Optimal. Leaf size=31 \[ \frac{F^a \text{Gamma}\left (5,-b \log (F) (c+d x)^n\right )}{b^5 d n \log ^5(F)} \]
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Rubi [A] time = 0.0639668, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.04 \[ \frac{F^a \text{Gamma}\left (5,-b \log (F) (c+d x)^n\right )}{b^5 d n \log ^5(F)} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 + 5*n),x]
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Rubi in Sympy [A] time = 6.32169, size = 29, normalized size = 0.94 \[ \frac{F^{a} \Gamma{\left (5,- b \left (c + d x\right )^{n} \log{\left (F \right )} \right )}}{b^{5} d n \log{\left (F \right )}^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(a+b*(d*x+c)**n)*(d*x+c)**(-1+5*n),x)
[Out]
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Mathematica [B] time = 0.0475101, size = 94, normalized size = 3.03 \[ \frac{F^{a+b (c+d x)^n} \left (b^4 \log ^4(F) (c+d x)^{4 n}-4 b^3 \log ^3(F) (c+d x)^{3 n}+12 b^2 \log ^2(F) (c+d x)^{2 n}-24 b \log (F) (c+d x)^n+24\right )}{b^5 d n \log ^5(F)} \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 + 5*n),x]
[Out]
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Maple [A] time = 0.033, size = 95, normalized size = 3.1 \[{\frac{ \left ({b}^{4} \left ( \left ( dx+c \right ) ^{n} \right ) ^{4} \left ( \ln \left ( F \right ) \right ) ^{4}-4\,{b}^{3} \left ( \left ( dx+c \right ) ^{n} \right ) ^{3} \left ( \ln \left ( F \right ) \right ) ^{3}+12\,{b}^{2} \left ( \left ( dx+c \right ) ^{n} \right ) ^{2} \left ( \ln \left ( F \right ) \right ) ^{2}-24\,b \left ( dx+c \right ) ^{n}\ln \left ( F \right ) +24 \right ){F}^{a+b \left ( dx+c \right ) ^{n}}}{ \left ( \ln \left ( F \right ) \right ) ^{5}{b}^{5}nd}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(a+b*(d*x+c)^n)*(d*x+c)^(-1+5*n),x)
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Maxima [A] time = 0.7999, size = 146, normalized size = 4.71 \[ \frac{{\left ({\left (d x + c\right )}^{4 \, n} F^{a} b^{4} \log \left (F\right )^{4} - 4 \,{\left (d x + c\right )}^{3 \, n} F^{a} b^{3} \log \left (F\right )^{3} + 12 \,{\left (d x + c\right )}^{2 \, n} F^{a} b^{2} \log \left (F\right )^{2} - 24 \,{\left (d x + c\right )}^{n} F^{a} b \log \left (F\right ) + 24 \, F^{a}\right )} F^{{\left (d x + c\right )}^{n} b}}{b^{5} d n \log \left (F\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^(5*n - 1)*F^((d*x + c)^n*b + a),x, algorithm="maxima")
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Fricas [A] time = 0.26053, size = 132, normalized size = 4.26 \[ \frac{{\left ({\left (d x + c\right )}^{4 \, n} b^{4} \log \left (F\right )^{4} - 4 \,{\left (d x + c\right )}^{3 \, n} b^{3} \log \left (F\right )^{3} + 12 \,{\left (d x + c\right )}^{2 \, n} b^{2} \log \left (F\right )^{2} - 24 \,{\left (d x + c\right )}^{n} b \log \left (F\right ) + 24\right )} e^{\left ({\left (d x + c\right )}^{n} b \log \left (F\right ) + a \log \left (F\right )\right )}}{b^{5} d n \log \left (F\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^(5*n - 1)*F^((d*x + c)^n*b + a),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)**(-1+5*n),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (d x + c\right )}^{5 \, n - 1} F^{{\left (d x + c\right )}^{n} b + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^(5*n - 1)*F^((d*x + c)^n*b + a),x, algorithm="giac")
[Out]