Calculate antiderivative of y = cos x/(1 + sinx)?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should evaluate the anti-derivative of the given function, hence, you need to evaluate the indefinite integral of the given function.

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

`1 + sin x = t => cos xdx = dt`

Replacing the variable yields:

`int cos x/(1 + sin x)dx = int (dt)/t => int (dt)/t = ln|t| + c`

Changing back the variable yields:

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

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

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