Optimal. Leaf size=24 \[ -\frac{x^{-6 n} \left (a+b x^n\right )^6}{6 a n} \]
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Rubi [A] time = 0.004856, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {264} \[ -\frac{x^{-6 n} \left (a+b x^n\right )^6}{6 a n} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int x^{-1-6 n} \left (a+b x^n\right )^5 \, dx &=-\frac{x^{-6 n} \left (a+b x^n\right )^6}{6 a n}\\ \end{align*}
Mathematica [A] time = 0.008275, size = 24, normalized size = 1. \[ -\frac{x^{-6 n} \left (a+b x^n\right )^6}{6 a n} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.02, size = 88, normalized size = 3.7 \begin{align*} -{\frac{{b}^{5}}{n{x}^{n}}}-{\frac{5\,a{b}^{4}}{2\,n \left ({x}^{n} \right ) ^{2}}}-{\frac{10\,{a}^{2}{b}^{3}}{3\,n \left ({x}^{n} \right ) ^{3}}}-{\frac{5\,{a}^{3}{b}^{2}}{2\,n \left ({x}^{n} \right ) ^{4}}}-{\frac{{a}^{4}b}{n \left ({x}^{n} \right ) ^{5}}}-{\frac{{a}^{5}}{6\,n \left ({x}^{n} \right ) ^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.33857, size = 155, normalized size = 6.46 \begin{align*} -\frac{6 \, b^{5} x^{5 \, n} + 15 \, a b^{4} x^{4 \, n} + 20 \, a^{2} b^{3} x^{3 \, n} + 15 \, a^{3} b^{2} x^{2 \, n} + 6 \, a^{4} b x^{n} + a^{5}}{6 \, n x^{6 \, n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.21082, size = 97, normalized size = 4.04 \begin{align*} -\frac{6 \, b^{5} x^{5 \, n} + 15 \, a b^{4} x^{4 \, n} + 20 \, a^{2} b^{3} x^{3 \, n} + 15 \, a^{3} b^{2} x^{2 \, n} + 6 \, a^{4} b x^{n} + a^{5}}{6 \, n x^{6 \, n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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