Optimal. Leaf size=16 \[ \frac {x \log (x)}{b^2 \sqrt {b x^2}} \]
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Rubi [A]
time = 0.00, antiderivative size = 16, 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, 29}
\begin {gather*} \frac {x \log (x)}{b^2 \sqrt {b x^2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 29
Rubi steps
\begin {align*} \int \frac {x^4}{\left (b x^2\right )^{5/2}} \, dx &=\frac {x \int \frac {1}{x} \, dx}{b^2 \sqrt {b x^2}}\\ &=\frac {x \log (x)}{b^2 \sqrt {b x^2}}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 0.94 \begin {gather*} \frac {x^5 \log (x)}{\left (b x^2\right )^{5/2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 14, normalized size = 0.88
method | result | size |
default | \(\frac {x^{5} \ln \left (x \right )}{\left (b \,x^{2}\right )^{\frac {5}{2}}}\) | \(14\) |
risch | \(\frac {x \ln \left (x \right )}{b^{2} \sqrt {b \,x^{2}}}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 6, normalized size = 0.38 \begin {gather*} \frac {\log \left (x\right )}{b^{\frac {5}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 16, normalized size = 1.00 \begin {gather*} \frac {\sqrt {b x^{2}} \log \left (x\right )}{b^{3} x} \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^{4}}{\left (b x^{2}\right )^{\frac {5}{2}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.18, size = 11, normalized size = 0.69 \begin {gather*} \frac {\log \left ({\left | x \right |}\right )}{b^{\frac {5}{2}} \mathrm {sgn}\left (x\right )} \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 = -0.06 \begin {gather*} \int \frac {x^4}{{\left (b\,x^2\right )}^{5/2}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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