Optimal. Leaf size=19 \[ \frac {x^{n/2} \log (x)}{\sqrt {b x^n}} \]
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Rubi [A]
time = 0.00, antiderivative size = 19, 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}
\begin {gather*} \frac {x^{n/2} \log (x)}{\sqrt {b x^n}} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 29
Rubi steps
\begin {align*} \int \frac {x^{-1+\frac {n}{2}}}{\sqrt {b x^n}} \, dx &=\frac {x^{n/2} \int \frac {1}{x} \, dx}{\sqrt {b x^n}}\\ &=\frac {x^{n/2} \log (x)}{\sqrt {b x^n}}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 19, normalized size = 1.00 \begin {gather*} \frac {x^{n/2} \log (x)}{\sqrt {b x^n}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 20, normalized size = 1.05
method | result | size |
risch | \(\frac {x^{\frac {n}{2}} \ln \left (x \right )}{\sqrt {b \,x^{n}}}\) | \(20\) |
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 30, normalized size = 1.58 \begin {gather*} \frac {\sqrt {b x^{2} x^{n - 2}} \log \left (x\right )}{b x x^{\frac {1}{2} \, n - 1}} \end {gather*}
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 {gather*} \int \frac {x^{\frac {n}{2} - 1}}{\sqrt {b x^{n}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.93, size = 20, normalized size = 1.05 \begin {gather*} \frac {2 \, \log \left (\sqrt {{\left | x \right |}^{n}} \sqrt {{\left | b \right |}}\right )}{\sqrt {b} n} \end {gather*}
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 \begin {gather*} \int \frac {x^{\frac {n}{2}-1}}{\sqrt {b\,x^n}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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