`intsqrt(e^x-1)dxi se q u a lto` `2[sqrt(e^x-1)-tan^(-1)sqrt(e^x-1)]+c` `sqrt(e^x-1)-tan^(-1)sqrt(e^x-1)+c` `sqrt(e^x-1)+tan^(-1)sqrt(e^x-1)+c` `2[sqrt(e^x-1)-tan^(-1)sqrt(e^x-1)]+c`

int sqrt(e^(x)-1)dx is equal to

int(dx)/(e^xsqrt(2e^x-1))= 2sec^(-1)sqrt(2e^x)+c -2tan^(-1)1/(sqrt(2e-1))+c 2sec^(-1)(sqrt(2)e^x)+c (d) (2sqrt(2e^x-1))/2e^x 2tan^(-1)sqrt(2e^x-1)+c

IfI=int(dx)/(x^3sqrt(x^2-1)),t h e nIe q u a l s a. 1/2((sqrt(x^2-1))/(x^3)+tan^(-1)sqrt(x^2-1))+C b. 1/2((sqrt(x^2-1))/(x^2)+xtan^(-1)sqrt(x^2-1))+C c. 1/2((sqrt(x^2-1))/x+tan^(-1)sqrt(x^2-1))+C d. 1/2((sqrt(x^2-1))/(x^2)+tan^(-1)sqrt(x^2-1))+C

int(dx)/(sqrt(2e^(x)-1))=

If tan^(-1)(sqrt(1+x^2-1))/x=4^0 then

int_(-1)^(1/2)(e^x(2-x^2)dx)/((1-x)sqrt(1-x^2))i se q u a lto (sqrt(e))/2(sqrt(3)+1) (b) (sqrt(3e))/2 sqrt(3e) (d) sqrt(e/3)

y=tan^(-1)(x/(1+sqrt(1-x^2)))

y = tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))),find dy/dx.

Prove that (tan^(-1)1/e)^2+(2e)/((e^2+1)<(tan^(-1)e)^2+2/(sqrt(e^2+1))

If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (-1)/(2|x|sqrt(x^2-1)) (b) (-1)/(2xsqrt(x^2-1)) 1/(2xsqrt(x^2-1)) (d) none of these