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Integral of tg(4*x) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1            
  /            
 |             
 |  tan(4*x) dx
 |             
/              
0              
$$\int\limits_{0}^{1} \tan{\left(4 x \right)}\, dx$$
Integral(tan(4*x), (x, 0, 1))
Detail solution
  1. Rewrite the integrand:

  2. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

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

        1. The integral of is .

        So, the result is:

      Now substitute back in:

    Method #2

    1. Let .

      Then let and substitute :

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

        1. Let .

          Then let and substitute :

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

            1. The integral of is .

            So, the result is:

          Now substitute back in:

        So, the result is:

      Now substitute back in:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                               
 |                   log(cos(4*x))
 | tan(4*x) dx = C - -------------
 |                         4      
/                                 
$$\int \tan{\left(4 x \right)}\, dx = C - \frac{\log{\left(\cos{\left(4 x \right)} \right)}}{4}$$
The graph
The answer [src]
  log(-cos(4))   pi*I
- ------------ - ----
       4          4  
$$- \frac{\log{\left(- \cos{\left(4 \right)} \right)}}{4} - \frac{i \pi}{4}$$
=
=
  log(-cos(4))   pi*I
- ------------ - ----
       4          4  
$$- \frac{\log{\left(- \cos{\left(4 \right)} \right)}}{4} - \frac{i \pi}{4}$$
-log(-cos(4))/4 - pi*i/4
Numerical answer [src]
1.6900933662682
1.6900933662682

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