Optimal. Leaf size=14 \[ \frac{2 \sqrt{b x^n}}{n} \]
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Rubi [A] time = 0.0032852, antiderivative size = 14, 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} \[ \frac{2 \sqrt{b x^n}}{n} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{\sqrt{b x^n}}{x} \, dx &=\left (x^{-n/2} \sqrt{b x^n}\right ) \int x^{-1+\frac{n}{2}} \, dx\\ &=\frac{2 \sqrt{b x^n}}{n}\\ \end{align*}
Mathematica [A] time = 0.0015657, size = 14, normalized size = 1. \[ \frac{2 \sqrt{b x^n}}{n} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 13, normalized size = 0.9 \begin{align*} 2\,{\frac{\sqrt{b{x}^{n}}}{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 [A] time = 1.80259, size = 23, normalized size = 1.64 \begin{align*} \frac{2 \, \sqrt{b x^{n}}}{n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.36662, size = 22, normalized size = 1.57 \begin{align*} \begin{cases} \frac{2 \sqrt{b} \sqrt{x^{n}}}{n} & \text{for}\: n \neq 0 \\\sqrt{b} \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 [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sqrt{b x^{n}}}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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