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6/cos^2(2x)dx

Solving integrals/ 6/cos^2(2x)

Integral of 6/cos^2(2x) dx

The solution

You have entered [src]

  pi             
  --             
  6              
   /             
  |              
  |      6       
  |  --------- dx
  |     2        
  |  cos (2*x)   
  |              
 /               
-pi              
----             
 6

$$\int\limits_{- \frac{\pi}{6}}^{\frac{\pi}{6}} \frac{6}{\cos^{2}{\left(2 x \right)}}\, dx$$

Integral(6/cos(2*x)^2, (x, -pi/6, pi/6))

Detail solution

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

$\int \frac{6}{\cos^{2}{\left(2 x \right)}}\, dx = 6 \int \frac{1}{\cos^{2}{\left(2 x \right)}}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\frac{\sin{\left(2 x \right)}}{2 \cos{\left(2 x \right)}}$
So, the result is: $\frac{3 \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}}$
Now simplify:

$3 \tan{\left(2 x \right)}$
Add the constant of integration:

$3 \tan{\left(2 x \right)}+ \mathrm{constant}$

The answer is:

$3 \tan{\left(2 x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                              
 |     6              3*sin(2*x)
 | --------- dx = C + ----------
 |    2                cos(2*x) 
 | cos (2*x)                    
 |                              
/

$$\int \frac{6}{\cos^{2}{\left(2 x \right)}}\, dx = C + \frac{3 \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

    ___
6*\/ 3

$$6 \sqrt{3}$$

    ___
6*\/ 3

$$6 \sqrt{3}$$

6*sqrt(3)

Numerical answer [src]

10.3923048454133

10.3923048454133

The graph

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

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Identical expressions

Integral of 6/cos^2(2x) dx

Limits of integration:

The graph:

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The solution