Integral of ctg dx

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$$\int\limits_{0}^{\frac{\pi}{2}} \cot{\left(x \right)}\, dx$$

Integral(cot(x), (x, 0, pi/2))

Detail solution

Rewrite the integrand:

$\cot{\left(x \right)} = \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
Let $u = \sin{\left(x \right)}$ .

Then let $du = \cos{\left(x \right)} dx$ and substitute $du$ :

$\int \frac{1}{u}\, du$
1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
Now substitute $u$ back in:

$\log{\left(\sin{\left(x \right)} \right)}$
Add the constant of integration:

$\log{\left(\sin{\left(x \right)} \right)}+ \mathrm{constant}$

The answer is:

$\log{\left(\sin{\left(x \right)} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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 | cot(x) dx = C + log(sin(x))
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$$\int \cot{\left(x \right)}\, dx = C + \log{\left(\sin{\left(x \right)} \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

43.6388555484324

43.6388555484324

The graph

Use the examples entering the upper and lower limits of integration.