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

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

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

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

The function f (x) =1+ x ln (x+ sqrt(1+ x ^(2)))-sqrt(1- x^(2)) is:

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

Prove that f(x)=sqrt(|x|-x) is continuous for all xgeq0 .

Prove that f(x)=sqrt(|x|-x) is continuous for all xgeq0.

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

Show that : 2tan^(-1)x+sin^(-1)(2x)/(1+x^2) is constant for xgeq1, find that constant.

Show that : 2tan^(-1)x+sin^(-1)((2x)/(1+x^2)) is constant for xgeq1, find that constant.