Integral of cos(3z)dz dx

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 I + 2*pi           
     /              
    |               
    |    cos(3*z) dz
    |               
   /                
 pi - I

$$\int\limits_{\pi - i}^{2 \pi + i} \cos{\left(3 z \right)}\, dz$$

Integral(cos(3*z), (z, pi - i, i + 2*pi))

Detail solution

Let $u = 3 z$ .

Then let $du = 3 dz$ and substitute $\frac{du}{3}$ :

$\int \frac{\cos{\left(u \right)}}{3}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \cos{\left(u \right)}\, du = \frac{\int \cos{\left(u \right)}\, du}{3}$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
  So, the result is: $\frac{\sin{\left(u \right)}}{3}$
Now substitute $u$ back in:

$\frac{\sin{\left(3 z \right)}}{3}$
Add the constant of integration:

$\frac{\sin{\left(3 z \right)}}{3}+ \mathrm{constant}$

The answer is:

$\frac{\sin{\left(3 z \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          
 |                   sin(3*z)
 | cos(3*z) dz = C + --------
 |                      3    
/

$$\int \cos{\left(3 z \right)}\, dz = C + \frac{\sin{\left(3 z \right)}}{3}$$

Simplify

The answer [src]

$$0$$

Numerical answer [src]

(-3.69880140875628e-15 - 5.75457954702547e-22j)

(-3.69880140875628e-15 - 5.75457954702547e-22j)

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