Optimal. Leaf size=53 \[ \frac{b F^a \log (F) \text{ExpIntegralEi}\left (b \log (F) (c+d x)^3\right )}{3 d}-\frac{F^{a+b (c+d x)^3}}{3 d (c+d x)^3} \]
[Out]
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Rubi [A] time = 0.202287, antiderivative size = 53, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.095 \[ \frac{b F^a \log (F) \text{ExpIntegralEi}\left (b \log (F) (c+d x)^3\right )}{3 d}-\frac{F^{a+b (c+d x)^3}}{3 d (c+d x)^3} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b*(c + d*x)^3)/(c + d*x)^4,x]
[Out]
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Rubi in Sympy [A] time = 9.22558, size = 46, normalized size = 0.87 \[ \frac{F^{a} b \log{\left (F \right )} \operatorname{Ei}{\left (b \left (c + d x\right )^{3} \log{\left (F \right )} \right )}}{3 d} - \frac{F^{a + b \left (c + d x\right )^{3}}}{3 d \left (c + d x\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(a+b*(d*x+c)**3)/(d*x+c)**4,x)
[Out]
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Mathematica [A] time = 0.0494521, size = 47, normalized size = 0.89 \[ \frac{F^a \left (b \log (F) \text{ExpIntegralEi}\left (b \log (F) (c+d x)^3\right )-\frac{F^{b (c+d x)^3}}{(c+d x)^3}\right )}{3 d} \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b*(c + d*x)^3)/(c + d*x)^4,x]
[Out]
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Maple [F] time = 0.06, size = 0, normalized size = 0. \[ \int{\frac{{F}^{a+b \left ( dx+c \right ) ^{3}}}{ \left ( dx+c \right ) ^{4}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(a+b*(d*x+c)^3)/(d*x+c)^4,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{{\left (d x + c\right )}^{3} b + a}}{{\left (d x + c\right )}^{4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((d*x + c)^3*b + a)/(d*x + c)^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.259746, size = 198, normalized size = 3.74 \[ \frac{{\left (b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3}\right )} F^{a}{\rm Ei}\left ({\left (b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3}\right )} \log \left (F\right )\right ) \log \left (F\right ) - F^{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}}{3 \,{\left (d^{4} x^{3} + 3 \, c d^{3} x^{2} + 3 \, c^{2} d^{2} x + c^{3} d\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((d*x + c)^3*b + a)/(d*x + c)^4,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)**4,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{{\left (d x + c\right )}^{3} b + a}}{{\left (d x + c\right )}^{4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^((d*x + c)^3*b + a)/(d*x + c)^4,x, algorithm="giac")
[Out]