Optimal. Leaf size=22 \[ \frac {x^{n/2} \log (x)}{b \sqrt {b x^n}} \]
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Rubi [A] time = 0.00, antiderivative size = 22, normalized size of antiderivative = 1.00, 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} \[ \frac {x^{n/2} \log (x)}{b \sqrt {b x^n}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 29
Rubi steps
\begin {align*} \int \frac {x^{-1+\frac {3 n}{2}}}{\left (b x^n\right )^{3/2}} \, dx &=\frac {x^{n/2} \int \frac {1}{x} \, dx}{b \sqrt {b x^n}}\\ &=\frac {x^{n/2} \log (x)}{b \sqrt {b x^n}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 0.86 \[ \frac {x^{3 n/2} \log (x)}{\left (b x^n\right )^{3/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 20, normalized size = 0.91 \[ \frac {\sqrt {b x^{n}} \log \relax (x)}{b^{2} x^{\frac {1}{2} \, n}} \]
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 \[ \int \frac {x^{\frac {3}{2} \, n - 1}}{\left (b x^{n}\right )^{\frac {3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 23, normalized size = 1.05 \[ \frac {x^{\frac {n}{2}} \ln \relax (x )}{\sqrt {b \,x^{n}}\, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{\frac {3}{2} \, n - 1}}{\left (b x^{n}\right )^{\frac {3}{2}}}\,{d x} \]
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 \[ \int \frac {x^{\frac {3\,n}{2}-1}}{{\left (b\,x^n\right )}^{3/2}} \,d x \]
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 \[ \int \frac {x^{\frac {3 n}{2} - 1}}{\left (b x^{n}\right )^{\frac {3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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