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  • Identical expressions

  • x*sin^ two (z)*siny*cosy*cosz
  • x multiply by sinus of squared (z) multiply by sinus of y multiply by co sinus of e of y multiply by co sinus of e of z
  • x multiply by sinus of to the power of two (z) multiply by sinus of y multiply by co sinus of e of y multiply by co sinus of e of z
  • x*sin2(z)*siny*cosy*cosz
  • x*sin2z*siny*cosy*cosz
  • x*sin²(z)*siny*cosy*cosz
  • x*sin to the power of 2(z)*siny*cosy*cosz
  • xsin^2(z)sinycosycosz
  • xsin2(z)sinycosycosz
  • xsin2zsinycosycosz
  • xsin^2zsinycosycosz
  • x*sin^2(z)*siny*cosy*coszdx
Solving integrals/ x*sin^2(z)*siny*cosy*cosz

Integral of x*sin^2(z)*siny*cosy*cosz dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                                  
  /                                  
 |                                   
 |       2                           
 |  x*sin (z)*sin(y)*cos(y)*cos(z) dx
 |                                   
/                                    
0
$$\int\limits_{0}^{1} x \sin^{2}{\left(z \right)} \sin{\left(y \right)} \cos{\left(y \right)} \cos{\left(z \right)}\, dx$$ 
Integral((((x*sin(z)^2)*sin(y))*cos(y))*cos(z), (x, 0, 1))
Detail solution

  1. The integral of a constant times a function is the constant times the integral of the function:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of is when :

      So, the result is:

    So, the result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                       
 |                                          2    2                        
 |      2                                  x *sin (z)*cos(y)*cos(z)*sin(y)
 | x*sin (z)*sin(y)*cos(y)*cos(z) dx = C + -------------------------------
 |                                                        2               
/
$$\int x \sin^{2}{\left(z \right)} \sin{\left(y \right)} \cos{\left(y \right)} \cos{\left(z \right)}\, dx = C + \frac{x^{2} \sin{\left(y \right)} \sin^{2}{\left(z \right)} \cos{\left(y \right)} \cos{\left(z \right)}}{2}$$
Simplify
The answer [src] 
   2                        
sin (z)*cos(y)*cos(z)*sin(y)
----------------------------
             2
$$\frac{\sin{\left(y \right)} \sin^{2}{\left(z \right)} \cos{\left(y \right)} \cos{\left(z \right)}}{2}$$ 
=
= 
   2                        
sin (z)*cos(y)*cos(z)*sin(y)
----------------------------
             2
$$\frac{\sin{\left(y \right)} \sin^{2}{\left(z \right)} \cos{\left(y \right)} \cos{\left(z \right)}}{2}$$ 
sin(z)^2*cos(y)*cos(z)*sin(y)/2

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

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