Question

First make a substitution and then use integration by parts to evaluate. The integral of (x)(ln(x+3))dx What do you substitute first?

Answer 1

let y = x+3
then dy =dx

(y-3) ln y dy

= y ln y dy - 3 ln y dy

= y ln y dy - 3/y

let u = ln y then dv = y dy
so v = (1/2)y^2 and du = dy/y
so
(1/2)y^2 ln y -(1/2)ydy -3/y

(1/2)y^2 ln y - (1/4)y^2 - 3/y
but remember y = x + 3 :)

Answer 2

screw dis