Question

Evaluate the integral of (e^y+y^e)dy from 0 to 1

Answer 1

$\int_0^1(e^y+y^e)dy = e^y+\cfrac{y^{e+1}}{e+1}|_0^1 = e + \cfrac{1}{e+1} - 1= \\ = \cfrac{(e-1)(e+1)+1}{e+1} = \cfrac{e^2-1+1}{e+1} = \cfrac{e^2}{e+1}$