Optimal. Leaf size=54 \[ -\frac{F^a (c+d x)^3 \left (-b \log (F) (c+d x)^n\right )^{-3/n} \text{Gamma}\left (\frac{3}{n},-b \log (F) (c+d x)^n\right )}{d n} \]
[Out]
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Rubi [A] time = 0.0626757, antiderivative size = 54, 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 \[ -\frac{F^a (c+d x)^3 \left (-b \log (F) (c+d x)^n\right )^{-3/n} \text{Gamma}\left (\frac{3}{n},-b \log (F) (c+d x)^n\right )}{d n} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b*(c + d*x)^n)*(c + d*x)^2,x]
[Out]
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Rubi in Sympy [A] time = 6.01635, size = 48, normalized size = 0.89 \[ - \frac{F^{a} \left (- b \left (c + d x\right )^{n} \log{\left (F \right )}\right )^{- \frac{3}{n}} \left (c + d x\right )^{3} \Gamma{\left (\frac{3}{n},- b \left (c + d x\right )^{n} \log{\left (F \right )} \right )}}{d n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(a+b*(d*x+c)**n)*(d*x+c)**2,x)
[Out]
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Mathematica [A] time = 0.0297984, size = 54, normalized size = 1. \[ -\frac{F^a (c+d x)^3 \left (-b \log (F) (c+d x)^n\right )^{-3/n} \text{Gamma}\left (\frac{3}{n},-b \log (F) (c+d x)^n\right )}{d n} \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b*(c + d*x)^n)*(c + d*x)^2,x]
[Out]
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Maple [F] time = 0.079, size = 0, normalized size = 0. \[ \int{F}^{a+b \left ( dx+c \right ) ^{n}} \left ( dx+c \right ) ^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(a+b*(d*x+c)^n)*(d*x+c)^2,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (d x + c\right )}^{2} F^{{\left (d x + c\right )}^{n} b + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^2*F^((d*x + c)^n*b + a),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left ({\left (d^{2} x^{2} + 2 \, c d x + c^{2}\right )} F^{{\left (d x + c\right )}^{n} b + a}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^2*F^((d*x + c)^n*b + a),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**(a+b*(d*x+c)**n)*(d*x+c)**2,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (d x + c\right )}^{2} F^{{\left (d x + c\right )}^{n} b + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^2*F^((d*x + c)^n*b + a),x, algorithm="giac")
[Out]