Integral of tan2xdx dx

You have entered [src]

  1              
  /              
 |               
 |  tan(2*x)*1 dx
 |               
/                
0

$$\int\limits_{0}^{1} \tan{\left(2 x \right)} 1\, dx$$

Integral(tan(2*x)*1, (x, 0, 1))

Detail solution

Let $u = 2 x$ .

Then let $du = 2 dx$ and substitute $\frac{du}{2}$ :

$\int \frac{\tan{\left(u \right)}}{4}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\tan{\left(u \right)}}{2}\, du = \frac{\int \tan{\left(u \right)}\, du}{2}$
  1. Rewrite the integrand:
    
    $\tan{\left(u \right)} = \frac{\sin{\left(u \right)}}{\cos{\left(u \right)}}$
  2. Let $u = \cos{\left(u \right)}$ .
    
    Then let $du = - \sin{\left(u \right)} du$ 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:
    
    $- \log{\left(\cos{\left(u \right)} \right)}$
  So, the result is: $- \frac{\log{\left(\cos{\left(u \right)} \right)}}{2}$
Now substitute $u$ back in:

$- \frac{\log{\left(\cos{\left(2 x \right)} \right)}}{2}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                 
 |                     log(cos(2*x))
 | tan(2*x)*1 dx = C - -------------
 |                           2      
/

$$\int \tan{\left(2 x \right)} 1\, dx = C - \frac{\log{\left(\cos{\left(2 x \right)} \right)}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

nan

$$\text{NaN}$$

nan

$$\text{NaN}$$

Упростить

Numerical answer [src]

-0.96117546625349

-0.96117546625349

The graph

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