How do you use substitution to integrate $\frac{cos x}{sin x} d x$ $cos x/sin x dx$ ?

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Answer 1 · 2015-07-29T17:21:16

The procedure is outlined below.

We have to evaluate, $\int \frac{cos x}{sin x} \cdot d x$ $int Cos x/Sin x * dx$

So, let $sin x = t$ $Sin x = t$
$\Rightarrow cos x \cdot d x = d t$ $implies Cos x*dx = dt$ (By simple differentiation)

Thus the integral $\int \frac{cos x}{sin x} \cdot d x = \int \frac{d t}{t}$ $int Cos x/Sin x *dx = int dt/t$
$= ln t + C$ $= Ln t + C$

In terms of $x$ $x$ , the integral is,

$\int \frac{cos x}{sin x} \cdot d x = ln (sin x) + C$ $int Cos x/Sin x * dx = Ln (Sin x) + C$ , where $C$ $C$ is the integration constant.

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