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Solving integrals/ cos(3x-5)

Integral of cos(3x-5) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  0                
  /                
 |                 
 |  cos(3*x - 5) dx
 |                 
/                  
-oo
$$\int\limits_{-\infty}^{0} \cos{\left(3 x - 5 \right)}\, dx$$ 
Integral(cos(3*x - 5), (x, -oo, 0))
Detail solution

  1. Let .

    Then let and substitute :

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

      1. The integral of cosine is sine:

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                  
 |                       sin(3*x - 5)
 | cos(3*x - 5) dx = C + ------------
 |                            3      
/
$$\int \cos{\left(3 x - 5 \right)}\, dx = C + \frac{\sin{\left(3 x - 5 \right)}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   1   sin(5)  1   sin(5) 
<- - - ------, - - ------>
   3     3     3     3
$$\left\langle - \frac{1}{3} - \frac{\sin{\left(5 \right)}}{3}, \frac{1}{3} - \frac{\sin{\left(5 \right)}}{3}\right\rangle$$ 
=
= 
   1   sin(5)  1   sin(5) 
<- - - ------, - - ------>
   3     3     3     3
$$\left\langle - \frac{1}{3} - \frac{\sin{\left(5 \right)}}{3}, \frac{1}{3} - \frac{\sin{\left(5 \right)}}{3}\right\rangle$$ 
AccumBounds(-1/3 - sin(5)/3, 1/3 - sin(5)/3)

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

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