Optimal. Leaf size=19 \[ \frac{\left (a+b x^n\right )^3}{3 b n} \]
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Rubi [A] time = 0.0044414, 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} \[ \frac{\left (a+b x^n\right )^3}{3 b n} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x^{-1+n} \left (a+b x^n\right )^2 \, dx &=\frac{\left (a+b x^n\right )^3}{3 b n}\\ \end{align*}
Mathematica [A] time = 0.0038543, size = 19, normalized size = 1. \[ \frac{\left (a+b x^n\right )^3}{3 b n} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.013, size = 42, normalized size = 2.2 \begin{align*}{\frac{{a}^{2}{{\rm e}^{n\ln \left ( x \right ) }}}{n}}+{\frac{ab \left ({{\rm e}^{n\ln \left ( x \right ) }} \right ) ^{2}}{n}}+{\frac{{b}^{2} \left ({{\rm e}^{n\ln \left ( x \right ) }} \right ) ^{3}}{3\,n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.974294, size = 23, normalized size = 1.21 \begin{align*} \frac{{\left (b x^{n} + a\right )}^{3}}{3 \, b n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.05083, size = 66, normalized size = 3.47 \begin{align*} \frac{b^{2} x^{3 \, n} + 3 \, a b x^{2 \, n} + 3 \, a^{2} x^{n}}{3 \, n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 3.66632, size = 37, normalized size = 1.95 \begin{align*} \begin{cases} \frac{a^{2} x^{n}}{n} + \frac{a b x^{2 n}}{n} + \frac{b^{2} x^{3 n}}{3 n} & \text{for}\: n \neq 0 \\\left (a + b\right )^{2} \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 [A] time = 1.18935, size = 43, normalized size = 2.26 \begin{align*} \frac{b^{2} x^{3 \, n} + 3 \, a b x^{2 \, n} + 3 \, a^{2} x^{n}}{3 \, n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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