IN such questions u shud use this:-

 

_{[0 ]}^{[ a]} f(x)dx = _{[0 ]}^{[ a]} f(a-x)dx

 

Here ,  I = _{[0 ]}^{[ ]} xdx/(1+sinx) = _{[ ]}^{[ ]} ( - x)dx/(1+sinx)          

 [ as sin(-x)=sinx]

2I = _{[0 ]}^{[ ]} dx/(1+sinx) = 2  _{[0 ]}^{[/2 ]} dx/(1+sinx)

Now rationalise it by multiplying both numerator and denominator with 1-sinx

2I =  2_{[0 ]}^{[/2 ]} (1-sinx)dx/(1-sin²x)

    = 2_{[0 ]}^{[/2 ]} (1-sinx)dx/cos²x

    = 2_{[ 0]}^{[/2 ]} (sec²x-tanxsecx)dx

    = 2 [ tanx - secx ]₀^/2

     = 4

I = 2

 

I hope my explanation is correct......

plz rate if it helps u.......