Question

Integrate loge^x.dx​

Answer 1

For Finding Integration of lnx (log x),

1. Write ∫ log x dx = ∫ (log x) . 1 dx.
2. Take first function as log x, second function as 1.
3. Use integration by Parts and solve

Answer 2

Step-by-step explanation:

Strategy: Use Integration by Parts.

(integral)ln(x) dx

set

u = ln(x), dv = dx

then we find

du = (1/x) dx, v = x

substitute

(integral) ln(x) dx = (integral) u dv

and use integration by parts

= uv - (integral) v du

substitute u=ln(x), v=x, and du=(1/x)dx

= ln(x) x - (integral) x (1/x) dx

= ln(x) x - (integral) dx

= ln(x) x - x + C

= x ln(x) - x + C.

Q.E.D.