Optimal. Leaf size=26 \[ \frac {(5 x+3) \log (5 x+3)}{10 \sqrt {(5 x+3)^2}} \]
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Rubi [A] time = 0.01, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.273, Rules used = {247, 15, 29} \[ \frac {(5 x+3) \log (10 x+6)}{10 \sqrt {(5 x+3)^2}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 29
Rule 247
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {(6+10 x)^2}} \, dx &=\frac {1}{10} \operatorname {Subst}\left (\int \frac {1}{\sqrt {x^2}} \, dx,x,6+10 x\right )\\ &=\frac {(6+10 x) \operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,6+10 x\right )}{10 \sqrt {(6+10 x)^2}}\\ &=\frac {(3+5 x) \log (3+5 x)}{10 \sqrt {(3+5 x)^2}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 26, normalized size = 1.00 \[ \frac {(10 x+6) \log (10 x+6)}{10 \sqrt {(10 x+6)^2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 8, normalized size = 0.31 \[ \frac {1}{10} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 15, normalized size = 0.58 \[ \frac {1}{10} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \mathrm {sgn}\left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 26, normalized size = 1.00 \[ \frac {\left (5 x +3\right ) \sqrt {4}\, \ln \left (5 x +3\right )}{20 \sqrt {\left (5 x +3\right )^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.13, size = 6, normalized size = 0.23 \[ \frac {1}{10} \, \log \left (x + \frac {3}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.26, size = 14, normalized size = 0.54 \[ \frac {\ln \left (10\,x+6\right )\,\mathrm {sign}\left (10\,x+6\right )}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 7, normalized size = 0.27 \[ \frac {\log {\left (10 x + 6 \right )}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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