Optimal. Leaf size=73 \[ \frac{\left ((d+e x)^3\right )^{-m} F^{c \left (a-\frac{b d}{e}\right )} \left (-\frac{b c \log (F) (d+e x)}{e}\right )^{3 m} \text{Gamma}\left (1-3 m,-\frac{b c \log (F) (d+e x)}{e}\right )}{b c \log (F)} \]
[Out]
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Rubi [A] time = 0.103617, antiderivative size = 73, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 41, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.049 \[ \frac{\left ((d+e x)^3\right )^{-m} F^{c \left (a-\frac{b d}{e}\right )} \left (-\frac{b c \log (F) (d+e x)}{e}\right )^{3 m} \text{Gamma}\left (1-3 m,-\frac{b c \log (F) (d+e x)}{e}\right )}{b c \log (F)} \]
Antiderivative was successfully verified.
[In] Int[F^(c*(a + b*x))/(d^3 + 3*d^2*e*x + 3*d*e^2*x^2 + e^3*x^3)^m,x]
[Out]
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Rubi in Sympy [A] time = 26.2484, size = 65, normalized size = 0.89 \[ \frac{F^{\frac{c \left (a e - b d\right )}{e}} \left (\frac{b c \left (- d - e x\right ) \log{\left (F \right )}}{e}\right )^{3 m} \left (\left (d + e x\right )^{3}\right )^{- m} \Gamma{\left (- 3 m + 1,\frac{b c \left (- d - e x\right ) \log{\left (F \right )}}{e} \right )}}{b c \log{\left (F \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(c*(b*x+a))/((e**3*x**3+3*d*e**2*x**2+3*d**2*e*x+d**3)**m),x)
[Out]
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Mathematica [A] time = 0.0466042, size = 75, normalized size = 1.03 \[ -\frac{(d+e x) \left ((d+e x)^3\right )^{-m} F^{a c-\frac{b c d}{e}} \left (-\frac{b c \log (F) (d+e x)}{e}\right )^{3 m-1} \text{Gamma}\left (1-3 m,-\frac{b c \log (F) (d+e x)}{e}\right )}{e} \]
Antiderivative was successfully verified.
[In] Integrate[F^(c*(a + b*x))/(d^3 + 3*d^2*e*x + 3*d*e^2*x^2 + e^3*x^3)^m,x]
[Out]
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Maple [F] time = 0.082, size = 0, normalized size = 0. \[ \int{\frac{{F}^{c \left ( bx+a \right ) }}{ \left ({e}^{3}{x}^{3}+3\,d{e}^{2}{x}^{2}+3\,{d}^{2}ex+{d}^{3} \right ) ^{m}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(c*(b*x+a))/((e^3*x^3+3*d*e^2*x^2+3*d^2*e*x+d^3)^m),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{{\left (b x + a\right )} c}}{{\left (e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right )}^{m}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((b*x + a)*c)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)^m,x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{F^{b c x + a c}}{{\left (e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right )}^{m}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((b*x + a)*c)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)^m,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**(c*(b*x+a))/((e**3*x**3+3*d*e**2*x**2+3*d**2*e*x+d**3)**m),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{{\left (b x + a\right )} c}}{{\left (e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right )}^{m}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((b*x + a)*c)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)^m,x, algorithm="giac")
[Out]