Optimal. Leaf size=114 \[ -\frac {F^{a+b (c+d x)^n} \left (-b^5 \log ^5(F) (c+d x)^{5 n}+5 b^4 \log ^4(F) (c+d x)^{4 n}-20 b^3 \log ^3(F) (c+d x)^{3 n}+60 b^2 \log ^2(F) (c+d x)^{2 n}-120 b \log (F) (c+d x)^n+120\right )}{b^6 d n \log ^6(F)} \]
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Rubi [C] time = 0.04, antiderivative size = 32, normalized size of antiderivative = 0.28, number of steps used = 1, number of rules used = 1, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {2218} \[ -\frac {F^a \text {Gamma}\left (6,-b \log (F) (c+d x)^n\right )}{b^6 d n \log ^6(F)} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int F^{a+b (c+d x)^n} (c+d x)^{-1+6 n} \, dx &=-\frac {F^a \Gamma \left (6,-b (c+d x)^n \log (F)\right )}{b^6 d n \log ^6(F)}\\ \end {align*}
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Mathematica [C] time = 0.01, size = 32, normalized size = 0.28 \[ -\frac {F^a \Gamma \left (6,-b (c+d x)^n \log (F)\right )}{b^6 d n \log ^6(F)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 116, normalized size = 1.02 \[ \frac {{\left ({\left (d x + c\right )}^{5 \, n} b^{5} \log \relax (F)^{5} - 5 \, {\left (d x + c\right )}^{4 \, n} b^{4} \log \relax (F)^{4} + 20 \, {\left (d x + c\right )}^{3 \, n} b^{3} \log \relax (F)^{3} - 60 \, {\left (d x + c\right )}^{2 \, n} b^{2} \log \relax (F)^{2} + 120 \, {\left (d x + c\right )}^{n} b \log \relax (F) - 120\right )} e^{\left ({\left (d x + c\right )}^{n} b \log \relax (F) + a \log \relax (F)\right )}}{b^{6} d n \log \relax (F)^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (d x + c\right )}^{6 \, n - 1} F^{{\left (d x + c\right )}^{n} b + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 113, normalized size = 0.99 \[ \frac {\left (b^{5} \left (d x +c \right )^{5 n} \ln \relax (F )^{5}-5 b^{4} \left (d x +c \right )^{4 n} \ln \relax (F )^{4}+20 b^{3} \left (d x +c \right )^{3 n} \ln \relax (F )^{3}-60 b^{2} \left (d x +c \right )^{2 n} \ln \relax (F )^{2}+120 b \left (d x +c \right )^{n} \ln \relax (F )-120\right ) F^{b \left (d x +c \right )^{n}+a}}{b^{6} d n \ln \relax (F )^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.05, size = 129, normalized size = 1.13 \[ \frac {{\left ({\left (d x + c\right )}^{5 \, n} F^{a} b^{5} \log \relax (F)^{5} - 5 \, {\left (d x + c\right )}^{4 \, n} F^{a} b^{4} \log \relax (F)^{4} + 20 \, {\left (d x + c\right )}^{3 \, n} F^{a} b^{3} \log \relax (F)^{3} - 60 \, {\left (d x + c\right )}^{2 \, n} F^{a} b^{2} \log \relax (F)^{2} + 120 \, {\left (d x + c\right )}^{n} F^{a} b \log \relax (F) - 120 \, F^{a}\right )} F^{{\left (d x + c\right )}^{n} b}}{b^{6} d n \log \relax (F)^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.01 \[ \int F^{a+b\,{\left (c+d\,x\right )}^n}\,{\left (c+d\,x\right )}^{6\,n-1} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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