`(1)/(x(x^(4)-1))`

Explanation

माना `I = int (1)/(x(x^(4)-1))dx`
`=int(x^(3))/(x^(4)(x^(4)-1))dx" माना "x^(4)=t`
`=(1)/(4)int(4x^(3))/(x^(4)(x^(4)-1))dx" "rArr 4x^(3)dx=dt`
`therefore" "I=(1)/(4)int(1dt)/(t(t-1))=(1)/(4)int(dt)/((t-1))`
`rArr" "1=A(t-1)+Bt" ...(1)"`
`{:(t=0,"तो ",1=A(0-1)+0,rArr.,A=-1),(t=1,"तो ",1=0+B,rArr.,B=1):}`
`therefore (1)/(t(t-1))=(-1)/(t)+(1)/(t-1)`
`therefore" "I=(1)/(4)int(-(1)/(t)+(1)/(t-1))dt`
`" "=(1)/(4){-log|t|+log|t-1|}+C`
`" "=(1)/(4)log|(t-1)/(t)|+C=(1)/(4)log|(x^(4)-1)/(x^(4))|+C`माना