Question

Evaluate : `∫(e^x + 1)/(e^x + x)` dx

Answer 1

Let I = `∫(e^x + 1)/(e^x + x)` dx

` = ∫((d/dx(e^x + x)))/(e^x + x)`dx      .....`[∵ d/dx(e^x + x) = e^x + 1]`

∴ I = `log |e^x + x| + c`    .....`[∵∫(f'(x))/f(x) dx = log |f(x)| + c]`