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x^2*sin(5x)

Integral of x^2*sin(5x) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src]
 pi               
  /               
 |                
 |   2            
 |  x *sin(5*x) dx
 |                
/                 
-pi               
$$\int\limits_{- \pi}^{\pi} x^{2} \sin{\left(5 x \right)}\, dx$$
Integral(x^2*sin(5*x), (x, -pi, pi))
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. 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 cosine is sine:

        So, the result is:

      Now substitute back in:

    Now evaluate the sub-integral.

  3. 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 sine is negative cosine:

        So, the result is:

      Now substitute back in:

    So, the result is:

  4. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                            
 |                                    2                        
 |  2                   2*cos(5*x)   x *cos(5*x)   2*x*sin(5*x)
 | x *sin(5*x) dx = C + ---------- - ----------- + ------------
 |                         125            5             25     
/                                                              
$${{10\,x\,\sin \left(5\,x\right)+\left(2-25\,x^2\right)\,\cos \left( 5\,x\right)}\over{125}}$$
The graph
The answer [src]
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Numerical answer [src]
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The graph
Integral of x^2*sin(5x) dx

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