Optimal. Leaf size=19 \[ -\frac{2}{(n+4) x^2 \sqrt{b x^n}} \]
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Rubi [A] time = 0.0038454, antiderivative size = 19, 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} \[ -\frac{2}{(n+4) x^2 \sqrt{b x^n}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{x^3 \sqrt{b x^n}} \, dx &=\frac{x^{n/2} \int x^{-3-\frac{n}{2}} \, dx}{\sqrt{b x^n}}\\ &=-\frac{2}{(4+n) x^2 \sqrt{b x^n}}\\ \end{align*}
Mathematica [A] time = 0.0042067, size = 19, normalized size = 1. \[ -\frac{2}{(n+4) x^2 \sqrt{b x^n}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 18, normalized size = 1. \begin{align*} -2\,{\frac{1}{ \left ( 4+n \right ){x}^{2}\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 [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 [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\sqrt{b x^{n}} x^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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