Sec 52 17 What is the integral of fxxln1 x2 Solution let z

Sec 5.2 # 17. What is the integral of

f(x)=xln(1 + x^2)

Solution

let z = 1+x^2 dz = 2x dx ==> (1/2) dz = x dx then, (1/2) integral ln z dz ==> by integration by parts, u = ln z v = z du = 1/z dz dv = dz (z/2) ln z - (1/2) integral dz ==> (z/2) ln z - (z/2) + C ==> ((1+x^2)/2) ln (1+x^2) - (1+x^2)/2 + C answer