Optimal. Leaf size=41 \[ \frac{\sqrt{\pi } \text{Erfi}\left (\sqrt{c} \sqrt{\log (f)} (a+b x)\right )}{2 b \sqrt{c} \sqrt{\log (f)}} \]
[Out]
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Rubi [A] time = 0.0213947, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{\sqrt{\pi } \text{Erfi}\left (\sqrt{c} \sqrt{\log (f)} (a+b x)\right )}{2 b \sqrt{c} \sqrt{\log (f)}} \]
Antiderivative was successfully verified.
[In] Int[f^(c*(a + b*x)^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int f^{a^{2} c + 2 a b c x + b^{2} c x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(c*(b*x+a)**2),x)
[Out]
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Mathematica [A] time = 0.00597152, size = 41, normalized size = 1. \[ \frac{\sqrt{\pi } \text{Erfi}\left (\sqrt{c} \sqrt{\log (f)} (a+b x)\right )}{2 b \sqrt{c} \sqrt{\log (f)}} \]
Antiderivative was successfully verified.
[In] Integrate[f^(c*(a + b*x)^2),x]
[Out]
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Maple [A] time = 0.028, size = 41, normalized size = 1. \[ -{\frac{\sqrt{\pi }}{2\,b}{\it Erf} \left ( -b\sqrt{-c\ln \left ( f \right ) }x+{ac\ln \left ( f \right ){\frac{1}{\sqrt{-c\ln \left ( f \right ) }}}} \right ){\frac{1}{\sqrt{-c\ln \left ( f \right ) }}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(c*(b*x+a)^2),x)
[Out]
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Maxima [A] time = 0.833927, size = 54, normalized size = 1.32 \[ \frac{\sqrt{\pi } \operatorname{erf}\left (\sqrt{-c \log \left (f\right )} b x - \frac{a c \log \left (f\right )}{\sqrt{-c \log \left (f\right )}}\right )}{2 \, \sqrt{-c \log \left (f\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^((b*x + a)^2*c),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.271681, size = 47, normalized size = 1.15 \[ \frac{\sqrt{\pi } \operatorname{erf}\left (\frac{\sqrt{-b^{2} c \log \left (f\right )}{\left (b x + a\right )}}{b}\right )}{2 \, \sqrt{-b^{2} c \log \left (f\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^((b*x + a)^2*c),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int f^{c \left (a + b x\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(c*(b*x+a)**2),x)
[Out]
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GIAC/XCAS [A] time = 0.253157, size = 45, normalized size = 1.1 \[ -\frac{\sqrt{\pi } \operatorname{erf}\left (-\sqrt{-c{\rm ln}\left (f\right )} b{\left (x + \frac{a}{b}\right )}\right )}{2 \, \sqrt{-c{\rm ln}\left (f\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^((b*x + a)^2*c),x, algorithm="giac")
[Out]