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

please help me to solve:


1) integral 2X *X / (X *X +1)(X *X +1)   dx


2)  integral dx/( X *X*X*X+X *X +2)

Grade:12

1 Answers

vikas askiitian expert
509 Points
13 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

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