Mister Exam

Other calculators


x^4cosx

Integral of x^4cosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

    Let and let .

    Then .

    To find :

    1. The integral of cosine is sine:

    Now evaluate the sub-integral.

  2. Use integration by parts:

    Let and let .

    Then .

    To find :

    1. The integral of sine is negative cosine:

    Now evaluate the sub-integral.

  3. Use integration by parts:

    Let and let .

    Then .

    To find :

    1. The integral of cosine is sine:

    Now evaluate the sub-integral.

  4. Use integration by parts:

    Let and let .

    Then .

    To find :

    1. The integral of sine is negative cosine:

    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 cosine is sine:

    So, the result is:

  6. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                                                   
 |                                                                                    
 |  4                              4                            2             3       
 | x *cos(x) dx = C + 24*sin(x) + x *sin(x) - 24*x*cos(x) - 12*x *sin(x) + 4*x *cos(x)
 |                                                                                    
/                                                                                     
$$\int x^{4} \cos{\left(x \right)}\, dx = C + x^{4} \sin{\left(x \right)} + 4 x^{3} \cos{\left(x \right)} - 12 x^{2} \sin{\left(x \right)} - 24 x \cos{\left(x \right)} + 24 \sin{\left(x \right)}$$
The graph
The answer [src]
-20*cos(1) + 13*sin(1)
$$- 20 \cos{\left(1 \right)} + 13 \sin{\left(1 \right)}$$
=
=
-20*cos(1) + 13*sin(1)
$$- 20 \cos{\left(1 \right)} + 13 \sin{\left(1 \right)}$$
Numerical answer [src]
0.13307668513986
0.13307668513986
The graph
Integral of x^4cosx dx

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