" 6."e^(sin^(-1)x)" ."

If f(x) = frac{sin^(-1)x}{sqrt (1-x^2)} , g(x)=e^(sin^(-1)x) , then int f(x)g(x) dx =........................ A) e^(sin^(-1)x) (sin^(-1)x-1) + c B) e^( sin^(-1)x) (1- sin^(-1)x) + c C) e^(sin^(-1)x) (sin^(-1)x+1) + c D) -e^(sin^(-1)x) (sin^(-1)x-1) + c

The derivative of e^(sin^(-1)x) is :

Which pair of functions is identical? a. sin^(-1)(sinx) " and " sin(sin^(-1)x) b. log_(e)e^(x),e^(log_(e)x) c. log_(e)x^(2),2log_(e)x d. None of the above

(d)/(dx){sin^(-1)(e^(x))} is equal to (a) e^(x)sin^(-1)(e^(x)) (b) (e^(x))/(sqrt(1-e^(2x))) (c) (e^(x))/(1-e^(x)) (d) e^(x)cos^(-1)x]]

Integrate with respect to x (sin^(-1)x) (e^(sin^(-1)x))/(sqrt(1 - x^2))

int e^(sin^(-1)x)((log_(e)x)/(sqrt(1-x^(2)))+(1)/(x))dx is equal to

int e^(sin^(-1)x)((log_(e)x)/(sqrt(1-x^(2)))+(1)/(x))dx is equal to

int e^(sin^(-1)x)((log_(e)x)/(sqrt(1-x^(2)))+(1)/(x))dx is equal to

int e^(sin^(-1)x)((log_(e)x)/(sqrt(1-x^(2)))+(1)/(x))dx is equal to

If y=e^("sin"^(-1)x)andz=e^(-"cos"^(-1)x) , prove that dy/(dz)=e^(pi//2) .