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Solving integrals/ cos(x)+sin(3x)

Integral of cos(x)+sin(3x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Integrate term-by-term:

    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 sine is negative cosine:

        So, the result is:

      Now substitute back in:

    1. The integral of cosine is sine:

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                              
 |                              cos(3*x)         
 | (cos(x) + sin(3*x)) dx = C - -------- + sin(x)
 |                                 3             
/
$$\int \left(\sin{\left(3 x \right)} + \cos{\left(x \right)}\right)\, dx = C + \sin{\left(x \right)} - \frac{\cos{\left(3 x \right)}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
2/3
$$\frac{2}{3}$$ 
=
= 
2/3
$$\frac{2}{3}$$ 
2/3
Numerical answer [src] 
0.666666666666667
0.666666666666667

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

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