Optimal. Leaf size=21 \[ \frac {a x^2}{2}+\frac {b x^{n+2}}{n+2} \]
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Rubi [A] time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {14} \[ \frac {a x^2}{2}+\frac {b x^{n+2}}{n+2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int x \left (a+b x^n\right ) \, dx &=\int \left (a x+b x^{1+n}\right ) \, dx\\ &=\frac {a x^2}{2}+\frac {b x^{2+n}}{2+n}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 21, normalized size = 1.00 \[ \frac {a x^2}{2}+\frac {b x^{n+2}}{n+2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.74, size = 28, normalized size = 1.33 \[ \frac {2 \, b x^{2} x^{n} + {\left (a n + 2 \, a\right )} x^{2}}{2 \, {\left (n + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 29, normalized size = 1.38 \[ \frac {2 \, b x^{2} x^{n} + a n x^{2} + 2 \, a x^{2}}{2 \, {\left (n + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 23, normalized size = 1.10 \[ \frac {b \,x^{2} {\mathrm e}^{n \ln \relax (x )}}{n +2}+\frac {a \,x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 19, normalized size = 0.90 \[ \frac {1}{2} \, a x^{2} + \frac {b x^{n + 2}}{n + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.24, size = 20, normalized size = 0.95 \[ \frac {a\,x^2}{2}+\frac {b\,x^n\,x^2}{n+2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.29, size = 51, normalized size = 2.43 \[ \begin {cases} \frac {a n x^{2}}{2 n + 4} + \frac {2 a x^{2}}{2 n + 4} + \frac {2 b x^{2} x^{n}}{2 n + 4} & \text {for}\: n \neq -2 \\\frac {a x^{2}}{2} + b \log {\relax (x )} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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