Optimal. Leaf size=21 \[ \frac{2 \left (a+b x^n\right )^{3/2}}{3 b n} \]
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Rubi [A] time = 0.0055118, antiderivative size = 21, 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 = {261} \[ \frac{2 \left (a+b x^n\right )^{3/2}}{3 b n} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x^{-1+n} \sqrt{a+b x^n} \, dx &=\frac{2 \left (a+b x^n\right )^{3/2}}{3 b n}\\ \end{align*}
Mathematica [A] time = 0.0059373, size = 21, normalized size = 1. \[ \frac{2 \left (a+b x^n\right )^{3/2}}{3 b n} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.017, size = 18, normalized size = 0.9 \begin{align*}{\frac{2}{3\,bn} \left ( a+b{x}^{n} \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.950077, size = 23, normalized size = 1.1 \begin{align*} \frac{2 \,{\left (b x^{n} + a\right )}^{\frac{3}{2}}}{3 \, b n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.01527, size = 39, normalized size = 1.86 \begin{align*} \frac{2 \,{\left (b x^{n} + a\right )}^{\frac{3}{2}}}{3 \, b n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 4.54024, size = 48, normalized size = 2.29 \begin{align*} \frac{2 a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{n}}{a}}}{3 b n} + \frac{2 \sqrt{a} x^{n} \sqrt{1 + \frac{b x^{n}}{a}}}{3 n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13554, size = 23, normalized size = 1.1 \begin{align*} \frac{2 \,{\left (b x^{n} + a\right )}^{\frac{3}{2}}}{3 \, b n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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