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aswin suresh Grade: 12
        

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)

6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

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

6 years ago
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