Question

Please I need serious help

(((1-e^(-x))cosx)dx/x???

Answer 1

If I read this correctly, you want to find
∫ (((1-e^(-x))cosx) dx
First, I'd balance the parentheses. Let's try
∫ cosx (1 - e^-x) dx
= ∫cosx dx - ∫ e^-x cosx dx
The first term is easy, so let's use integration by parts on the second, letting
u cosx, du = -sinx dx
dv = e^-x, v = -e^-x
That ends up giving us something with e^-x sinx, so we do it again. In the end, after all that, we get
∫ cosx (1 - e^-x) dx = sinx + 1/2 e^-x (cosx - sinx)

However, if you really meant
∫ cosx (1 - e^-x)/x dx then you're out of luck.