Optimal. Leaf size=19 \[ \frac{\left (a+b x^n\right )^4}{4 b n} \]
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Rubi [A] time = 0.0045087, 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} \[ \frac{\left (a+b x^n\right )^4}{4 b n} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x^{-1+n} \left (a+b x^n\right )^3 \, dx &=\frac{\left (a+b x^n\right )^4}{4 b n}\\ \end{align*}
Mathematica [A] time = 0.0036553, size = 19, normalized size = 1. \[ \frac{\left (a+b x^n\right )^4}{4 b n} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.014, size = 60, normalized size = 3.2 \begin{align*}{\frac{{a}^{3}{{\rm e}^{n\ln \left ( x \right ) }}}{n}}+{\frac{{b}^{2}a \left ({{\rm e}^{n\ln \left ( x \right ) }} \right ) ^{3}}{n}}+{\frac{{b}^{3} \left ({{\rm e}^{n\ln \left ( x \right ) }} \right ) ^{4}}{4\,n}}+{\frac{3\,b{a}^{2} \left ({{\rm e}^{n\ln \left ( x \right ) }} \right ) ^{2}}{2\,n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.95788, size = 23, normalized size = 1.21 \begin{align*} \frac{{\left (b x^{n} + a\right )}^{4}}{4 \, b n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.27201, size = 93, normalized size = 4.89 \begin{align*} \frac{b^{3} x^{4 \, n} + 4 \, a b^{2} x^{3 \, n} + 6 \, a^{2} b x^{2 \, n} + 4 \, a^{3} x^{n}}{4 \, n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 4.69126, size = 54, normalized size = 2.84 \begin{align*} \begin{cases} \frac{a^{3} x^{n}}{n} + \frac{3 a^{2} b x^{2 n}}{2 n} + \frac{a b^{2} x^{3 n}}{n} + \frac{b^{3} x^{4 n}}{4 n} & \text{for}\: n \neq 0 \\\left (a + b\right )^{3} \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 = 1.20417, size = 61, normalized size = 3.21 \begin{align*} \frac{b^{3} x^{4 \, n} + 4 \, a b^{2} x^{3 \, n} + 6 \, a^{2} b x^{2 \, n} + 4 \, a^{3} x^{n}}{4 \, n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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