vikas askiitian expert
Last Activity: 14 Years ago
1) 2x2/(x2+1)2 dx
= [2(x2+1) - 2]dx/(x2+1)2
=[2/(x2+1) - 2/(x2+1)2]dx
I = 2tan-1x - 2dx/(x2+1)2
I - 2tan-1x = -2dx /(x2+1)2 .........................1
taking RHS
put x = tan@ so
dx = sec2@d@
now
RHS = -2d@/sec2@ = -2cos2@ = -(1+cos2@)d@
=-(@ + sin2@ /2) + c
=- [ tan-1x + sin(2tan-1x)/2] + c
put RHS in eq 1 then
I = tan-1x - sin(2tan-1x) / 2 + c or
I = tan-1x - x/1+x2 + c