Question

Integrate (2 ln x)/x

Answer 1

do a u substitution.

Let:
\[u = \ln(x)\]

Answer 2

\[\int\limits_{}^{}\frac{2lnx}{x}dx = ?\]

Answer 3

put \(t = lnx\) then you have \(dx = dtx\)

Answer 4

take lnx=u you will get dx=dt/x

Answer 5

oh

Answer 6

then the integral becomes \(2\int t dt\)\[2\frac{t^2}{2} + C\]

Answer 7

\[\int\limits_{}^{}\frac{2\ln x}{x}dx = 2 \int\limits_{}^{}\ln x \frac{1}{x} dx \]
substitute with\[u = \ln x\]
how do we get
\[\int\limits_{}^{}udu\] ?