`IfI=int(dx)/((a^2-b^2x^2)^(3/2)),t h e nIe q u a l` (a)`x/(sqrt(a^2-b^2x^2))+C` (b) `x/(2sqrt(a^2-b^2x^2))+C` (c)`(a x)/(sqrt(a^2-b^2x^2))+C` (d) none of these

If y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)),then (dy)/(dx)is equal to (a)(a y)/(xsqrt(a^2-x^2)) (b) (a y)/(sqrt(a^2-x^2)) (c)(a y)/(xsqrt(a^2-x^2)) (d) none of these

int(1+x^(4))/((1-x^(4))^((3)/(2)))dx is e q u a l to (1)/(sqrt(x^(2)-(1)/(x^(2))))+c (b) (1)/(sqrt((1)/(x^(2))-x^(2)))+c(1)/(sqrt((1)/(x^(2))+x^(2)))+c(d) None of these

int(1)/(a^(2)-b^(2)cos^(2)x)dx(a>b)=(1)/(a sqrt(a^(2)-b^(2)))tan^(-1)[(a tan x)/(sqrt(a^(2)-b^(2)))]+c

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

IfI=int(dx)/((2ax+x^(2))^((3)/(2))), then I is equal to (a) -(x+a)/(sqrt(2ax+x^(2)))+c(b)-(1)/(a)(x+a)/(sqrt(2ax+x^(2)))+c(c)-(1)/(a^(2))(x+a)/(sqrt(2ax+x^(2)))+c(d)-(1)/(a^(3))(x+a)/(sqrt(2ax+x^(3)))+c

Evaluate: int(sqrt((a^(2)+b^(2))/(2)))/(sqrt((3a^(2)+b^(2))/(2)))(x*dx)/(sqrt((x^(2)-a^(2))(b^(2)-x^(2))))

int(sqrt(e^(x)))/(sqrt(a^(2)e^(x)+b^(2)e^(-x)))dx

If int(dx)/((a^(2)-b^(2)x^(2))^((3)/(2)))=(x)/(c sqrt(a^(2)-b^(2)x^(2)))+d ,then the value of "c" is equal to

If a sin x+b cos(x+theta)+b cos(x-theta)=d then the minimum value of |cos theta| is equal to (a) (1)/(2|b|)sqrt(d^(2)-a^(2))( b )(1)/(2|a|)sqrt(d^(2)-a^(2))(c)(1)/(2|d|)sqrt(d^(2)-a^(2))(d) none of these

Find the integral int(1)/(sqrt(a^(2)+b^(2)x^(2)))dx],[" A."(1)/(b)log bx+sqrt(a^(2)+b^(2)x^(2))|+Cquad " B."(1)/(b)log bx-sqrt(a^(2)+b^(2)x^(2))|+C],[" C."(1)/(a)log bx+sqrt(a^(2)+b^(2)x^(2))|+Cquad " D."(1)/(a)log bx-sqrt(a^(2)+b^(2)x^(2))|+C]