intergration

1. Let u = 3+4x, du=4 dx
∫ ln(3+4x) dx
=(1/4) ∫ ln (4x+3) (4dx)
= (1/4) ∫ ln u du
= (1/4) [ u ln u - ∫ u d(ln u)] Integration by parts
= (1/4) [ u ln u - ∫ u (1/u) du]
= (1/4) [ u ln u - ∫ du]
= (1/4) ( u ln u - u ) +C
= (1/4) (4x+3) [-1 + ln 4x+3] +C

2. Let u = ln x, du = (1/x)dx = dx/x
∫ 1/(xlnx) dx
= ∫ (1/ln x) (dx/x)
= ∫ (1/u) du
= ln |u| +C
= ln |ln x| +C

3. Let t = x-1, dt= dx
∫(x-2)/(x-1)^2 dx
= ∫ (t-1)/t^2 dt
= ∫ (1/t) - (1/t^2) dt
= ln |t| + (1/t) +C
=ln | x-1| + 1/(x -1) +C

PS: It should be "ln (LN)", not "In"

It should be 'integration' not 'intergration'.