# What is antiderivative of y=sinx/(1+cosx)?

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### 1 Answer

You need to evaluate the anti-derivative of the given function, hence, you need to evaluate the indefinite integral, such that:

`int ydx = int sinx/(1+cosx) dx`

You should come up with the following substitution to evaluate the integral, such that:

`1 + cos x = t => -sin x dx = dt => sin x dx = -dt`

Replacing the variable, yields:

`int sinx/(1+cosx) dx = int (-dt)/t = -ln |t| + c`

Replacing back `1 + cos x` for `t` yields:

`int sinx/(1+cosx) dx = -ln|1 + cos x| + c`

`int sinx/(1+cosx) dx = ln|1 + cos x|^(-1) + c`

`int sinx/(1+cosx) dx = ln|1/(1 + cos x)| + c`

**Hence, evaluating the anti-derivative of the given function, yields **`int sinx/(1+cosx) dx = ln|1/(1 + cos x)| + c.`