Optimal. Leaf size=39 \[ \frac{f^{a-\frac{b^2}{4 c}} \text{ExpIntegralEi}\left (\frac{\log (f) (b+2 c x)^2}{4 c}\right )}{4 c} \]
[Out]
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Rubi [A] time = 0.0604502, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048 \[ \frac{f^{a-\frac{b^2}{4 c}} \text{ExpIntegralEi}\left (\frac{\log (f) (b+2 c x)^2}{4 c}\right )}{4 c} \]
Antiderivative was successfully verified.
[In] Int[f^(a + b*x + c*x^2)/(b + 2*c*x),x]
[Out]
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Rubi in Sympy [A] time = 5.74068, size = 29, normalized size = 0.74 \[ \frac{f^{a - \frac{b^{2}}{4 c}} \operatorname{Ei}{\left (\frac{\left (b + 2 c x\right )^{2} \log{\left (f \right )}}{4 c} \right )}}{4 c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(c*x**2+b*x+a)/(2*c*x+b),x)
[Out]
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Mathematica [A] time = 0.020148, size = 39, normalized size = 1. \[ \frac{f^{a-\frac{b^2}{4 c}} \text{ExpIntegralEi}\left (\frac{\log (f) (b+2 c x)^2}{4 c}\right )}{4 c} \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b*x + c*x^2)/(b + 2*c*x),x]
[Out]
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Maple [A] time = 0.026, size = 40, normalized size = 1. \[ -{\frac{1}{4\,c}{f}^{{\frac{4\,ac-{b}^{2}}{4\,c}}}{\it Ei} \left ( 1,-{\frac{ \left ( 2\,cx+b \right ) ^{2}\ln \left ( f \right ) }{4\,c}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(c*x^2+b*x+a)/(2*c*x+b),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{c x^{2} + b x + a}}{2 \, c x + b}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(c*x^2 + b*x + a)/(2*c*x + b),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.264996, size = 63, normalized size = 1.62 \[ \frac{{\rm Ei}\left (\frac{{\left (4 \, c^{2} x^{2} + 4 \, b c x + b^{2}\right )} \log \left (f\right )}{4 \, c}\right )}{4 \, c f^{\frac{b^{2} - 4 \, a c}{4 \, c}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(c*x^2 + b*x + a)/(2*c*x + b),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{a + b x + c x^{2}}}{b + 2 c x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(c*x**2+b*x+a)/(2*c*x+b),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{c x^{2} + b x + a}}{2 \, c x + b}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(c*x^2 + b*x + a)/(2*c*x + b),x, algorithm="giac")
[Out]