Optimal. Leaf size=19 \[ x^{-n/2} \log (x) \sqrt{b x^n} \]
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Rubi [A] time = 0.0029187, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105, Rules used = {15, 29} \[ x^{-n/2} \log (x) \sqrt{b x^n} \]
Antiderivative was successfully verified.
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Rule 15
Rule 29
Rubi steps
\begin{align*} \int x^{-1-\frac{n}{2}} \sqrt{b x^n} \, dx &=\left (x^{-n/2} \sqrt{b x^n}\right ) \int \frac{1}{x} \, dx\\ &=x^{-n/2} \sqrt{b x^n} \log (x)\\ \end{align*}
Mathematica [A] time = 0.0036891, size = 19, normalized size = 1. \[ x^{-n/2} \log (x) \sqrt{b x^n} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.025, size = 22, normalized size = 1.2 \begin{align*}{\ln \left ( x \right ) \sqrt{b \left ({x}^{{\frac{n}{2}}} \right ) ^{2}} \left ({x}^{{\frac{n}{2}}} \right ) ^{-1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{b x^{n}} x^{-\frac{1}{2} \, n - 1}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.75533, size = 68, normalized size = 3.58 \begin{align*} x x^{-\frac{1}{2} \, n - 1} \sqrt{\frac{b}{x^{2} x^{-n - 2}}} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21357, size = 8, normalized size = 0.42 \begin{align*} \sqrt{b} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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