[" 11."(x cos^(-1)x)/(sqrt(1-x^(2)))quad " 12."x],[" 15."(x^(2)+1)log x]

If y=(x cos^(-1)x)/(sqrt(1-x^(2)))-log sqrt(1-x^(2)), then prove that (dy)/(dx)=(co^(1-x)x)/((1-x^(2))^((3)/(2)))

(log(x+sqrt(x^(2)+1)))/(x) is

If f(x)=2x+cos^(-1) x+log (sqrt(1+x^(2))-x) , then f(x) is-

[" (v) Differentiate "log[(sqrt(1+x^(2))+x)/(sqrt(1+x^(2))-x)]" w.r.t."],[cos(log x)]

int x((ln(x+sqrt(1+x^(2))))/(sqrt(1+x^(2)))dx

int((x)/(sqrt(1+x^(2)))-1)log(x+sqrt(1+x^(2)))backslash dx

(sqrt(x^(2)+1))/(x^(4))[log(x^(2)+1)-2log x]

int x((ln(x+sqrt(1+x^(2))))/(sqrt(1+x^(2))))dx=a sqrt(1+x^(2))ln(x+sqrt(1+x^(2)))+bx

If f(x)=2 x cot ^(-1)x + log (sqrt(1+x^2)-x then f(x)