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x^4*sin(x)

Integral of x^4*sin(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1             
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 |   4          
 |  x *sin(x) dx
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0               
$$\int\limits_{0}^{1} x^{4} \sin{\left(x \right)}\, dx$$
Integral(x^4*sin(x), (x, 0, 1))
Detail solution
  1. Use integration by parts:

    Let and let .

    Then .

    To find :

    1. The integral of sine is negative cosine:

    Now evaluate the sub-integral.

  2. Use integration by parts:

    Let and let .

    Then .

    To find :

    1. The integral of cosine is sine:

    Now evaluate the sub-integral.

  3. Use integration by parts:

    Let and let .

    Then .

    To find :

    1. The integral of sine is negative cosine:

    Now evaluate the sub-integral.

  4. Use integration by parts:

    Let and let .

    Then .

    To find :

    1. The integral of cosine is sine:

    Now evaluate the sub-integral.

  5. 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:

  6. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                                                   
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 |  4                              4                           3              2       
 | x *sin(x) dx = C - 24*cos(x) - x *cos(x) - 24*x*sin(x) + 4*x *sin(x) + 12*x *cos(x)
 |                                                                                    
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$$\left(4\,x^3-24\,x\right)\,\sin x+\left(-x^4+12\,x^2-24\right)\, \cos x$$
The graph
The answer [src]
24 - 20*sin(1) - 13*cos(1)
$$-20\,\sin 1-13\,\cos 1+24$$
=
=
24 - 20*sin(1) - 13*cos(1)
$$- 20 \sin{\left(1 \right)} - 13 \cos{\left(1 \right)} + 24$$
Numerical answer [src]
0.146650327556254
0.146650327556254
The graph
Integral of x^4*sin(x) dx

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