \left (F\right )^{2} - 70 \,{\left (b d^{5} x^{4} + 4 \, b c d^{4} x^{3} + 6 \, b c^{2} d^{3} x^{2} + 4 \, b c^{3} d^{2} x + b c^{4} d\right )} \log \left (F\right )\right )} F^{\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}} \sqrt{-\frac{b \log \left (F\right )}{d^{2}}}}{32 \,{\left (b^{4} d^{9} x^{7} + 7 \, b^{4} c d^{8} x^{6} + 21 \, b^{4} c^{2} d^{7} x^{5} + 35 \, b^{4} c^{3} d^{6} x^{4} + 35 \, b^{4} c^{4} d^{5} x^{3} + 21 \, b^{4} c^{5} d^{4} x^{2} + 7 \, b^{4} c^{6} d^{3} x + b^{4} c^{7} d^{2}\right )} \sqrt{-\frac{b \log \left (F\right )}{d^{2}}} \log \left (F\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(a + b/(d*x + c)^2)/(d*x + c)^10,x, algorithm="fricas")
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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**(a+b/(d*x+c)**2)/(d*x+c)**10,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{a + \frac{b}{{\left (d x + c\right )}^{2}}}}{{\left (d x + c\right )}^{10}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(a + b/(d*x + c)^2)/(d*x + c)^10,x, algorithm="giac")
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