[" 12."(4x+2)sqrt(x)],[" 15."(x)/(9-4x^(2))]

If 2sin^(-1)((9-4x^(2))/(9+4x^(2)))+3cos^(-1)((12x)/(9+4x^(2)))+tan^(-1)((12x)/(9-4x^(2)))=lambda(pi)/(2) for x=(-17)/(13) "then" lambda

If 2sin^(-1)((9-4x^(2))/(9+4x^(2)))+3cos^(-1)((12x)/(9+4x^(2)))+tan^(-1)((12x)/(9-4x^(2)))=(lambda pi)/(2) for x=(-17)/(13) then lambda

int(dx)/(sqrt(15+4x-4x^2))=

(i) int(dx)/(x sqrt(4x^(2)-9))

Integrate (8)/(sqrt(1-(4x)^(2)))+(27)/(sqrt(1-9x^(2)))-(15)/(1+25x^(2)) with respect to x .

(1)/(sqrt(15+4x-4x^(2)))

Lt_(x to oo) (sqrt(3+9x^(2))+sqrt(4x^(2)-1))/(sqrt(1+16x^(2))-sqrt(9x^(2)+2))=

Integrate the following w.r.to .x. 8/(sqrt(1-(4x)^2))+27/(sqrt(1-9x^2))-15/(1+25x^2)