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How do you use substitution to integrate #cos x/sin x dx#?

Answer 1

Ezekiel Alexander

The procedure is outlined below.

We have to evaluate, #int Cos x/Sin x * dx#

So, let #Sin x = t# #implies Cos x*dx = dt# (By simple differentiation)

Thus the integral #int Cos x/Sin x *dx = int dt/t# #= Ln t + C#

In terms of #x#, the integral is,

#int Cos x/Sin x * dx = Ln (Sin x) + C#, where #C# is the integration constant.

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Answer 2

Evelyn Agard

To integrate (\frac{\cos(x)}{\sin(x)} , dx) using substitution, let (u = \sin(x)). Then, (du = \cos(x) , dx). Substituting these into the integral gives (\int \frac{1}{u} , du), which integrates to (\ln|u| + C). Finally, replace (u) with (\sin(x)) to obtain the final answer: (\ln|\sin(x)| + C).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.