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Identical expressions
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Similar expressions
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Solving integrals/ (1-sin^3x)/(sin^2x)

Integral of (1-sin^3x)/(sin^2x) dx

The solution

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  1               
  /               
 |                
 |         3      
 |  1 - sin (x)   
 |  ----------- dx
 |       2        
 |    sin (x)     
 |                
/                 
0

$$\int\limits_{0}^{1} \frac{1 - \sin^{3}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\, dx$$

Integral((1 - sin(x)^3)/(sin(x)^2), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\frac{1 - \sin^{3}{\left(x \right)}}{\sin^{2}{\left(x \right)}} = - \sin{\left(x \right)} + \frac{1}{\sin^{2}{\left(x \right)}}$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \sin{\left(x \right)}\right)\, dx = - \int \sin{\left(x \right)}\, dx$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
  So, the result is: $\cos{\left(x \right)}$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $- \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
The result is: $\cos{\left(x \right)} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
Now simplify:

$\frac{\sin{\left(x \right)} - 1}{\tan{\left(x \right)}}$
Add the constant of integration:

$\frac{\sin{\left(x \right)} - 1}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer is:

$\frac{\sin{\left(x \right)} - 1}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                    
 |                                     
 |        3                            
 | 1 - sin (x)          cos(x)         
 | ----------- dx = C - ------ + cos(x)
 |      2               sin(x)         
 |   sin (x)                           
 |                                     
/

$$\int \frac{1 - \sin^{3}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\, dx = C + \cos{\left(x \right)} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

Упростить

Numerical answer [src]

1.3793236779486e+19

1.3793236779486e+19

The graph

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

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Identical expressions

Similar expressions

Integral of (1-sin^3x)/(sin^2x) dx

Limits of integration:

The graph:

Piecewise:

The solution