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Integral of x^2cos(3x^3+5) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
 oo                    
  /                    
 |                     
 |   2    /   3    \   
 |  x *cos\3*x  + 5/ dx
 |                     
/                      
1                      
$$\int\limits_{1}^{\infty} x^{2} \cos{\left(3 x^{3} + 5 \right)}\, dx$$
Integral(x^2*cos(3*x^3 + 5), (x, 1, oo))
Detail solution
  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:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                       
 |                              /   3    \
 |  2    /   3    \          sin\3*x  + 5/
 | x *cos\3*x  + 5/ dx = C + -------------
 |                                 9      
/                                         
$$\int x^{2} \cos{\left(3 x^{3} + 5 \right)}\, dx = C + \frac{\sin{\left(3 x^{3} + 5 \right)}}{9}$$
The answer [src]
   1   sin(8)  1   sin(8) 
<- - - ------, - - ------>
   9     9     9     9    
$$\left\langle - \frac{1}{9} - \frac{\sin{\left(8 \right)}}{9}, \frac{1}{9} - \frac{\sin{\left(8 \right)}}{9}\right\rangle$$
=
=
   1   sin(8)  1   sin(8) 
<- - - ------, - - ------>
   9     9     9     9    
$$\left\langle - \frac{1}{9} - \frac{\sin{\left(8 \right)}}{9}, \frac{1}{9} - \frac{\sin{\left(8 \right)}}{9}\right\rangle$$

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