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please help me to solve: 1) integral 2X *X / (X *X +1)(X *X +1)ย ย dx 2)ย integral dx/( X *X*X*X+X *X +2)
please help me to solve:
1) integral 2X *X / (X *X +1)(X *X +1)ย ย dx
2)ย integral dx/( X *X*X*X+X *X +2)
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
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
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