Optimal. Leaf size=19 \[ \frac{\left (a+b x^n\right )^6}{6 b n} \]
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Rubi [A] time = 0.0050139, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {261} \[ \frac{\left (a+b x^n\right )^6}{6 b n} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x^{-1+n} \left (a+b x^n\right )^5 \, dx &=\frac{\left (a+b x^n\right )^6}{6 b n}\\ \end{align*}
Mathematica [A] time = 0.0045616, size = 19, normalized size = 1. \[ \frac{\left (a+b x^n\right )^6}{6 b n} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.018, size = 84, normalized size = 4.4 \begin{align*}{\frac{{b}^{5} \left ({x}^{n} \right ) ^{6}}{6\,n}}+{\frac{a{b}^{4} \left ({x}^{n} \right ) ^{5}}{n}}+{\frac{5\,{a}^{2}{b}^{3} \left ({x}^{n} \right ) ^{4}}{2\,n}}+{\frac{10\,{a}^{3}{b}^{2} \left ({x}^{n} \right ) ^{3}}{3\,n}}+{\frac{5\,{a}^{4}b \left ({x}^{n} \right ) ^{2}}{2\,n}}+{\frac{{a}^{5}{x}^{n}}{n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.978927, size = 23, normalized size = 1.21 \begin{align*} \frac{{\left (b x^{n} + a\right )}^{6}}{6 \, b n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.34633, size = 151, normalized size = 7.95 \begin{align*} \frac{b^{5} x^{6 \, n} + 6 \, a b^{4} x^{5 \, n} + 15 \, a^{2} b^{3} x^{4 \, n} + 20 \, a^{3} b^{2} x^{3 \, n} + 15 \, a^{4} b x^{2 \, n} + 6 \, a^{5} x^{n}}{6 \, n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 15.3076, size = 88, normalized size = 4.63 \begin{align*} \begin{cases} \frac{a^{5} x^{n}}{n} + \frac{5 a^{4} b x^{2 n}}{2 n} + \frac{10 a^{3} b^{2} x^{3 n}}{3 n} + \frac{5 a^{2} b^{3} x^{4 n}}{2 n} + \frac{a b^{4} x^{5 n}}{n} + \frac{b^{5} x^{6 n}}{6 n} & \text{for}\: n \neq 0 \\\left (a + b\right )^{5} \log{\left (x \right )} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.20247, size = 96, normalized size = 5.05 \begin{align*} \frac{b^{5} x^{6 \, n} + 6 \, a b^{4} x^{5 \, n} + 15 \, a^{2} b^{3} x^{4 \, n} + 20 \, a^{3} b^{2} x^{3 \, n} + 15 \, a^{4} b x^{2 \, n} + 6 \, a^{5} x^{n}}{6 \, n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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