सिद्ध करे कि
`sin^(-1)sqrt((u)/(1+u))-sin^(-1)((u-1)/(1+u))=sin^(-1)sqrt((1)/(1+u)),(uge1)`

int(1)/(sqrt(u))du

If y=tan^(-1)((u)/(sqrt(1-u^(2)))) and x=sec^(-1)((1)/(2u^(2)-1))u in(0,(1)/(sqrt(2)))uu((1)/(sqrt(2)),1), prove that 2(dy)/(dx)+1=0

int (du) / (u sqrt (u ^ (2) -1))

If y = tan^(-1)(u/sqrt(1-u^2)) and x = sec^(-1)(1/(2u^2-1)) , u in (0,1/sqrt2)uu(1/sqrt2,1) , prove that 2dy/dx+ 1 = 0 .

If y = tan^(-1)(u/sqrt(1-u^2)) and x = sec^(-1)(1/(2u^2-1)) , u in (0,1/sqrt2)uu(1/sqrt2,1) , prove that 2dy/dx+ 1 = 0 .

u=sin(m cos^(-1)x),v=cos(m sin^(-1)x), provethat (du)/(dv)=sqrt((1-u^(2))/(1-v^(2)))

If u=sin(mcos^(-1)x),v=cos(msin^(-1)x),p rov et h a t(d u)/(d v)=sqrt((1-u^2)/(1-v^2))