How do you find the antiderivative of $(sinx - cosx)/cosx dx$ ?

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Answer 1 · 2015-02-19T21:35:48

Hello,

The answer is $-ln(|cos(x)|) - x + c$ .

Write $\frac{\sin(x)-\cos(x)}{\cos(x)} = \frac{\sin(x)}{\cos(x)} - 1 = -\frac{\cos'(x)}{cos(x)} -1$ .

You recognize $\int (u')/u = ln(|u|) + c$ , therefore the antiderivative of your function is

$-ln(|cos(x)|) - x + c$

where c is an arbitrary real constant.

How do you find the antiderivative of (sinx - cosx)/cosx dx(sinx - cosx)/cosx dx?