1.

int _(0)^(1) (x)/(x^(2)+1)dx

Answer»

SOLUTION :`"Let "I= int_(0)^(1)(x)/(x^(2)+1)DX`
`"Let" x^(2)+1=t rArr XDX=(dt)/(2)`
`x=0 rArr t=1`
`" and" x=1 rArr t=2`
`:. I= int_(1)^(2) (1)/(t).(dt)/(2) =(1)/(2) int_(1)^(2) (1)/(t)dt =(1)/(2) [log |t|]_(1)^(2)`
`=(1)/(2)[log |2|-log |1|]=(1)/(2)log 2.`


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