Prove that `e^x+sqrt(1+e^(2x))geq(1+x)+sqrt(2+2x+x^2)AAx in R`

Prove that e^(x) ge 1 +x and hence e^(x) +sqrt(1+e^(2x))ge(1+x)+sqrt(2+2x+x^(2)) forall x in R

Evaluate: 1/(sqrt(1-e^(2x)))dx

Prove that sin^(-1). ((x + sqrt(1 - x^(2))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)

Prove that sqrt(x^2+2x+1)-sqrt(x^2-2x+1) = {-2 , x 1}

Solve sqrt(x-2)geq-1.

Prove that sin [2 tan^(-1) {sqrt((1 -x)/(1 + x))}] = sqrt(1 - x^(2))

The value of integral inte^x(1/(sqrt(1+x^2))+(1-2x^2)/(sqrt((1+x^2)^5)))dxi se q u a lto e^x(1/(sqrt(1+x^2))+1/(sqrt((1+x^2)^3)))+c e^x(1/(sqrt(1+x^2))-1/(sqrt((1+x^2)^3)))+c e^x(1/(sqrt(1+x^2))+1/(sqrt((1+x^2)^5)))+c none of these

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

Prove that : cos [ tan^(-1) { sin (cot^(-1) x)}]= sqrt((x^2 +1)/(x^2 +2))

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