" 42."(1)/(4sqrt(4x^(3)-1))+cos^(2)(5x+8)

int(1)/(sqrt(4+8x-5x^(2)))dx

int_(-(1)/(sqrt(3)))^(-(1)/(sqrt(3)))(x^(4))/(1-x^(4))cos^(-1)((2x)/(1+x^(2)))dx

If y=cos^(-1)(cos x) then (dy)/(dx) at x=(5 pi)/(4) is (i) 1( ii) -1( iii) (1)/(sqrt(2))( iv) sqrt(2) at x=(5 pi)/(4) is (i)

The number of real solution(s) of the equation sin^(-1)sqrt(x^(2)-5x+5)+cos^(-1)sqrt(4x-x^(2)-3)=pi is/are

The number of real solutions of tan^(-1)sqrt(x^(2)-3x+2)+cos^(-1)sqrt(4x-x^(2)-3)=pi is

The number of real solutions of tan^(-1)sqrt(x^(2)-3x+2)+cos^(-1)sqrt(4x-x^(2)-3)=pi is

lim_(x=oo)(sqrt(x^(2)+1)-3sqrt(x^(2)+1))/(4sqrt(x^(4)+1)-5sqrt(x^(4)-1)) is equal to

cos^(-1)((x^(2))/(6)+sqrt(1-(x^(2))/(9))sqrt(1-(x^(2))/(4)))=cos^(-1)((x)/(3))-cos^(-1)((x)/(2)) hold for all x belonging to