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Integral of d{x}:
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Identical expressions
one / one +cos(6x)
1 divide by 1 plus co sinus of e of (6x)
one divide by one plus co sinus of e of (6x)
1/1+cos6x
1 divide by 1+cos(6x)
1/1+cos(6x)dx
Similar expressions
1/1-cos(6x)
1/(1+cos6x)

Solving integrals/ 1/1+cos(6x)

Integral of 1/1+cos(6x) dx

The solution

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  1                  
  /                  
 |                   
 |  (1 + cos(6*x)) dx
 |                   
/                    
0

$$\int\limits_{0}^{1} \left(\cos{\left(6 x \right)} + 1\right)\, dx$$

Integral(1 + cos(6*x), (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Let $u = 6 x$ .
  
  Then let $du = 6 dx$ and substitute $\frac{du}{6}$ :
  
  $\int \frac{\cos{\left(u \right)}}{36}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{\cos{\left(u \right)}}{6}\, du = \frac{\int \cos{\left(u \right)}\, du}{6}$
    1. The integral of cosine is sine:
      
      $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
    So, the result is: $\frac{\sin{\left(u \right)}}{6}$
  Now substitute $u$ back in:
  
  $\frac{\sin{\left(6 x \right)}}{6}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $x + \frac{\sin{\left(6 x \right)}}{6}$
Add the constant of integration:

$x + \frac{\sin{\left(6 x \right)}}{6}+ \mathrm{constant}$

The answer is:

$x + \frac{\sin{\left(6 x \right)}}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                    
 |                             sin(6*x)
 | (1 + cos(6*x)) dx = C + x + --------
 |                                6    
/

$${{\sin \left(6\,x\right)}\over{6}}+x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

    sin(6)
1 + ------
      6

$${{\sin 6+6}\over{6}}$$

    sin(6)
1 + ------
      6

$$\frac{\sin{\left(6 \right)}}{6} + 1$$

Simplify

Numerical answer [src]

0.953430750300179

0.953430750300179

The graph

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

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Identical expressions

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Integral of 1/1+cos(6x) dx

Limits of integration:

The graph:

Piecewise:

The solution