Integral of 2tgx dx

The solution

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  p            
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 |  2*tan(x) dx
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-p             
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 4

$$\int\limits_{- \frac{p}{4}}^{\frac{p}{4}} 2 \tan{\left(x \right)}\, dx$$

Integral(2*tan(x), (x, -p/4, p/4))

Detail solution

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

$\int 2 \tan{\left(x \right)}\, dx = 2 \int \tan{\left(x \right)}\, dx$
1. Rewrite the integrand:
  
  $\tan{\left(x \right)} = \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$
2. Let $u = \cos{\left(x \right)}$ .
  
  Then let $du = - \sin{\left(x \right)} dx$ and substitute $- du$ :
  
  $\int \frac{1}{u}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- \frac{1}{u}\right)\, du = - \int \frac{1}{u}\, du$
    1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
    So, the result is: $- \log{\left(u \right)}$
  Now substitute $u$ back in:
  
  $- \log{\left(\cos{\left(x \right)} \right)}$
So, the result is: $- 2 \log{\left(\cos{\left(x \right)} \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                               
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 | 2*tan(x) dx = C - 2*log(cos(x))
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/

$$2\,\log \sec x$$

Simplify

The answer [src]

$$0$$

Simplify

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

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Integral of 2tgx dx

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