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

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

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

Evaluate: int e^x/sqrt (e^(2x)-9)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 }

Evaluate: int(e^x)/(sqrt(16-e^(2x)))

int(e^x[1+sqrt(1-x^2)sin^-1x])/sqrt(1-x^2)dx

Solve sqrt(x-2)geq-1.

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