Mister Exam

Integral of x*sin3xdx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  5              
  /              
 |               
 |  x*sin(3*x) dx
 |               
/                
0                
$$\int\limits_{0}^{5} x \sin{\left(3 x \right)}\, dx$$
Integral(x*sin(3*x), (x, 0, 5))
Detail solution
  1. Use integration by parts:

    Let and let .

    Then .

    To find :

    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:

    Now evaluate the sub-integral.

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

    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:

    So, the result is:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                         
 |                     sin(3*x)   x*cos(3*x)
 | x*sin(3*x) dx = C + -------- - ----------
 |                        9           3     
/                                           
$$\int x \sin{\left(3 x \right)}\, dx = C - \frac{x \cos{\left(3 x \right)}}{3} + \frac{\sin{\left(3 x \right)}}{9}$$
The graph
The answer [src]
  5*cos(15)   sin(15)
- --------- + -------
      3          9   
$$\frac{\sin{\left(15 \right)}}{9} - \frac{5 \cos{\left(15 \right)}}{3}$$
=
=
  5*cos(15)   sin(15)
- --------- + -------
      3          9   
$$\frac{\sin{\left(15 \right)}}{9} - \frac{5 \cos{\left(15 \right)}}{3}$$
-5*cos(15)/3 + sin(15)/9
Numerical answer [src]
1.33840072589327
1.33840072589327

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