Optimal. Leaf size=49 \[ -\frac{F^a \left (-b \log (F) (c+d x)^3\right )^{2/3} \text{Gamma}\left (-\frac{2}{3},-b \log (F) (c+d x)^3\right )}{3 d (c+d x)^2} \]
[Out]
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Rubi [A] time = 0.0999681, 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 \[ -\frac{F^a \left (-b \log (F) (c+d x)^3\right )^{2/3} \text{Gamma}\left (-\frac{2}{3},-b \log (F) (c+d x)^3\right )}{3 d (c+d x)^2} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b*(c + d*x)^3)/(c + d*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 5.29846, size = 49, normalized size = 1. \[ - \frac{F^{a} \left (- b \left (c + d x\right )^{3} \log{\left (F \right )}\right )^{\frac{2}{3}} \Gamma{\left (- \frac{2}{3},- b \left (c + d x\right )^{3} \log{\left (F \right )} \right )}}{3 d \left (c + d x\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(a+b*(d*x+c)**3)/(d*x+c)**3,x)
[Out]
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Mathematica [A] time = 0.113851, size = 63, normalized size = 1.29 \[ -\frac{F^a \left (F^{b (c+d x)^3}-\left (-b \log (F) (c+d x)^3\right )^{2/3} \text{Gamma}\left (\frac{1}{3},-b \log (F) (c+d x)^3\right )\right )}{2 d (c+d x)^2} \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b*(c + d*x)^3)/(c + d*x)^3,x]
[Out]
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Maple [F] time = 0.053, size = 0, normalized size = 0. \[ \int{\frac{{F}^{a+b \left ( dx+c \right ) ^{3}}}{ \left ( dx+c \right ) ^{3}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(a+b*(d*x+c)^3)/(d*x+c)^3,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{{\left (d x + c\right )}^{3} b + a}}{{\left (d x + c\right )}^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((d*x + c)^3*b + a)/(d*x + c)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.250853, size = 200, normalized size = 4.08 \[ -\frac{{\left (b d^{3} x^{2} + 2 \, b c d^{2} x + b c^{2} d\right )} F^{a} \Gamma \left (\frac{1}{3}, -{\left (b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3}\right )} \log \left (F\right )\right ) \log \left (F\right ) + \left (-b d^{3} \log \left (F\right )\right )^{\frac{1}{3}} F^{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}}{2 \,{\left (d^{3} x^{2} + 2 \, c d^{2} x + c^{2} d\right )} \left (-b d^{3} \log \left (F\right )\right )^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((d*x + c)^3*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)**3)/(d*x+c)**3,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{{\left (d x + c\right )}^{3} b + a}}{{\left (d x + c\right )}^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((d*x + c)^3*b + a)/(d*x + c)^3,x, algorithm="giac")
[Out]