Optimal. Leaf size=14 \[ -\frac{2}{n \sqrt{b x^n}} \]
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Rubi [A] time = 0.0029323, 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} \[ -\frac{2}{n \sqrt{b x^n}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{x \sqrt{b x^n}} \, dx &=\frac{x^{n/2} \int x^{-1-\frac{n}{2}} \, dx}{\sqrt{b x^n}}\\ &=-\frac{2}{n \sqrt{b x^n}}\\ \end{align*}
Mathematica [A] time = 0.0023034, size = 14, normalized size = 1. \[ -\frac{2}{n \sqrt{b x^n}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 13, normalized size = 0.9 \begin{align*} -2\,{\frac{1}{n\sqrt{b{x}^{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 = 1.69845, size = 35, normalized size = 2.5 \begin{align*} -\frac{2 \, \sqrt{b x^{n}}}{b n x^{n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.65637, size = 24, normalized size = 1.71 \begin{align*} \begin{cases} - \frac{2}{\sqrt{b} n \sqrt{x^{n}}} & \text{for}\: n \neq 0 \\\frac{\log{\left (x \right )}}{\sqrt{b}} & \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{1}{\sqrt{b x^{n}} x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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