Tính 1/x ln 2 . log 2 . xdx

7/22

Tính \[\int {\frac{1}{{x.\ln 2}}.{{\log }_2}x{\rm{d}}x} \].

\[\log {x^2} + C\].

\(\frac{{\log _2^2x}}{2} + C\).

\(\log _2^2x + C\).

\(\frac{{{{\log }_2}{x^2}}}{2} + C\)

Giải thích

Ta có \[\int {\frac{1}{{x.\ln 2}}.{{\log }_2}x{\rm{d}}x} = \int {{{\log }_2}x.} \left( {\frac{1}{{x.\ln 2}}} \right){\rm{d}}x = {\int {{{\log }_2}x.\left( {{{\log }_2}x} \right)} ^\prime }{\rm{d}}x = \int {{{\log }_2}x} {\rm{d}}x\left( {{{\log }_2}x} \right) = \frac{{\log _2^2x}}{2} + C.\]