Optimal. Leaf size=21 \[ -\frac {2 \sqrt {b x^n}}{(2-n) x} \]
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Rubi [A] time = 0.01, antiderivative size = 21, 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} \[ -\frac {2 \sqrt {b x^n}}{(2-n) x} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {\sqrt {b x^n}}{x^2} \, dx &=\left (x^{-n/2} \sqrt {b x^n}\right ) \int x^{-2+\frac {n}{2}} \, dx\\ &=-\frac {2 \sqrt {b x^n}}{(2-n) x}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 0.90 \[ \frac {2 \sqrt {b x^n}}{(n-2) x} \]
Antiderivative was successfully verified.
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fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
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 \[ \int \frac {\sqrt {b x^{n}}}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 0.86 \[ \frac {2 \sqrt {b \,x^{n}}}{\left (n -2\right ) x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {\sqrt {b\,x^n}}{x^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \begin {cases} \frac {2 \sqrt {b} \sqrt {x^{n}}}{n x - 2 x} & \text {for}\: n \neq 2 \\\int \frac {\sqrt {b x^{2}}}{x^{2}}\, dx & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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