Optimal. Leaf size=19 \[ \frac {\left (a+b x^n\right )^4}{4 b n} \]
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Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 1.00 \[ \frac {\left (a+b x^n\right )^4}{4 b n} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.66, size = 45, normalized size = 2.37 \[ \frac {b^{3} x^{4 \, n} + 4 \, a b^{2} x^{3 \, n} + 6 \, a^{2} b x^{2 \, n} + 4 \, a^{3} x^{n}}{4 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.15, size = 45, normalized size = 2.37 \[ \frac {b^{3} x^{4 \, n} + 4 \, a b^{2} x^{3 \, n} + 6 \, a^{2} b x^{2 \, n} + 4 \, a^{3} x^{n}}{4 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.02, size = 60, normalized size = 3.16 \[ \frac {a^{3} {\mathrm e}^{n \ln \relax (x )}}{n}+\frac {3 a^{2} b \,{\mathrm e}^{2 n \ln \relax (x )}}{2 n}+\frac {a \,b^{2} {\mathrm e}^{3 n \ln \relax (x )}}{n}+\frac {b^{3} {\mathrm e}^{4 n \ln \relax (x )}}{4 n} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 17, normalized size = 0.89 \[ \frac {{\left (b x^{n} + a\right )}^{4}}{4 \, b n} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.30, size = 51, normalized size = 2.68 \[ \frac {a^3\,x^n}{n}+\frac {b^3\,x^{4\,n}}{4\,n}+\frac {3\,a^2\,b\,x^{2\,n}}{2\,n}+\frac {a\,b^2\,x^{3\,n}}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 5.48, size = 54, normalized size = 2.84 \[ \begin {cases} \frac {a^{3} x^{n}}{n} + \frac {3 a^{2} b x^{2 n}}{2 n} + \frac {a b^{2} x^{3 n}}{n} + \frac {b^{3} x^{4 n}}{4 n} & \text {for}\: n \neq 0 \\\left (a + b\right )^{3} \log {\relax (x )} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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