Integral of 3cos5x dx

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 |  3*cos(5*x) dx
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$$\int\limits_{0}^{1} 3 \cos{\left(5 x \right)}\, dx$$

Integral(3*cos(5*x), (x, 0, 1))

Detail solution

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

$\int 3 \cos{\left(5 x \right)}\, dx = 3 \int \cos{\left(5 x \right)}\, dx$
1. Let $u = 5 x$ .
  
  Then let $du = 5 dx$ and substitute $\frac{du}{5}$ :
  
  $\int \frac{\cos{\left(u \right)}}{25}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{\cos{\left(u \right)}}{5}\, du = \frac{\int \cos{\left(u \right)}\, du}{5}$
    1. The integral of cosine is sine:
      
      $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
    So, the result is: $\frac{\sin{\left(u \right)}}{5}$
  Now substitute $u$ back in:
  
  $\frac{\sin{\left(5 x \right)}}{5}$
So, the result is: $\frac{3 \sin{\left(5 x \right)}}{5}$
Add the constant of integration:

$\frac{3 \sin{\left(5 x \right)}}{5}+ \mathrm{constant}$

The answer is:

$\frac{3 \sin{\left(5 x \right)}}{5}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                              
 |                     3*sin(5*x)
 | 3*cos(5*x) dx = C + ----------
 |                         5     
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$${{3\,\sin \left(5\,x\right)}\over{5}}$$

Simplify

The answer [src]

3*sin(5)
--------
   5

$${{3\,\sin 5}\over{5}}$$

3*sin(5)
--------
   5

$$\frac{3 \sin{\left(5 \right)}}{5}$$

Упростить

Numerical answer [src]

-0.575354564797883

-0.575354564797883

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