Optimal. Leaf size=19 \[ \frac{2 x^3 \sqrt{b x^n}}{n+6} \]
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Rubi [A] time = 0.0050222, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {15, 30} \[ \frac{2 x^3 \sqrt{b x^n}}{n+6} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int x^2 \sqrt{b x^n} \, dx &=\left (x^{-n/2} \sqrt{b x^n}\right ) \int x^{2+\frac{n}{2}} \, dx\\ &=\frac{2 x^3 \sqrt{b x^n}}{6+n}\\ \end{align*}
Mathematica [A] time = 0.0032968, size = 19, normalized size = 1. \[ \frac{2 x^3 \sqrt{b x^n}}{n+6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 18, normalized size = 1. \begin{align*} 2\,{\frac{{x}^{3}\sqrt{b{x}^{n}}}{6+n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.26267, size = 24, normalized size = 1.26 \begin{align*} \frac{2 \, \sqrt{b} x^{3} x^{\frac{1}{2} \, n}}{n + 6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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