Question

compute the integrals
∫3 ( ln(2x)/x ) dx

Answer 1

let u = ln 2x

Answer 2

yes how to solve it then
i did not know :(

Answer 3

is du= -2 dx

Answer 4

\[\int\limits \frac{ 3\ln 2x }{ x }dx\Rightarrow \frac{ 3 }{ 2 }\int\limits u du\]

Answer 5

du = 2/x dx

Answer 6

so it will be 3/2 ∫ ln 2x . 2/x dx ???

Answer 7

\[\int\limits \frac{ 3\ln 2x }{ x }dx= \frac{ 3 }{ 2}\int\limits \ln 2x\cdot \frac{ 2 }{ x }dx=\frac{ 3 }{ 2}\int\limits u \,du\]

Answer 8

\[=\frac{ 3 }{ 4 }\left( \ln 2x \right)^2 + C\]

Answer 9

thank you (L)