Integral of 2ctgx dx

The solution

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$$\int\limits_{\frac{\pi}{4}}^{\frac{\pi}{2}} 2 \cot{\left(x \right)}\, dx$$

Integral(2*cot(x), (x, pi/4, pi/2))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int 2 \cot{\left(x \right)}\, dx = 2 \int \cot{\left(x \right)}\, dx$
1. Rewrite the integrand:
  
  $\cot{\left(x \right)} = \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
2. 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:
  
  $\log{\left(\sin{\left(x \right)} \right)}$
So, the result is: $2 \log{\left(\sin{\left(x \right)} \right)}$
Add the constant of integration:

$2 \log{\left(\sin{\left(x \right)} \right)}+ \mathrm{constant}$

The answer is:

$2 \log{\left(\sin{\left(x \right)} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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 | 2*cot(x) dx = C + 2*log(sin(x))
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$$\int 2 \cot{\left(x \right)}\, dx = C + 2 \log{\left(\sin{\left(x \right)} \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

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-2*log|-----|
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$$- 2 \log{\left(\frac{\sqrt{2}}{2} \right)}$$

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      |\/ 2 |
-2*log|-----|
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$$- 2 \log{\left(\frac{\sqrt{2}}{2} \right)}$$

-2*log(sqrt(2)/2)

Numerical answer [src]

0.693147180559945

0.693147180559945

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

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Integral of 2ctgx dx

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The solution