Optimal. Leaf size=49 \[ \frac{F^a \text{Gamma}\left (\frac{1}{3},-\frac{b \log (F)}{(c+d x)^3}\right )}{3 d (c+d x) \sqrt [3]{-\frac{b \log (F)}{(c+d x)^3}}} \]
[Out]
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Rubi [A] time = 0.0778039, antiderivative size = 49, 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 \[ \frac{F^a \text{Gamma}\left (\frac{1}{3},-\frac{b \log (F)}{(c+d x)^3}\right )}{3 d (c+d x) \sqrt [3]{-\frac{b \log (F)}{(c+d x)^3}}} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b/(c + d*x)^3)/(c + d*x)^2,x]
[Out]
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Rubi in Sympy [A] time = 5.9025, size = 44, normalized size = 0.9 \[ \frac{F^{a} \Gamma{\left (\frac{1}{3},- \frac{b \log{\left (F \right )}}{\left (c + d x\right )^{3}} \right )}}{3 d \sqrt [3]{- \frac{b \log{\left (F \right )}}{\left (c + d x\right )^{3}}} \left (c + d x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(a+b/(d*x+c)**3)/(d*x+c)**2,x)
[Out]
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Mathematica [A] time = 0.0367174, size = 49, normalized size = 1. \[ \frac{F^a \text{Gamma}\left (\frac{1}{3},-\frac{b \log (F)}{(c+d x)^3}\right )}{3 d (c+d x) \sqrt [3]{-\frac{b \log (F)}{(c+d x)^3}}} \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b/(c + d*x)^3)/(c + d*x)^2,x]
[Out]
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Maple [F] time = 0.051, size = 0, normalized size = 0. \[ \int{\frac{1}{ \left ( dx+c \right ) ^{2}}{F}^{a+{\frac{b}{ \left ( dx+c \right ) ^{3}}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(a+b/(d*x+c)^3)/(d*x+c)^2,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{a + \frac{b}{{\left (d x + c\right )}^{3}}}}{{\left (d x + c\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(a + b/(d*x + c)^3)/(d*x + c)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.265686, size = 73, normalized size = 1.49 \[ \frac{F^{a} \Gamma \left (\frac{1}{3}, -\frac{b \log \left (F\right )}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right )}{3 \, d^{2} \left (-\frac{b \log \left (F\right )}{d^{3}}\right )^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(a + b/(d*x + c)^3)/(d*x + c)^2,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)**3)/(d*x+c)**2,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{a + \frac{b}{{\left (d x + c\right )}^{3}}}}{{\left (d x + c\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(a + b/(d*x + c)^3)/(d*x + c)^2,x, algorithm="giac")
[Out]