Show that 1+x ln`(x+sqrt(x^2+1))geqsqrt(1+x^2)` for all `xgeq0.`

Solve x+sqrt(x)geqsqrt(x)-3 .

Show that : tan (cos^(-1)x) = (sqrt(1-x^(2)))/x

If f is a real function such that f(x)>0,f^(prime)(xx) is continuous for all real xa n da xf^(prime)(x)geq2sqrt(f(x))-2af(x),(a x!=2), show that sqrt(f(x))geq(sqrt(f(1)))/x ,xgeq1.

The function f (x) = log (x + sqrt(x^2 +1)) is

Show that "cosec"^(-1) (x/(sqrt(x^(2)-1))) = sec^(-1) (x) , | x | gt 1

Show that cot ( sin^(-1) x ) ( sqrt(1-x^2))/(x) ,-1 lex le 1 and x ne 0

If int x((ln(x+sqrt(1+x^2)))/sqrt(1+x^2)) dx=asqrt(1+x^2)ln(x+sqrt(1+x^2))+bx+c then

Evaluate int(log_(e)(x+sqrt(x^(2)+1)))/(sqrt(x^(2)+1))dx.