Optimal. Leaf size=15 \[ \frac {\sqrt {b x^2} \log (x)}{x} \]
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Rubi [A]
time = 0.00, antiderivative size = 15, 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 {\sqrt {b x^2} \log (x)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 29
Rubi steps
\begin {align*} \int \frac {\sqrt {b x^2}}{x^2} \, dx &=\frac {\sqrt {b x^2} \int \frac {1}{x} \, dx}{x}\\ &=\frac {\sqrt {b x^2} \log (x)}{x}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 0.93 \begin {gather*} \frac {b x \log (x)}{\sqrt {b x^2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 14, normalized size = 0.93
method | result | size |
default | \(\frac {\ln \left (x \right ) \sqrt {b \,x^{2}}}{x}\) | \(14\) |
risch | \(\frac {\ln \left (x \right ) \sqrt {b \,x^{2}}}{x}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 13, normalized size = 0.87 \begin {gather*} \frac {\sqrt {b x^{2}} \log \left (x\right )}{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 {\sqrt {b x^{2}}}{x^{2}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.23, size = 9, normalized size = 0.60 \begin {gather*} \sqrt {b} \log \left ({\left | x \right |}\right ) \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 = -0.07 \begin {gather*} \int \frac {\sqrt {b\,x^2}}{x^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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