Indefinite integration

Question

Find the indefinite integral for the following:

(indefinite integral) (6)/(8e^x+4)dx

Thank you in advance

Answer 1

I = ∫6/(8e^x + 4)dx; u = 8e^x + 4; du = 8e^xdx; dx = du/(u-4);

I = 6∫du/[u(u - 4)] = 6/4[ (1/(u-4) - 1/u)du = 3/2[lnIu-4I - lnIuI + C = 3/2lnI(u - 4)/uI + C = 3/2lnI8e^x/(8e^x + 4)I + C;.