Evaluate
\sqrt{21}\ln(10)\approx 10.551770483
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\int \frac{\sqrt{21}}{x}\mathrm{d}x
Evaluate the indefinite integral first.
\sqrt{21}\int \frac{1}{x}\mathrm{d}x
Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.
\sqrt{21}\ln(|x|)
Use \int \frac{1}{x}\mathrm{d}x=\ln(|x|) from the table of common integrals to obtain the result.
21^{\frac{1}{2}}\ln(|10|)-21^{\frac{1}{2}}\ln(|1|)
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
\sqrt{21}\ln(10)
Simplify.
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