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Solving integrals/ siny/y^3

Integral of siny/y^3 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  x          
  /          
 |           
 |  sin(y)   
 |  ------ dx
 |     3     
 |    y      
 |           
/            
0
∫0xsin⁡(y)y3 dx\int\limits_{0}^{x} \frac{\sin{\left(y \right)}}{y^{3}}\, dx 
Integral(sin(y)/(y^3), (x, 0, x))
Detail solution

  1. The integral of a constant is the constant times the variable of integration:

    ∫sin⁡(y)y3 dx=xsin⁡(y)y3\int \frac{\sin{\left(y \right)}}{y^{3}}\, dx = \frac{x \sin{\left(y \right)}}{y^{3}}

  2. Add the constant of integration:

    xsin⁡(y)y3+constant\frac{x \sin{\left(y \right)}}{y^{3}}+ \mathrm{constant}

The answer is:

xsin⁡(y)y3+constant\frac{x \sin{\left(y \right)}}{y^{3}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                        
 |                         
 | sin(y)          x*sin(y)
 | ------ dx = C + --------
 |    3                3   
 |   y                y    
 |                         
/
x sin⁡yy3{{x\,\sin y}\over{y^3}}
Simplify
The answer [src] 
x*sin(y)
--------
    3   
   y
x sin⁡yy3{{x\,\sin y}\over{y^3}} 
=
= 
x*sin(y)
--------
    3   
   y
xsin⁡(y)y3\frac{x \sin{\left(y \right)}}{y^{3}}
Упростить

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

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