Optimal. Leaf size=14 \[ -\frac {2}{n \sqrt {b x^n}} \]
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Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ -\frac {2}{n \sqrt {b x^n}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.86, size = 20, normalized size = 1.43 \[ -\frac {2 \, \sqrt {b x^{n}}}{b n x^{n}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {b x^{n}} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.93 \[ -\frac {2}{\sqrt {b \,x^{n}}\, n} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 12, normalized size = 0.86 \[ -\frac {2}{\sqrt {b x^{n}} n} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.97, size = 20, normalized size = 1.43 \[ -\frac {2\,\sqrt {b\,x^n}}{b\,n\,x^n} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.04, size = 24, normalized size = 1.71 \[ \begin {cases} - \frac {2}{\sqrt {b} n \sqrt {x^{n}}} & \text {for}\: n \neq 0 \\\frac {\log {\relax (x )}}{\sqrt {b}} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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