`int log x(log(x+2)dx` का मान है

Explanation

`int logx(logx+2)dx`
`= int {logx)^(2)+2(logx)}dx`
माना `log x=t rArr x=e^(t)rArr dx=e^(t)dt`
`:. Int [(logx^(2))+2 log x] dx`
`= int e^(t)*(t^(2)+2t)dt`
`= int t^(2)e^(t)dt+2int te^(t)dt`
`=t^(2)e^(t)-2int te^(t)dt+2int te^(t)dt`
`=e^(t)*t^(2)+C=x*(logx)^(2)+C`