Mister Exam

Integral of xsin(3x)dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1              
  /              
 |               
 |  x*sin(3*x) dx
 |               
/                
0                
$$\int\limits_{0}^{1} x \sin{\left(3 x \right)}\, dx$$
Integral(x*sin(3*x), (x, 0, 1))
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]
  cos(3)   sin(3)
- ------ + ------
    3        9   
$$\frac{\sin{\left(3 \right)}}{9} - \frac{\cos{\left(3 \right)}}{3}$$
=
=
  cos(3)   sin(3)
- ------ + ------
    3        9   
$$\frac{\sin{\left(3 \right)}}{9} - \frac{\cos{\left(3 \right)}}{3}$$
-cos(3)/3 + sin(3)/9
Numerical answer [src]
0.345677499762356
0.345677499762356
The graph
Integral of xsin(3x)dx dx

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