Integral

{(1-e^(-x))cos(x)}dx)/x

I read sir obleck work yesterday night but I couldn't respond as I was banned I don't know why

Any specific function to use here

Help me am bother not to fail this

Hmm. Now you are just dividing the integral by x?

Well, using integration by parts twice, you easily get
∫ e^-x cosx dx = 1/2 e^-x (sinx - cosx)
So, your integral works out
∫(1-e^-x) cosx dx = ∫ cosx dx - ∫ e^-x cosx dx
= sinx + 1/2 e^-x (cosx - sinx) + C

Now just divide all that by x

If you really are dividing by x inside the integral, you are out of luck.

∫ cosx/x dx and ∫ e^x/x dx cannot be done using the normal elementary functions. They are special functions defined by the integral.

In any case, go to wolframalpha.com and type in your function. It will show you what it thinks you typed, and if you scroll down, you will come to its integral.

The second part is what I need I knew this wasn't something that can be done elementary.......

Thanks anyway have given up already...

This is beyond me for now.........

To solve the integral ∫(1 - e^(-x))cos(x)dx/x, we can apply integration by parts.

Integration by parts is a technique used to evaluate an integral where the integrand can be separated into two functions, such that their product can be rewritten as the derivative of one function multiplied by the other function.

The formula for integration by parts is as follows:
∫u * dv = u * v - ∫v * du

In this case, we can choose:
u = (1 - e^(-x))
dv = cos(x)/x

To find du, we differentiate u with respect to x:
du = d/dx(1 - e^(-x)) dx = e^(-x) dx

To find v, we integrate dv with respect to x:
v = ∫(cos(x)/x) dx

Finding the integral of v requires another technique called the exponential integral, but since this is an explanation bot and not a calculator bot, I won't be able to provide you with the result.

Using the formula for integration by parts, we have:
∫(1 - e^(-x))cos(x)dx/x = u * v - ∫v * du

Replacing the values of u, v, du, and finding the integral, we get:
∫(1 - e^(-x))cos(x)dx/x = (1 - e^(-x)) * v - ∫v * e^(-x) dx

The next step would be to evaluate the integral of v * e^(-x), but as mentioned earlier, this requires using the exponential integral function.