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2cosx^2
Identical expressions
two cosx^2
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two co sinus of e of x squared
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2cosx^2dx
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1/((sin(x))^2*(cos(x))^2)

Integral of 2cosx^2 dx

The solution

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 2*pi            
   /             
  |              
  |       2      
  |  2*cos (x) dx
  |              
 /               
 0

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

Integral(2*cos(x)^2, (x, 0, 2*pi))

Detail solution

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

$\int 2 \cos^{2}{\left(x \right)}\, dx = 2 \int \cos^{2}{\left(x \right)}\, dx$
1. Rewrite the integrand:
  
  $\cos^{2}{\left(x \right)} = \frac{\cos{\left(2 x \right)}}{2} + \frac{1}{2}$
2. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{\cos{\left(2 x \right)}}{2}\, dx = \frac{\int \cos{\left(2 x \right)}\, dx}{2}$
    1. Let $u = 2 x$ .
      
      Then let $du = 2 dx$ and substitute $\frac{du}{2}$ :
      
      $\int \frac{\cos{\left(u \right)}}{2}\, du$
      1. The integral of a constant times a function is the constant times the integral of the function:
        
        $\int \cos{\left(u \right)}\, du = \frac{\int \cos{\left(u \right)}\, du}{2}$
        
        The integral of cosine is sine:
        
        $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
        
        So, the result is: $\frac{\sin{\left(u \right)}}{2}$
      Now substitute $u$ back in:
      
      $\frac{\sin{\left(2 x \right)}}{2}$
    So, the result is: $\frac{\sin{\left(2 x \right)}}{4}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int \frac{1}{2}\, dx = \frac{x}{2}$
  The result is: $\frac{x}{2} + \frac{\sin{\left(2 x \right)}}{4}$
So, the result is: $x + \frac{\sin{\left(2 x \right)}}{2}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

2*pi

$$2 \pi$$

2*pi

$$2 \pi$$

2*pi

Numerical answer [src]

6.28318530717959

6.28318530717959

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

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Integral of 2cosx^2 dx

Limits of integration:

The graph:

Piecewise:

The solution