integrate (dx/(x*sqrt(lnx))?

Question

details please

Answer 1

Ok, here you need to use substitution :

integrate(dx / x*sqrt(lnx))

sqrt(lnx) = (lnx)^-1/2

well, let`s use the substitution : lnx = t

in other words, e^t= x

then dx = e^t*dt

Now when we use the substitutions :

integrate( e^t*dt / e^t*t^-1/2)

integrate( dt / t^-1/2)

this will result = 2*t^1/2

t = lnx, then the final result will be : 2*lnx^1/2

Answer 2

Let z= ln x

So it becomes dz/sqrt(z)

The integral is 2 sqrt(ln x) + c

Answer 3

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Answer 4

i know only differentiation