Is this right or wrong

evaluate the following integrals
A) lnx/x^2

solution
let u = lnx so that du/dx = 1/x
therefore lnx/x^2 = u/(x^3/3)
= (u^2/2) / (x^3/3)
= 3u^2/2x^3
= 2(lnx)^2/2x^3

B) cos^2x sinx dx

solution
let u = sinx
cos^2x sinx dx = (1-sin^2x) sinx dx
= (1-u^2) du
= u - u^3/3 + c
= sinx - sin^3x/3 + c

A) A valid substitution must change all x variables to u variables.
You have attempted to change the dx to du, but it must be in the integrand.
Since u=lnx, x=e^u and integral of [u/e^(3u)]du which itegrates using product rule

B) u=sinx gives du=cosxdx and integral of cosxsinxdu giving usqrt(1-u^2)du which
integrates to (-1/3)(1-u^2)^(3/2) =(-1/3)(1-sin^2x)^(3/2)=(-1/3)cos^3(x)
But a better sub is u=cosx, du=-sinxdx giving integral of -u^2du, which is easy.

A) -ln(x + 1) / x + C => integration by parts

B) - cos^3(x)/3 + C => substitution