`int_(1)^(e)x ln x dx`, किसके बराबर है ?

Options

A. `(e+1)/(4)`
B. `(e^(2)+1)/(4)`
C. `(e-1)/(4)`
D. `(e^(2)-1)/(4)`

Answer

B

Explanation

माना `l=int_(1)^(e)xlog x dx`
`[logx.intxdx]_(1)^(e)-int_(1)^(e)[(d)/(dx){logx}.intxdx]d`
`=[logx.(x^(2))/(2)]_(1)^(e)-int_(1)^(e)(1)/(x).(x^(2))/(2)dx`
`=(e^(2))/(2)-1/2xx1/2[x^(2)]_(1)^(e)`
`=(e^(2))/(2)-([e^(2)-1])/(4)`
`=(2e^(2)-e^(2)+1)/(4)=(e^(2)+1)/(4)`