Optimal. Leaf size=44 \[ \frac{\sqrt{\pi } F^a \text{Erfi}\left (\sqrt{b} \sqrt{\log (F)} (c+d x)\right )}{2 \sqrt{b} d \sqrt{\log (F)}} \]
[Out]
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Rubi [A] time = 0.02603, antiderivative size = 44, 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 \[ \frac{\sqrt{\pi } F^a \text{Erfi}\left (\sqrt{b} \sqrt{\log (F)} (c+d x)\right )}{2 \sqrt{b} d \sqrt{\log (F)}} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b*(c + d*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 2.61782, size = 41, normalized size = 0.93 \[ \frac{\sqrt{\pi } F^{a} \operatorname{erfi}{\left (\sqrt{b} \left (c + d x\right ) \sqrt{\log{\left (F \right )}} \right )}}{2 \sqrt{b} d \sqrt{\log{\left (F \right )}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(a+b*(d*x+c)**2),x)
[Out]
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Mathematica [A] time = 0.00764215, size = 44, normalized size = 1. \[ \frac{\sqrt{\pi } F^a \text{Erfi}\left (\sqrt{b} \sqrt{\log (F)} (c+d x)\right )}{2 \sqrt{b} d \sqrt{\log (F)}} \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b*(c + d*x)^2),x]
[Out]
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Maple [A] time = 0.027, size = 44, normalized size = 1. \[ -{\frac{{F}^{a}\sqrt{\pi }}{2\,d}{\it Erf} \left ( -d\sqrt{-b\ln \left ( F \right ) }x+{cb\ln \left ( F \right ){\frac{1}{\sqrt{-b\ln \left ( F \right ) }}}} \right ){\frac{1}{\sqrt{-b\ln \left ( F \right ) }}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(a+b*(d*x+c)^2),x)
[Out]
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Maxima [A] time = 0.925755, size = 78, normalized size = 1.77 \[ \frac{\sqrt{\pi } F^{b c^{2} + a} \operatorname{erf}\left (\sqrt{-b \log \left (F\right )} d x - \frac{b c \log \left (F\right )}{\sqrt{-b \log \left (F\right )}}\right )}{2 \, \sqrt{-b \log \left (F\right )} F^{b c^{2}} d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((d*x + c)^2*b + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.262297, size = 51, normalized size = 1.16 \[ \frac{\sqrt{\pi } F^{a} \operatorname{erf}\left (\frac{\sqrt{-b d^{2} \log \left (F\right )}{\left (d x + c\right )}}{d}\right )}{2 \, \sqrt{-b d^{2} \log \left (F\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((d*x + c)^2*b + a),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int F^{a + b \left (c + d x\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F**(a+b*(d*x+c)**2),x)
[Out]
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GIAC/XCAS [A] time = 0.236733, size = 51, normalized size = 1.16 \[ -\frac{\sqrt{\pi } \operatorname{erf}\left (-\sqrt{-b{\rm ln}\left (F\right )} d{\left (x + \frac{c}{d}\right )}\right ) e^{\left (a{\rm ln}\left (F\right )\right )}}{2 \, \sqrt{-b{\rm ln}\left (F\right )} d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((d*x + c)^2*b + a),x, algorithm="giac")
[Out]