Optimal. Leaf size=54 \[ -\frac{F^a \left (-b \log (F) (c+d x)^n\right )^{2/n} \text{Gamma}\left (-\frac{2}{n},-b \log (F) (c+d x)^n\right )}{d n (c+d x)^2} \]
[Out]
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Rubi [A] time = 0.0603146, 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 \[ -\frac{F^a \left (-b \log (F) (c+d x)^n\right )^{2/n} \text{Gamma}\left (-\frac{2}{n},-b \log (F) (c+d x)^n\right )}{d n (c+d x)^2} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b*(c + d*x)^n)/(c + d*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 6.1897, size = 49, normalized size = 0.91 \[ - \frac{F^{a} \left (- b \left (c + d x\right )^{n} \log{\left (F \right )}\right )^{\frac{2}{n}} \Gamma{\left (- \frac{2}{n},- b \left (c + d x\right )^{n} \log{\left (F \right )} \right )}}{d n \left (c + d x\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(a+b*(d*x+c)**n)/(d*x+c)**3,x)
[Out]
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Mathematica [A] time = 0.0293063, size = 54, normalized size = 1. \[ -\frac{F^a \left (-b \log (F) (c+d x)^n\right )^{2/n} \text{Gamma}\left (-\frac{2}{n},-b \log (F) (c+d x)^n\right )}{d n (c+d x)^2} \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b*(c + d*x)^n)/(c + d*x)^3,x]
[Out]
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Maple [F] time = 0.036, size = 0, normalized size = 0. \[ \int{\frac{{F}^{a+b \left ( dx+c \right ) ^{n}}}{ \left ( dx+c \right ) ^{3}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(a+b*(d*x+c)^n)/(d*x+c)^3,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{{\left (d x + c\right )}^{n} b + a}}{{\left (d x + c\right )}^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((d*x + c)^n*b + a)/(d*x + c)^3,x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{F^{{\left (d x + c\right )}^{n} b + a}}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((d*x + c)^n*b + a)/(d*x + c)^3,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)**3,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{{\left (d x + c\right )}^{n} b + a}}{{\left (d x + c\right )}^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((d*x + c)^n*b + a)/(d*x + c)^3,x, algorithm="giac")
[Out]