Optimal. Leaf size=17 \[ \frac{2 x \sqrt{b x^n}}{n+2} \]
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Rubi [A] time = 0.004238, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {15, 30} \[ \frac{2 x \sqrt{b x^n}}{n+2} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \sqrt{b x^n} \, dx &=\left (x^{-n/2} \sqrt{b x^n}\right ) \int x^{n/2} \, dx\\ &=\frac{2 x \sqrt{b x^n}}{2+n}\\ \end{align*}
Mathematica [A] time = 0.0015152, size = 17, normalized size = 1. \[ \frac{2 x \sqrt{b x^n}}{n+2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 16, normalized size = 0.9 \begin{align*} 2\,{\frac{x\sqrt{b{x}^{n}}}{2+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 = 1.33939, size = 22, normalized size = 1.29 \begin{align*} \frac{2 \, \sqrt{b} x x^{\frac{1}{2} \, n}}{n + 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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