Optimal. Leaf size=50 \[ -\frac{F^a (c+d x) \left (-b \log (F) (c+d x)^n\right )^{-1/n} \text{Gamma}\left (\frac{1}{n},-b \log (F) (c+d x)^n\right )}{d n} \]
[Out]
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Rubi [A] time = 0.0196655, antiderivative size = 50, 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 \[ -\frac{F^a (c+d x) \left (-b \log (F) (c+d x)^n\right )^{-1/n} \text{Gamma}\left (\frac{1}{n},-b \log (F) (c+d x)^n\right )}{d n} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b*(c + d*x)^n),x]
[Out]
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Rubi in Sympy [A] time = 2.27071, size = 46, normalized size = 0.92 \[ - \frac{F^{a} \left (- b \left (c + d x\right )^{n} \log{\left (F \right )}\right )^{- \frac{1}{n}} \left (c + d x\right ) \Gamma{\left (\frac{1}{n},- b \left (c + d x\right )^{n} \log{\left (F \right )} \right )}}{d n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(a+b*(d*x+c)**n),x)
[Out]
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Mathematica [A] time = 0.0251039, size = 50, normalized size = 1. \[ -\frac{F^a (c+d x) \left (-b \log (F) (c+d x)^n\right )^{-1/n} \text{Gamma}\left (\frac{1}{n},-b \log (F) (c+d x)^n\right )}{d n} \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b*(c + d*x)^n),x]
[Out]
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Maple [F] time = 0.029, size = 0, normalized size = 0. \[ \int{F}^{a+b \left ( dx+c \right ) ^{n}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(a+b*(d*x+c)^n),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int F^{{\left (d x + c\right )}^{n} b + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((d*x + c)^n*b + a),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (F^{{\left (d x + c\right )}^{n} b + a}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((d*x + c)^n*b + a),x, algorithm="fricas")
[Out]
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F**(a+b*(d*x+c)**n),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int F^{{\left (d x + c\right )}^{n} b + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((d*x + c)^n*b + a),x, algorithm="giac")
[Out]