What is antiderivative of y =(sin x +cos x )/(sinx -cos x)?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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

`int (sin x + cos x)/(sin x - cos x)dx`

You should use the following substitution, such that:

`sin x - cos x = t => (cos x - (-sin x))dx = dt => (cos x + sin x)dx = dt`

Changing the variable, yields:

`int (sin x + cos x)/(sin x - cos x)dx = int (dt)/t`

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

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

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