Take the integral:
integral e^x sqrt(e^x + 1) dx
For the integrand e^x sqrt(e^x + 1), substitute u = e^x + 1 and du = e^x dx:
= integral sqrt(u) du
The integral of sqrt(u) is (2 u^(3/2))/3:
= (2 u^(3/2))/3 + constant
Substitute back for u = e^x + 1:
Answer: |= 2/3 (e^x + 1)^(3/2) + constant
